7212019

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7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 217

23 15

983123infin = 983089

983089983089 minus 983089

983089983089983088983088 + 983089

983089983089983089 minus 983089

983089983089983089983088983088983088 + 983089

983089983089983089983089 minus 983089

983089983089983089983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983089

983089983089 983089 minus 983089

983089983088983088 + 983089

983089983089983089 983089 minus 983089

983089983088983088983088 + 983089

983089983089983089983089 983089 minus 983089

983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983089

983089983089 983097983097

983089983088983088 + 983089

983089983089983089 983097983097983097

983089983088983088983088 + 983089

983089983089983089983089 983097983097983097983097

983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983097

983089983088983088 + 983097

983089983088983088983088 + 983097

983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983097

983089

983089983088983088 + 983089

983089983088983088983088 + 983089

983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983097

983089983089983088983088

983089 minus 983089983089983088

= 983097

983089983089983088983088

983089983088983097

= 983089

983089983088

24 15

ก 983160983089 = 983089

983090

983160983090 = 983160983089 minus 983089983092 = 983089983090 minus 983089983092

983160983091 = 983160983090 + 983089

983096 = 983089

983090 minus 983089

983092 + 983089

983096

983160983092 = 983160983091 minus 983089983089983094

= 983089983090 minus 983089

983092 + 983089

983096 minus 983089

983089983094

there4 983150 rarr infin

983148983145983149 983160983150 = 983160infin = 983089

983090 minus 983089

983092 + 983089

983096 minus 983089

983089983094 + 983086983086983086983086983086 =

983089983090

983089 minus minus

983089983090

= 983089

983091

0 12

14

1x 4

x1x2 x 3

2

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 317

25 16

983150 = 983089

infinΣ

983149983145983150 983089

983090983150 983084 983089

983091983150 + 983149983137983160 983089

(minus983090)983150 983084 983089

983091983150 =

983150 = 983089

infinΣ 983149983145983150

983089

983090983150 983084 983089

983091983150 +983150 = 983089

infinΣ 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150

983150 = 983089

infin

Σ 983149983145983150

983089

983090983150 983084

983089

983091983150

=983150 = 983089

infinΣ 983149983145983150

983089

983090983150 983084 983089983091983150

983149983145983150

983089983090

983084 983089983091

+ 983149983145983150

983089983092

983084 983089983094

+ 983149983145983150

983089983096

983084 983089983097

+ 983149983145983150

983089983089983094

983084 983089983089983090

+ 983149983145983150 983089

983091983090983084

983089

983089983093 + 983149983145983150 983089

983094983092983084

983089

983089983096 + 983086983086983086983086983086

= 983089983091 + 983089

983094 + 983089

983097 + 983089

983089983094 + 983089

983091983090 + 983089

983094983092 + 983086983086983086983086983086

= 983089

983091 + 983089

983094 + 983089

983097 +

983089983089983094

983089 minus 983089983090

= 983089983089

983089983096 + 983089

983096 = 983093983091

983095983090

=983150 = 983089

infinΣ 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150 983149983137983160 minus

983089983090

983084 983089983091 + 983149983137983160

983089983092

983084 983089983097 + 983149983137983160 minus

983089983096

983084 983089983090983095 + 983149983137983160

983089983089983094

983084 983089983096983089

+ 983149983137983160 minus 983089983091983090

983084 983089983090983092983091 + 983149983137983160

983089983094983092

983084 983089983095983090983097 + 983086983086983086983086983086

= 983089

983091 + 983089

983092 + 983089

983090983095 + 983089

983089983094 + 983089

983090983092983091 + 983089

983094983092 + 983086983086983086983086983086

=

983089983091 + 983089

983090983095 + 983089

983090983092983091 + 983086983086983086983086983086

+

983089983092 + 983089

983089983094 + 983089

983094983092 + 983086983086983086983086983086

=

983089983091

983089 minus 983089983097

+

983089983092

983089 minus 983089983092

= 983097983090983092 +

983089983091 =

983093983089983095983090

there4983150 = 983089

infinΣ

983149983145983150

983089

983090983150 983084 983089

983091983150 + 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150 = 983093983091

983095983090 + 983093983089

983095983090 = 983089983088983092

983095983090 = 983089983091

983097

28 18

983092 + 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086 + 983150

983090983150 + 983086983086983086983086983086 = 983092 + 983160

983160 = 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086

983089983090

983160 = 983089

983090983090 + 983090

983090983091 + 983086983086983086983086983086

983089

983090983160 = 983089

983090 + 983089

983090983090 + 983089

983090983091 + 983086983086983086983086983086

983089983090

983160 =983089983090

983089 minus 983089983090

rarr 983089983090

983160 = 983089 rarr 983160 = 983090

there4 983092 + 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086 = 983092 + 983160 = 983092 + 983090 = 983094

3

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 417

29 18

983123infin = 983089

983090 minus 983090

983092 + 983091

983096 minus 983092

983089983094 + 983086983086983086983086983086

minus983089983090

983123infin = minus 983089983092 + 983090

983096 minus 983091

983089983094 + 983086983086983086983086983086

983091983090

983123infin = 983089983090 minus 983089

983092 + 983089

983096 minus 983089

983089983094 + 983086983086983086983086983086

983091983090

983123infin =983089

983090

983089 minus minus

983089983090

rarr 983091983090

983123infin = 983089983091

rarr 983123infin = 983090983097

983150 rarr infin983148983145983149

983147 (983150 983091 + 983150 ) + 983091983150 983090 + 983090

(983091983150 + 983089)983091 = 983089

983090 minus 983090

983092 + 983091

983096 minus 983092

983089983094 + 983086983086983086983086983086

983147

983090983095 = 983090

983097

there4 983147 = 983094

30 19

983105 =983150 rarr infin

983148983145983149

983147 = 983089

983150 Σ 983089

(983147 + 983089)(983147 + 983090)

983105 =983147 = 983089

infinΣ 983089

(983147 + 983089)(983147 + 983090) = 983089

983090 sdot 983091 + 983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983086983086983086983086983086

983105 = 983089983091 minus 983090

983089983090 sdot 983091 = 983089

983090

34 21

=983137983150 983089

983150 983090 minus 983092983084 983137983145 = 983089

983145983090 minus 983092= 983089

(983145 minus 983090)(983145 + 983090)

=983145 = 983091

infinΣ 983137 983145

983145 = 983091

infinΣ 983089

(983145 minus 983090)(983145 + 983090)

= 983089

983089 sdot 983093 + 983089

983090 sdot 983094 + 983089

983091 sdot 983095 + 983089

983092 sdot 983096 + 983089

983093 sdot 983097 + 983086983086983086983086983086

= 983089983089 sdot 983093 + 983089983093 sdot 983097 + 983086983086983086983086983086 + 983089983090 sdot 983094 + 983089983094 sdot 983089983088 + 983086983086983086983086983086 + 983089983091 sdot 983095 + 983089983095 sdot 983089983089 + 983086983086983086983086983086

+

983089983092 sdot 983096

+ 983089983096 sdot 983089983090

+ 983086983086983086983086983086

= 983089983093 minus 983089

983089983089 + 983089

983094 minus 983090 983089983090 + 983089

983095 minus 983091 983089983091 + 983089

983096 minus 983092 983089983092

= 983089983092 + 983089

983096 + 983089

983089983090 + 983089

983089983094 = 983089983090 + 983094 + 983092 + 983091

983092983096 = 983090983093

983092983096

4

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 517

35 21

983150 = 983090

infinΣ 983089

983150 983092 minus 983150 983090 = 983105 rarr

983150 = 983090

infinΣ 983089

(983150 983090 minus 983089)983150 983090 = 983105 rarr

983150 = 983090

infinΣ

983089

983150 983090 minus 983089minus 983089

983150 983090 = 983105

983150 = 983090

infin

Σ 983089

983150 983090 = 983150 = 983090

infin

Σ 983089

983150 983090 minus 983089 minus 983105 = 983150 = 983090

infin

Σ 983089

(983150 minus 983089)(983150 + 983089) minus 983105

=

983089983089 sdot 983091

+ 983089983090 sdot 983092

+ 983089983091 sdot 983093

+ 983089983092 sdot 983094

+ 983086983086983086983086983086 minus 983105

= 983089

983089 sdot 983091 + 983089

983091 sdot 983093 + 983086983086983086983086983086 +

983089

983090 sdot 983092 + 983089

983092 sdot 983094 + 983086983086983086983086983086 minus 983105

= 983089983091 minus 983089

983089983089 +

983089983092 minus 983090

983089983090 minus 983105

= 983089

983090 + 983089

983092 minus 983105 = 983091

983092 minus 983105

36 22

983137983089 + 983137983090 + 983137983091 + 983086983086983086983086983086 + 983137983150 = 983150 983090983137983150 rarr 983155983150 = 983150 983090983137983150

983137983150 = 983155983150 minus 983155983150 minus 983089 rarr 983137983150 = 983150 983090983137983150 minus (983150 minus 983089)983090983137983150 minus 983089 rarr 983150 983090983137983150 minus 983137983150 = (983150 minus 983089)983090983137983150 minus 983089

(983150 983090 minus 983089)983137983150 = (983150 minus 983089)983090983137983150 minus983089 rarr (983150 minus 983089)(983150 + 983089)983137983150 = (983150 minus 983089)983090983137983150 minus 983089

983137983150 = (983150 minus 983089)(983150 + 983089) 983137983150 minus 983089

983137983090 = 983089983091 983137983089 = 983089983089 + 983090 983137983089

983137983091 = 983089

983090 983137983090 = 983089

983094983137983089 = 983089

983089 + 983090 + 983091983137983089

983137983092 = 983091

983093 983137983091 = 983089

983089983088983137983089 = 983089

983089 + 983090 + 983091 + 983092983137983089

983137983150 = 983089983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150

983137983089 = 983089983150 983090

(983150 + 983089) 983137983089 =

983090983137983089

983150 (983150 + 983089) = 983090983137983089

983150 983090 + 983150 = 983090983088983088

983150 983090 + 983150

there4983150 rarr infin

983148983145983149 983150 983090983137983150 =983150 rarr infin983148983145983149

983090983088983088983150 983090

983150 983090 + 983150 = 983090983088983088

37 22

ก 983137983150 = 983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150 983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) =

983150

983090(983150 + 983089)

983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) + 983089983090(983150 + 983090)(983150 + 983091)

there4 =983123infin 983089

983090

983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983089

983093 sdot 983094 + 983086983086983086983086983086

= 983089983090

983089983092 minus 983091

983089983091

= 983089

983094

5

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 617

กก

5 45

=983139983151983155983089983093 + 983156983137983150983094983088 983155983145983150983089983093 983139983151983155983089983093 + 983155983145983150983094983088983139983151983155983094983088 983155983145983150983089983093 = 983139983151983155983094983088 983139983151983155983089983093 + 983155983145983150983094983088 983155983145983150983089983093983139983151983155983094983088

= 983139983151983155 (983094983088 minus 983089983093 )983139983151983155 983094983088

= 983139983151983155983092983093

983139983151983155983094983088 =

983090

983090

983089983090

= 983090

9 47

983155983145983150983160 + 983139983151983155983160 = 983089983090

rarr (983155983145983150983160 + 983139983151983155 983160)983090 = 983089983092

rarr 983089 + 983090983155983145983150983160983139983151983155983160 = 983089983092 rarr 983155983145983150 983160 983139983151983155983160 = minus 983091

983096

there4 =983096(983155983145983150 983091983160 + 983139983151983155983091983160) 983096(983155983145983150983160 + 983139983151983155983160)(983155983145983150 983090983160 minus 983155983145983150983160983139983151983155983160 + 983139983151983155983090983160)

= 983096

983089983090

983089 minus

minus983091983096

= 983089983089

983090

11 48

983155983145983150983160 + 983139983151983155983160 = 983137 (983089) 983084 983155983145983150 983160 minus 983139983151983155 983160 = 983138 (983090)

(983089) + (983090) 983090983155983145983150983160 = 983137 + 983138 983084 (983089) minus (983090) 983090983139983151983155983160 = 983137 minus 983138

(1)(2) 983155983145983150 983090983160 minus 983139983151983155983090983160 = 983137983138 rarr 983139983151983155983090983160 minus 983155983145983150 983090983160 = minus 983137983138

=983155983145983150983092983160 983090983155983145983150983090983160983139983151983155983090983160 = 983090(983090983155983145983150983160983139983151983155983160)(983139983151983155983090983160 minus 983155983145983150 983090983160)

= (983090983155983145983150983160)(983090983139983151983155983160)[minus983137983138] = (983137 + 983138)(983137 minus 983138)(minus983137983138)

= (983137983090 minus 983138983090)(minus983137983138) = 983137983138983091 minus 983137983091983138

14 49

983089 + 983155983145983150983160983139983151983155 983160

983089 minus 983155983145983150983160983139983151983155 983160

= 983089 + 983105983139983151983155983160983155983145983150983160

983139983151983155983090983160 minus 983155983145983150 983090983160rarr 983139983151983155983160 + 983155983145983150983160

983139983151983155983160 minus 983155983145983150983160 = 983089 + 983105983139983151983155983160983155983145983150983160

(983139983151983155983160 minus 983155983145983150983160)(983139983151983155983160 + 983155983145983150 983160)

983089 + 983105983139983151983155983160983155983145983150983160 = (983139983151983155983160 + 983155983145983150983160)983090 = 983089 + 983090983139983151983155983160983155983145983150983160

ก 2 1983105 = 983090 rarr 983105983090983093983093983091 = 983090983090983093983093983091 983090983093983093983091

983092

16 50

983105 + 983106 = 983092983093 rarr 983156983137983150 (983105 + 983106) = 983156983137983150983092983093 rarr 983156983137983150983105 + 983156983137983150983106983089 minus 983156983137983150983105983156983137983150983106

= 983089

983156983137983150983105 + 983156983137983150983106 = 983089 minus 983156983137983150983105983156983137983150983106

983156983137983150983105 + 983156983137983150983106 + 983156983137983150983105983156983137983150983106 = 983089 rarr 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089

983089 + 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089 + 983089 rarr (983089 + 983156983137983150983105)(983089 + 983156983137983150 983106) = 983090

6

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 717

(983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 ) = 983090983084 (983089 + 983156983137983150983090 )(983089 + 983156983137983150 983092983091 ) = 983090983084 983086983086983086983086983086983086983086983086983086983086

983086983086983086983086983086983086983086983086983086983086983084 (983089 + 983156983137983150983090983090 )(983089 + 983156983137983150983090983091 ) = 983090

ก 983105 = (983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 )(983089 + 983156983137983150983090 )(983089 + 983156983137983150983092983091 ) 983086983086983086983086983086 (983089 + 983156983137983150983090983090 )

(983089 + 983156983137983150983090983091 )(983089 + 983156983137983150 983092983093 )

983105 = 983090983090983091

983148983151983143983105 = 983148983151983143983090983090983091 rarr 983148983151983143983105 = 983090983091983148983151983143983090 rarr 983148983151983143983105 = 983090983091(983088983086983091983088983089983088) = 983094983086983097983090983091

there4 A 7 ก (ก กก) 19 52

983155983145983150983160 + 983155983145983150983161 = 983089

983094 rarr 983090983155983145983150

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983094 (983089)

983139983151983155983160 + 983139983151983155 983161 = 983089

983091 rarr 983090983139983151983155

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983091 (983090)

(983089)(983090) 983084 983156983137983150

983160 + 983161

983090 = 983089983090

there4 983156983137983150 (983160 + 983161) = 983156983137983150983090

983160 + 983161

983090 =

983090983156983137983150 983160 + 983161

983090

983089 minus 983156983137983150 983090

983160 + 983161

983090

=983090

983089983090

983089 minus

983089983090

983090 = 983092

983091

20 52

983155983145983150983105 + 983155983145983150983106 = 983089 rarr 983090983155983145983150

983105 + 983106

983090 983139983151983155 983105 minus 983106

983090 = 983089 (983089)

983139983151983155983105 + 983139983151983155983106 = 983091

983090 rarr 983090983139983151983155

983105 + 983106

983090 983139983151983155

983105 minus 983106

983090 = 983091

983090 (983090)

(983089)(983090) 983084 983156983137983150

983105 + 983106

983090 = 983090

983091

there4 983139983151983155 (983105 + 983106) = 983139983151983155983090

983105 + 983106983090

=

983089 minus 983156983137983150 983090

983105 + 983106

983090

983089 + 983156983137983150 983090

983105 + 983106

983090

=983089 minus

983090

983091

983090

983089 +

983090983091

983090 = 983093

983089983091

21 53

=983150 = 983089

983092983092Σ 983139983151983155983150

983150 = 983089

983092983092Σ 983155983145983150983150

983139983151983155983089 + 983139983151983155983090 + 983139983151983155983091 + 983086983086983086983086983086 + 983139983151983155983092983091 + 983139983151983155983092983092

983155983145983150983089 + 983155983145983150 983090 + 983155983145983150983091 + 983086983086983086983086983086 + 983155983145983150983092983091 + 983155983145983150983092983092

= (983139983151983155 983092983092 + 983139983151983155983089 ) + (983139983151983155983092983091 + 983139983151983155 983090 ) + 983086983086983086983086983086 + (983139983151983155983090983091 + 983139983151983155 983090983090 )(983155983145983150983092983092 + 983155983145983150983089 ) + (983155983145983150983092983091 + 983155983145983150 983090 ) + 983086983086983086983086983086 + (983155983145983150983090983091 + 983155983145983150983090983090 )

= 983090983139983151983155

983092983093983090

983139983151983155 983092983091

983090 + 983090983139983151983155

983092983093983090

983139983151983155 983092983089

983090 + 983086983086983086983086983086 + 983090983139983151983155

983092983093983090

983139983151983155 983089

983090

983090983155983145983150 983092983093

983090 983139983151983155

983092983091983090

+ 983090983155983145983150 983092983093

983090 983139983151983155

983092983089983090

+ 983086983086983086983086983086 + 983090983155983145983150 983092983093

983090 983139983151983155

983089983090

7

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 817

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 917

26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1117

47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1217

ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 217

23 15

983123infin = 983089

983089983089 minus 983089

983089983089983088983088 + 983089

983089983089983089 minus 983089

983089983089983089983088983088983088 + 983089

983089983089983089983089 minus 983089

983089983089983089983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983089

983089983089 983089 minus 983089

983089983088983088 + 983089

983089983089983089 983089 minus 983089

983089983088983088983088 + 983089

983089983089983089983089 983089 minus 983089

983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983089

983089983089 983097983097

983089983088983088 + 983089

983089983089983089 983097983097983097

983089983088983088983088 + 983089

983089983089983089983089 983097983097983097983097

983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983097

983089983088983088 + 983097

983089983088983088983088 + 983097

983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983097

983089

983089983088983088 + 983089

983089983088983088983088 + 983089

983089983088983088983088983088 + 983086983086983086983086983086

983123infin = 983097

983089983089983088983088

983089 minus 983089983089983088

= 983097

983089983089983088983088

983089983088983097

= 983089

983089983088

24 15

ก 983160983089 = 983089

983090

983160983090 = 983160983089 minus 983089983092 = 983089983090 minus 983089983092

983160983091 = 983160983090 + 983089

983096 = 983089

983090 minus 983089

983092 + 983089

983096

983160983092 = 983160983091 minus 983089983089983094

= 983089983090 minus 983089

983092 + 983089

983096 minus 983089

983089983094

there4 983150 rarr infin

983148983145983149 983160983150 = 983160infin = 983089

983090 minus 983089

983092 + 983089

983096 minus 983089

983089983094 + 983086983086983086983086983086 =

983089983090

983089 minus minus

983089983090

= 983089

983091

0 12

14

1x 4

x1x2 x 3

2

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 317

25 16

983150 = 983089

infinΣ

983149983145983150 983089

983090983150 983084 983089

983091983150 + 983149983137983160 983089

(minus983090)983150 983084 983089

983091983150 =

983150 = 983089

infinΣ 983149983145983150

983089

983090983150 983084 983089

983091983150 +983150 = 983089

infinΣ 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150

983150 = 983089

infin

Σ 983149983145983150

983089

983090983150 983084

983089

983091983150

=983150 = 983089

infinΣ 983149983145983150

983089

983090983150 983084 983089983091983150

983149983145983150

983089983090

983084 983089983091

+ 983149983145983150

983089983092

983084 983089983094

+ 983149983145983150

983089983096

983084 983089983097

+ 983149983145983150

983089983089983094

983084 983089983089983090

+ 983149983145983150 983089

983091983090983084

983089

983089983093 + 983149983145983150 983089

983094983092983084

983089

983089983096 + 983086983086983086983086983086

= 983089983091 + 983089

983094 + 983089

983097 + 983089

983089983094 + 983089

983091983090 + 983089

983094983092 + 983086983086983086983086983086

= 983089

983091 + 983089

983094 + 983089

983097 +

983089983089983094

983089 minus 983089983090

= 983089983089

983089983096 + 983089

983096 = 983093983091

983095983090

=983150 = 983089

infinΣ 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150 983149983137983160 minus

983089983090

983084 983089983091 + 983149983137983160

983089983092

983084 983089983097 + 983149983137983160 minus

983089983096

983084 983089983090983095 + 983149983137983160

983089983089983094

983084 983089983096983089

+ 983149983137983160 minus 983089983091983090

983084 983089983090983092983091 + 983149983137983160

983089983094983092

983084 983089983095983090983097 + 983086983086983086983086983086

= 983089

983091 + 983089

983092 + 983089

983090983095 + 983089

983089983094 + 983089

983090983092983091 + 983089

983094983092 + 983086983086983086983086983086

=

983089983091 + 983089

983090983095 + 983089

983090983092983091 + 983086983086983086983086983086

+

983089983092 + 983089

983089983094 + 983089

983094983092 + 983086983086983086983086983086

=

983089983091

983089 minus 983089983097

+

983089983092

983089 minus 983089983092

= 983097983090983092 +

983089983091 =

983093983089983095983090

there4983150 = 983089

infinΣ

983149983145983150

983089

983090983150 983084 983089

983091983150 + 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150 = 983093983091

983095983090 + 983093983089

983095983090 = 983089983088983092

983095983090 = 983089983091

983097

28 18

983092 + 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086 + 983150

983090983150 + 983086983086983086983086983086 = 983092 + 983160

983160 = 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086

983089983090

983160 = 983089

983090983090 + 983090

983090983091 + 983086983086983086983086983086

983089

983090983160 = 983089

983090 + 983089

983090983090 + 983089

983090983091 + 983086983086983086983086983086

983089983090

983160 =983089983090

983089 minus 983089983090

rarr 983089983090

983160 = 983089 rarr 983160 = 983090

there4 983092 + 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086 = 983092 + 983160 = 983092 + 983090 = 983094

3

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 417

29 18

983123infin = 983089

983090 minus 983090

983092 + 983091

983096 minus 983092

983089983094 + 983086983086983086983086983086

minus983089983090

983123infin = minus 983089983092 + 983090

983096 minus 983091

983089983094 + 983086983086983086983086983086

983091983090

983123infin = 983089983090 minus 983089

983092 + 983089

983096 minus 983089

983089983094 + 983086983086983086983086983086

983091983090

983123infin =983089

983090

983089 minus minus

983089983090

rarr 983091983090

983123infin = 983089983091

rarr 983123infin = 983090983097

983150 rarr infin983148983145983149

983147 (983150 983091 + 983150 ) + 983091983150 983090 + 983090

(983091983150 + 983089)983091 = 983089

983090 minus 983090

983092 + 983091

983096 minus 983092

983089983094 + 983086983086983086983086983086

983147

983090983095 = 983090

983097

there4 983147 = 983094

30 19

983105 =983150 rarr infin

983148983145983149

983147 = 983089

983150 Σ 983089

(983147 + 983089)(983147 + 983090)

983105 =983147 = 983089

infinΣ 983089

(983147 + 983089)(983147 + 983090) = 983089

983090 sdot 983091 + 983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983086983086983086983086983086

983105 = 983089983091 minus 983090

983089983090 sdot 983091 = 983089

983090

34 21

=983137983150 983089

983150 983090 minus 983092983084 983137983145 = 983089

983145983090 minus 983092= 983089

(983145 minus 983090)(983145 + 983090)

=983145 = 983091

infinΣ 983137 983145

983145 = 983091

infinΣ 983089

(983145 minus 983090)(983145 + 983090)

= 983089

983089 sdot 983093 + 983089

983090 sdot 983094 + 983089

983091 sdot 983095 + 983089

983092 sdot 983096 + 983089

983093 sdot 983097 + 983086983086983086983086983086

= 983089983089 sdot 983093 + 983089983093 sdot 983097 + 983086983086983086983086983086 + 983089983090 sdot 983094 + 983089983094 sdot 983089983088 + 983086983086983086983086983086 + 983089983091 sdot 983095 + 983089983095 sdot 983089983089 + 983086983086983086983086983086

+

983089983092 sdot 983096

+ 983089983096 sdot 983089983090

+ 983086983086983086983086983086

= 983089983093 minus 983089

983089983089 + 983089

983094 minus 983090 983089983090 + 983089

983095 minus 983091 983089983091 + 983089

983096 minus 983092 983089983092

= 983089983092 + 983089

983096 + 983089

983089983090 + 983089

983089983094 = 983089983090 + 983094 + 983092 + 983091

983092983096 = 983090983093

983092983096

4

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 517

35 21

983150 = 983090

infinΣ 983089

983150 983092 minus 983150 983090 = 983105 rarr

983150 = 983090

infinΣ 983089

(983150 983090 minus 983089)983150 983090 = 983105 rarr

983150 = 983090

infinΣ

983089

983150 983090 minus 983089minus 983089

983150 983090 = 983105

983150 = 983090

infin

Σ 983089

983150 983090 = 983150 = 983090

infin

Σ 983089

983150 983090 minus 983089 minus 983105 = 983150 = 983090

infin

Σ 983089

(983150 minus 983089)(983150 + 983089) minus 983105

=

983089983089 sdot 983091

+ 983089983090 sdot 983092

+ 983089983091 sdot 983093

+ 983089983092 sdot 983094

+ 983086983086983086983086983086 minus 983105

= 983089

983089 sdot 983091 + 983089

983091 sdot 983093 + 983086983086983086983086983086 +

983089

983090 sdot 983092 + 983089

983092 sdot 983094 + 983086983086983086983086983086 minus 983105

= 983089983091 minus 983089

983089983089 +

983089983092 minus 983090

983089983090 minus 983105

= 983089

983090 + 983089

983092 minus 983105 = 983091

983092 minus 983105

36 22

983137983089 + 983137983090 + 983137983091 + 983086983086983086983086983086 + 983137983150 = 983150 983090983137983150 rarr 983155983150 = 983150 983090983137983150

983137983150 = 983155983150 minus 983155983150 minus 983089 rarr 983137983150 = 983150 983090983137983150 minus (983150 minus 983089)983090983137983150 minus 983089 rarr 983150 983090983137983150 minus 983137983150 = (983150 minus 983089)983090983137983150 minus 983089

(983150 983090 minus 983089)983137983150 = (983150 minus 983089)983090983137983150 minus983089 rarr (983150 minus 983089)(983150 + 983089)983137983150 = (983150 minus 983089)983090983137983150 minus 983089

983137983150 = (983150 minus 983089)(983150 + 983089) 983137983150 minus 983089

983137983090 = 983089983091 983137983089 = 983089983089 + 983090 983137983089

983137983091 = 983089

983090 983137983090 = 983089

983094983137983089 = 983089

983089 + 983090 + 983091983137983089

983137983092 = 983091

983093 983137983091 = 983089

983089983088983137983089 = 983089

983089 + 983090 + 983091 + 983092983137983089

983137983150 = 983089983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150

983137983089 = 983089983150 983090

(983150 + 983089) 983137983089 =

983090983137983089

983150 (983150 + 983089) = 983090983137983089

983150 983090 + 983150 = 983090983088983088

983150 983090 + 983150

there4983150 rarr infin

983148983145983149 983150 983090983137983150 =983150 rarr infin983148983145983149

983090983088983088983150 983090

983150 983090 + 983150 = 983090983088983088

37 22

ก 983137983150 = 983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150 983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) =

983150

983090(983150 + 983089)

983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) + 983089983090(983150 + 983090)(983150 + 983091)

there4 =983123infin 983089

983090

983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983089

983093 sdot 983094 + 983086983086983086983086983086

= 983089983090

983089983092 minus 983091

983089983091

= 983089

983094

5

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 617

กก

5 45

=983139983151983155983089983093 + 983156983137983150983094983088 983155983145983150983089983093 983139983151983155983089983093 + 983155983145983150983094983088983139983151983155983094983088 983155983145983150983089983093 = 983139983151983155983094983088 983139983151983155983089983093 + 983155983145983150983094983088 983155983145983150983089983093983139983151983155983094983088

= 983139983151983155 (983094983088 minus 983089983093 )983139983151983155 983094983088

= 983139983151983155983092983093

983139983151983155983094983088 =

983090

983090

983089983090

= 983090

9 47

983155983145983150983160 + 983139983151983155983160 = 983089983090

rarr (983155983145983150983160 + 983139983151983155 983160)983090 = 983089983092

rarr 983089 + 983090983155983145983150983160983139983151983155983160 = 983089983092 rarr 983155983145983150 983160 983139983151983155983160 = minus 983091

983096

there4 =983096(983155983145983150 983091983160 + 983139983151983155983091983160) 983096(983155983145983150983160 + 983139983151983155983160)(983155983145983150 983090983160 minus 983155983145983150983160983139983151983155983160 + 983139983151983155983090983160)

= 983096

983089983090

983089 minus

minus983091983096

= 983089983089

983090

11 48

983155983145983150983160 + 983139983151983155983160 = 983137 (983089) 983084 983155983145983150 983160 minus 983139983151983155 983160 = 983138 (983090)

(983089) + (983090) 983090983155983145983150983160 = 983137 + 983138 983084 (983089) minus (983090) 983090983139983151983155983160 = 983137 minus 983138

(1)(2) 983155983145983150 983090983160 minus 983139983151983155983090983160 = 983137983138 rarr 983139983151983155983090983160 minus 983155983145983150 983090983160 = minus 983137983138

=983155983145983150983092983160 983090983155983145983150983090983160983139983151983155983090983160 = 983090(983090983155983145983150983160983139983151983155983160)(983139983151983155983090983160 minus 983155983145983150 983090983160)

= (983090983155983145983150983160)(983090983139983151983155983160)[minus983137983138] = (983137 + 983138)(983137 minus 983138)(minus983137983138)

= (983137983090 minus 983138983090)(minus983137983138) = 983137983138983091 minus 983137983091983138

14 49

983089 + 983155983145983150983160983139983151983155 983160

983089 minus 983155983145983150983160983139983151983155 983160

= 983089 + 983105983139983151983155983160983155983145983150983160

983139983151983155983090983160 minus 983155983145983150 983090983160rarr 983139983151983155983160 + 983155983145983150983160

983139983151983155983160 minus 983155983145983150983160 = 983089 + 983105983139983151983155983160983155983145983150983160

(983139983151983155983160 minus 983155983145983150983160)(983139983151983155983160 + 983155983145983150 983160)

983089 + 983105983139983151983155983160983155983145983150983160 = (983139983151983155983160 + 983155983145983150983160)983090 = 983089 + 983090983139983151983155983160983155983145983150983160

ก 2 1983105 = 983090 rarr 983105983090983093983093983091 = 983090983090983093983093983091 983090983093983093983091

983092

16 50

983105 + 983106 = 983092983093 rarr 983156983137983150 (983105 + 983106) = 983156983137983150983092983093 rarr 983156983137983150983105 + 983156983137983150983106983089 minus 983156983137983150983105983156983137983150983106

= 983089

983156983137983150983105 + 983156983137983150983106 = 983089 minus 983156983137983150983105983156983137983150983106

983156983137983150983105 + 983156983137983150983106 + 983156983137983150983105983156983137983150983106 = 983089 rarr 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089

983089 + 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089 + 983089 rarr (983089 + 983156983137983150983105)(983089 + 983156983137983150 983106) = 983090

6

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 717

(983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 ) = 983090983084 (983089 + 983156983137983150983090 )(983089 + 983156983137983150 983092983091 ) = 983090983084 983086983086983086983086983086983086983086983086983086983086

983086983086983086983086983086983086983086983086983086983086983084 (983089 + 983156983137983150983090983090 )(983089 + 983156983137983150983090983091 ) = 983090

ก 983105 = (983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 )(983089 + 983156983137983150983090 )(983089 + 983156983137983150983092983091 ) 983086983086983086983086983086 (983089 + 983156983137983150983090983090 )

(983089 + 983156983137983150983090983091 )(983089 + 983156983137983150 983092983093 )

983105 = 983090983090983091

983148983151983143983105 = 983148983151983143983090983090983091 rarr 983148983151983143983105 = 983090983091983148983151983143983090 rarr 983148983151983143983105 = 983090983091(983088983086983091983088983089983088) = 983094983086983097983090983091

there4 A 7 ก (ก กก) 19 52

983155983145983150983160 + 983155983145983150983161 = 983089

983094 rarr 983090983155983145983150

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983094 (983089)

983139983151983155983160 + 983139983151983155 983161 = 983089

983091 rarr 983090983139983151983155

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983091 (983090)

(983089)(983090) 983084 983156983137983150

983160 + 983161

983090 = 983089983090

there4 983156983137983150 (983160 + 983161) = 983156983137983150983090

983160 + 983161

983090 =

983090983156983137983150 983160 + 983161

983090

983089 minus 983156983137983150 983090

983160 + 983161

983090

=983090

983089983090

983089 minus

983089983090

983090 = 983092

983091

20 52

983155983145983150983105 + 983155983145983150983106 = 983089 rarr 983090983155983145983150

983105 + 983106

983090 983139983151983155 983105 minus 983106

983090 = 983089 (983089)

983139983151983155983105 + 983139983151983155983106 = 983091

983090 rarr 983090983139983151983155

983105 + 983106

983090 983139983151983155

983105 minus 983106

983090 = 983091

983090 (983090)

(983089)(983090) 983084 983156983137983150

983105 + 983106

983090 = 983090

983091

there4 983139983151983155 (983105 + 983106) = 983139983151983155983090

983105 + 983106983090

=

983089 minus 983156983137983150 983090

983105 + 983106

983090

983089 + 983156983137983150 983090

983105 + 983106

983090

=983089 minus

983090

983091

983090

983089 +

983090983091

983090 = 983093

983089983091

21 53

=983150 = 983089

983092983092Σ 983139983151983155983150

983150 = 983089

983092983092Σ 983155983145983150983150

983139983151983155983089 + 983139983151983155983090 + 983139983151983155983091 + 983086983086983086983086983086 + 983139983151983155983092983091 + 983139983151983155983092983092

983155983145983150983089 + 983155983145983150 983090 + 983155983145983150983091 + 983086983086983086983086983086 + 983155983145983150983092983091 + 983155983145983150983092983092

= (983139983151983155 983092983092 + 983139983151983155983089 ) + (983139983151983155983092983091 + 983139983151983155 983090 ) + 983086983086983086983086983086 + (983139983151983155983090983091 + 983139983151983155 983090983090 )(983155983145983150983092983092 + 983155983145983150983089 ) + (983155983145983150983092983091 + 983155983145983150 983090 ) + 983086983086983086983086983086 + (983155983145983150983090983091 + 983155983145983150983090983090 )

= 983090983139983151983155

983092983093983090

983139983151983155 983092983091

983090 + 983090983139983151983155

983092983093983090

983139983151983155 983092983089

983090 + 983086983086983086983086983086 + 983090983139983151983155

983092983093983090

983139983151983155 983089

983090

983090983155983145983150 983092983093

983090 983139983151983155

983092983091983090

+ 983090983155983145983150 983092983093

983090 983139983151983155

983092983089983090

+ 983086983086983086983086983086 + 983090983155983145983150 983092983093

983090 983139983151983155

983089983090

7

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 817

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 917

26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1117

47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

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ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 317

25 16

983150 = 983089

infinΣ

983149983145983150 983089

983090983150 983084 983089

983091983150 + 983149983137983160 983089

(minus983090)983150 983084 983089

983091983150 =

983150 = 983089

infinΣ 983149983145983150

983089

983090983150 983084 983089

983091983150 +983150 = 983089

infinΣ 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150

983150 = 983089

infin

Σ 983149983145983150

983089

983090983150 983084

983089

983091983150

=983150 = 983089

infinΣ 983149983145983150

983089

983090983150 983084 983089983091983150

983149983145983150

983089983090

983084 983089983091

+ 983149983145983150

983089983092

983084 983089983094

+ 983149983145983150

983089983096

983084 983089983097

+ 983149983145983150

983089983089983094

983084 983089983089983090

+ 983149983145983150 983089

983091983090983084

983089

983089983093 + 983149983145983150 983089

983094983092983084

983089

983089983096 + 983086983086983086983086983086

= 983089983091 + 983089

983094 + 983089

983097 + 983089

983089983094 + 983089

983091983090 + 983089

983094983092 + 983086983086983086983086983086

= 983089

983091 + 983089

983094 + 983089

983097 +

983089983089983094

983089 minus 983089983090

= 983089983089

983089983096 + 983089

983096 = 983093983091

983095983090

=983150 = 983089

infinΣ 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150 983149983137983160 minus

983089983090

983084 983089983091 + 983149983137983160

983089983092

983084 983089983097 + 983149983137983160 minus

983089983096

983084 983089983090983095 + 983149983137983160

983089983089983094

983084 983089983096983089

+ 983149983137983160 minus 983089983091983090

983084 983089983090983092983091 + 983149983137983160

983089983094983092

983084 983089983095983090983097 + 983086983086983086983086983086

= 983089

983091 + 983089

983092 + 983089

983090983095 + 983089

983089983094 + 983089

983090983092983091 + 983089

983094983092 + 983086983086983086983086983086

=

983089983091 + 983089

983090983095 + 983089

983090983092983091 + 983086983086983086983086983086

+

983089983092 + 983089

983089983094 + 983089

983094983092 + 983086983086983086983086983086

=

983089983091

983089 minus 983089983097

+

983089983092

983089 minus 983089983092

= 983097983090983092 +

983089983091 =

983093983089983095983090

there4983150 = 983089

infinΣ

983149983145983150

983089

983090983150 983084 983089

983091983150 + 983149983137983160

983089

(minus983090)983150 983084 983089

983091983150 = 983093983091

983095983090 + 983093983089

983095983090 = 983089983088983092

983095983090 = 983089983091

983097

28 18

983092 + 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086 + 983150

983090983150 + 983086983086983086983086983086 = 983092 + 983160

983160 = 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086

983089983090

983160 = 983089

983090983090 + 983090

983090983091 + 983086983086983086983086983086

983089

983090983160 = 983089

983090 + 983089

983090983090 + 983089

983090983091 + 983086983086983086983086983086

983089983090

983160 =983089983090

983089 minus 983089983090

rarr 983089983090

983160 = 983089 rarr 983160 = 983090

there4 983092 + 983089

983090 + 983090

983090983090 + 983091

983090983091 + 983086983086983086983086983086 = 983092 + 983160 = 983092 + 983090 = 983094

3

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 417

29 18

983123infin = 983089

983090 minus 983090

983092 + 983091

983096 minus 983092

983089983094 + 983086983086983086983086983086

minus983089983090

983123infin = minus 983089983092 + 983090

983096 minus 983091

983089983094 + 983086983086983086983086983086

983091983090

983123infin = 983089983090 minus 983089

983092 + 983089

983096 minus 983089

983089983094 + 983086983086983086983086983086

983091983090

983123infin =983089

983090

983089 minus minus

983089983090

rarr 983091983090

983123infin = 983089983091

rarr 983123infin = 983090983097

983150 rarr infin983148983145983149

983147 (983150 983091 + 983150 ) + 983091983150 983090 + 983090

(983091983150 + 983089)983091 = 983089

983090 minus 983090

983092 + 983091

983096 minus 983092

983089983094 + 983086983086983086983086983086

983147

983090983095 = 983090

983097

there4 983147 = 983094

30 19

983105 =983150 rarr infin

983148983145983149

983147 = 983089

983150 Σ 983089

(983147 + 983089)(983147 + 983090)

983105 =983147 = 983089

infinΣ 983089

(983147 + 983089)(983147 + 983090) = 983089

983090 sdot 983091 + 983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983086983086983086983086983086

983105 = 983089983091 minus 983090

983089983090 sdot 983091 = 983089

983090

34 21

=983137983150 983089

983150 983090 minus 983092983084 983137983145 = 983089

983145983090 minus 983092= 983089

(983145 minus 983090)(983145 + 983090)

=983145 = 983091

infinΣ 983137 983145

983145 = 983091

infinΣ 983089

(983145 minus 983090)(983145 + 983090)

= 983089

983089 sdot 983093 + 983089

983090 sdot 983094 + 983089

983091 sdot 983095 + 983089

983092 sdot 983096 + 983089

983093 sdot 983097 + 983086983086983086983086983086

= 983089983089 sdot 983093 + 983089983093 sdot 983097 + 983086983086983086983086983086 + 983089983090 sdot 983094 + 983089983094 sdot 983089983088 + 983086983086983086983086983086 + 983089983091 sdot 983095 + 983089983095 sdot 983089983089 + 983086983086983086983086983086

+

983089983092 sdot 983096

+ 983089983096 sdot 983089983090

+ 983086983086983086983086983086

= 983089983093 minus 983089

983089983089 + 983089

983094 minus 983090 983089983090 + 983089

983095 minus 983091 983089983091 + 983089

983096 minus 983092 983089983092

= 983089983092 + 983089

983096 + 983089

983089983090 + 983089

983089983094 = 983089983090 + 983094 + 983092 + 983091

983092983096 = 983090983093

983092983096

4

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 517

35 21

983150 = 983090

infinΣ 983089

983150 983092 minus 983150 983090 = 983105 rarr

983150 = 983090

infinΣ 983089

(983150 983090 minus 983089)983150 983090 = 983105 rarr

983150 = 983090

infinΣ

983089

983150 983090 minus 983089minus 983089

983150 983090 = 983105

983150 = 983090

infin

Σ 983089

983150 983090 = 983150 = 983090

infin

Σ 983089

983150 983090 minus 983089 minus 983105 = 983150 = 983090

infin

Σ 983089

(983150 minus 983089)(983150 + 983089) minus 983105

=

983089983089 sdot 983091

+ 983089983090 sdot 983092

+ 983089983091 sdot 983093

+ 983089983092 sdot 983094

+ 983086983086983086983086983086 minus 983105

= 983089

983089 sdot 983091 + 983089

983091 sdot 983093 + 983086983086983086983086983086 +

983089

983090 sdot 983092 + 983089

983092 sdot 983094 + 983086983086983086983086983086 minus 983105

= 983089983091 minus 983089

983089983089 +

983089983092 minus 983090

983089983090 minus 983105

= 983089

983090 + 983089

983092 minus 983105 = 983091

983092 minus 983105

36 22

983137983089 + 983137983090 + 983137983091 + 983086983086983086983086983086 + 983137983150 = 983150 983090983137983150 rarr 983155983150 = 983150 983090983137983150

983137983150 = 983155983150 minus 983155983150 minus 983089 rarr 983137983150 = 983150 983090983137983150 minus (983150 minus 983089)983090983137983150 minus 983089 rarr 983150 983090983137983150 minus 983137983150 = (983150 minus 983089)983090983137983150 minus 983089

(983150 983090 minus 983089)983137983150 = (983150 minus 983089)983090983137983150 minus983089 rarr (983150 minus 983089)(983150 + 983089)983137983150 = (983150 minus 983089)983090983137983150 minus 983089

983137983150 = (983150 minus 983089)(983150 + 983089) 983137983150 minus 983089

983137983090 = 983089983091 983137983089 = 983089983089 + 983090 983137983089

983137983091 = 983089

983090 983137983090 = 983089

983094983137983089 = 983089

983089 + 983090 + 983091983137983089

983137983092 = 983091

983093 983137983091 = 983089

983089983088983137983089 = 983089

983089 + 983090 + 983091 + 983092983137983089

983137983150 = 983089983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150

983137983089 = 983089983150 983090

(983150 + 983089) 983137983089 =

983090983137983089

983150 (983150 + 983089) = 983090983137983089

983150 983090 + 983150 = 983090983088983088

983150 983090 + 983150

there4983150 rarr infin

983148983145983149 983150 983090983137983150 =983150 rarr infin983148983145983149

983090983088983088983150 983090

983150 983090 + 983150 = 983090983088983088

37 22

ก 983137983150 = 983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150 983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) =

983150

983090(983150 + 983089)

983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) + 983089983090(983150 + 983090)(983150 + 983091)

there4 =983123infin 983089

983090

983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983089

983093 sdot 983094 + 983086983086983086983086983086

= 983089983090

983089983092 minus 983091

983089983091

= 983089

983094

5

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 617

กก

5 45

=983139983151983155983089983093 + 983156983137983150983094983088 983155983145983150983089983093 983139983151983155983089983093 + 983155983145983150983094983088983139983151983155983094983088 983155983145983150983089983093 = 983139983151983155983094983088 983139983151983155983089983093 + 983155983145983150983094983088 983155983145983150983089983093983139983151983155983094983088

= 983139983151983155 (983094983088 minus 983089983093 )983139983151983155 983094983088

= 983139983151983155983092983093

983139983151983155983094983088 =

983090

983090

983089983090

= 983090

9 47

983155983145983150983160 + 983139983151983155983160 = 983089983090

rarr (983155983145983150983160 + 983139983151983155 983160)983090 = 983089983092

rarr 983089 + 983090983155983145983150983160983139983151983155983160 = 983089983092 rarr 983155983145983150 983160 983139983151983155983160 = minus 983091

983096

there4 =983096(983155983145983150 983091983160 + 983139983151983155983091983160) 983096(983155983145983150983160 + 983139983151983155983160)(983155983145983150 983090983160 minus 983155983145983150983160983139983151983155983160 + 983139983151983155983090983160)

= 983096

983089983090

983089 minus

minus983091983096

= 983089983089

983090

11 48

983155983145983150983160 + 983139983151983155983160 = 983137 (983089) 983084 983155983145983150 983160 minus 983139983151983155 983160 = 983138 (983090)

(983089) + (983090) 983090983155983145983150983160 = 983137 + 983138 983084 (983089) minus (983090) 983090983139983151983155983160 = 983137 minus 983138

(1)(2) 983155983145983150 983090983160 minus 983139983151983155983090983160 = 983137983138 rarr 983139983151983155983090983160 minus 983155983145983150 983090983160 = minus 983137983138

=983155983145983150983092983160 983090983155983145983150983090983160983139983151983155983090983160 = 983090(983090983155983145983150983160983139983151983155983160)(983139983151983155983090983160 minus 983155983145983150 983090983160)

= (983090983155983145983150983160)(983090983139983151983155983160)[minus983137983138] = (983137 + 983138)(983137 minus 983138)(minus983137983138)

= (983137983090 minus 983138983090)(minus983137983138) = 983137983138983091 minus 983137983091983138

14 49

983089 + 983155983145983150983160983139983151983155 983160

983089 minus 983155983145983150983160983139983151983155 983160

= 983089 + 983105983139983151983155983160983155983145983150983160

983139983151983155983090983160 minus 983155983145983150 983090983160rarr 983139983151983155983160 + 983155983145983150983160

983139983151983155983160 minus 983155983145983150983160 = 983089 + 983105983139983151983155983160983155983145983150983160

(983139983151983155983160 minus 983155983145983150983160)(983139983151983155983160 + 983155983145983150 983160)

983089 + 983105983139983151983155983160983155983145983150983160 = (983139983151983155983160 + 983155983145983150983160)983090 = 983089 + 983090983139983151983155983160983155983145983150983160

ก 2 1983105 = 983090 rarr 983105983090983093983093983091 = 983090983090983093983093983091 983090983093983093983091

983092

16 50

983105 + 983106 = 983092983093 rarr 983156983137983150 (983105 + 983106) = 983156983137983150983092983093 rarr 983156983137983150983105 + 983156983137983150983106983089 minus 983156983137983150983105983156983137983150983106

= 983089

983156983137983150983105 + 983156983137983150983106 = 983089 minus 983156983137983150983105983156983137983150983106

983156983137983150983105 + 983156983137983150983106 + 983156983137983150983105983156983137983150983106 = 983089 rarr 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089

983089 + 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089 + 983089 rarr (983089 + 983156983137983150983105)(983089 + 983156983137983150 983106) = 983090

6

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 717

(983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 ) = 983090983084 (983089 + 983156983137983150983090 )(983089 + 983156983137983150 983092983091 ) = 983090983084 983086983086983086983086983086983086983086983086983086983086

983086983086983086983086983086983086983086983086983086983086983084 (983089 + 983156983137983150983090983090 )(983089 + 983156983137983150983090983091 ) = 983090

ก 983105 = (983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 )(983089 + 983156983137983150983090 )(983089 + 983156983137983150983092983091 ) 983086983086983086983086983086 (983089 + 983156983137983150983090983090 )

(983089 + 983156983137983150983090983091 )(983089 + 983156983137983150 983092983093 )

983105 = 983090983090983091

983148983151983143983105 = 983148983151983143983090983090983091 rarr 983148983151983143983105 = 983090983091983148983151983143983090 rarr 983148983151983143983105 = 983090983091(983088983086983091983088983089983088) = 983094983086983097983090983091

there4 A 7 ก (ก กก) 19 52

983155983145983150983160 + 983155983145983150983161 = 983089

983094 rarr 983090983155983145983150

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983094 (983089)

983139983151983155983160 + 983139983151983155 983161 = 983089

983091 rarr 983090983139983151983155

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983091 (983090)

(983089)(983090) 983084 983156983137983150

983160 + 983161

983090 = 983089983090

there4 983156983137983150 (983160 + 983161) = 983156983137983150983090

983160 + 983161

983090 =

983090983156983137983150 983160 + 983161

983090

983089 minus 983156983137983150 983090

983160 + 983161

983090

=983090

983089983090

983089 minus

983089983090

983090 = 983092

983091

20 52

983155983145983150983105 + 983155983145983150983106 = 983089 rarr 983090983155983145983150

983105 + 983106

983090 983139983151983155 983105 minus 983106

983090 = 983089 (983089)

983139983151983155983105 + 983139983151983155983106 = 983091

983090 rarr 983090983139983151983155

983105 + 983106

983090 983139983151983155

983105 minus 983106

983090 = 983091

983090 (983090)

(983089)(983090) 983084 983156983137983150

983105 + 983106

983090 = 983090

983091

there4 983139983151983155 (983105 + 983106) = 983139983151983155983090

983105 + 983106983090

=

983089 minus 983156983137983150 983090

983105 + 983106

983090

983089 + 983156983137983150 983090

983105 + 983106

983090

=983089 minus

983090

983091

983090

983089 +

983090983091

983090 = 983093

983089983091

21 53

=983150 = 983089

983092983092Σ 983139983151983155983150

983150 = 983089

983092983092Σ 983155983145983150983150

983139983151983155983089 + 983139983151983155983090 + 983139983151983155983091 + 983086983086983086983086983086 + 983139983151983155983092983091 + 983139983151983155983092983092

983155983145983150983089 + 983155983145983150 983090 + 983155983145983150983091 + 983086983086983086983086983086 + 983155983145983150983092983091 + 983155983145983150983092983092

= (983139983151983155 983092983092 + 983139983151983155983089 ) + (983139983151983155983092983091 + 983139983151983155 983090 ) + 983086983086983086983086983086 + (983139983151983155983090983091 + 983139983151983155 983090983090 )(983155983145983150983092983092 + 983155983145983150983089 ) + (983155983145983150983092983091 + 983155983145983150 983090 ) + 983086983086983086983086983086 + (983155983145983150983090983091 + 983155983145983150983090983090 )

= 983090983139983151983155

983092983093983090

983139983151983155 983092983091

983090 + 983090983139983151983155

983092983093983090

983139983151983155 983092983089

983090 + 983086983086983086983086983086 + 983090983139983151983155

983092983093983090

983139983151983155 983089

983090

983090983155983145983150 983092983093

983090 983139983151983155

983092983091983090

+ 983090983155983145983150 983092983093

983090 983139983151983155

983092983089983090

+ 983086983086983086983086983086 + 983090983155983145983150 983092983093

983090 983139983151983155

983089983090

7

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 817

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 917

26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1117

47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1217

ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 417

29 18

983123infin = 983089

983090 minus 983090

983092 + 983091

983096 minus 983092

983089983094 + 983086983086983086983086983086

minus983089983090

983123infin = minus 983089983092 + 983090

983096 minus 983091

983089983094 + 983086983086983086983086983086

983091983090

983123infin = 983089983090 minus 983089

983092 + 983089

983096 minus 983089

983089983094 + 983086983086983086983086983086

983091983090

983123infin =983089

983090

983089 minus minus

983089983090

rarr 983091983090

983123infin = 983089983091

rarr 983123infin = 983090983097

983150 rarr infin983148983145983149

983147 (983150 983091 + 983150 ) + 983091983150 983090 + 983090

(983091983150 + 983089)983091 = 983089

983090 minus 983090

983092 + 983091

983096 minus 983092

983089983094 + 983086983086983086983086983086

983147

983090983095 = 983090

983097

there4 983147 = 983094

30 19

983105 =983150 rarr infin

983148983145983149

983147 = 983089

983150 Σ 983089

(983147 + 983089)(983147 + 983090)

983105 =983147 = 983089

infinΣ 983089

(983147 + 983089)(983147 + 983090) = 983089

983090 sdot 983091 + 983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983086983086983086983086983086

983105 = 983089983091 minus 983090

983089983090 sdot 983091 = 983089

983090

34 21

=983137983150 983089

983150 983090 minus 983092983084 983137983145 = 983089

983145983090 minus 983092= 983089

(983145 minus 983090)(983145 + 983090)

=983145 = 983091

infinΣ 983137 983145

983145 = 983091

infinΣ 983089

(983145 minus 983090)(983145 + 983090)

= 983089

983089 sdot 983093 + 983089

983090 sdot 983094 + 983089

983091 sdot 983095 + 983089

983092 sdot 983096 + 983089

983093 sdot 983097 + 983086983086983086983086983086

= 983089983089 sdot 983093 + 983089983093 sdot 983097 + 983086983086983086983086983086 + 983089983090 sdot 983094 + 983089983094 sdot 983089983088 + 983086983086983086983086983086 + 983089983091 sdot 983095 + 983089983095 sdot 983089983089 + 983086983086983086983086983086

+

983089983092 sdot 983096

+ 983089983096 sdot 983089983090

+ 983086983086983086983086983086

= 983089983093 minus 983089

983089983089 + 983089

983094 minus 983090 983089983090 + 983089

983095 minus 983091 983089983091 + 983089

983096 minus 983092 983089983092

= 983089983092 + 983089

983096 + 983089

983089983090 + 983089

983089983094 = 983089983090 + 983094 + 983092 + 983091

983092983096 = 983090983093

983092983096

4

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 517

35 21

983150 = 983090

infinΣ 983089

983150 983092 minus 983150 983090 = 983105 rarr

983150 = 983090

infinΣ 983089

(983150 983090 minus 983089)983150 983090 = 983105 rarr

983150 = 983090

infinΣ

983089

983150 983090 minus 983089minus 983089

983150 983090 = 983105

983150 = 983090

infin

Σ 983089

983150 983090 = 983150 = 983090

infin

Σ 983089

983150 983090 minus 983089 minus 983105 = 983150 = 983090

infin

Σ 983089

(983150 minus 983089)(983150 + 983089) minus 983105

=

983089983089 sdot 983091

+ 983089983090 sdot 983092

+ 983089983091 sdot 983093

+ 983089983092 sdot 983094

+ 983086983086983086983086983086 minus 983105

= 983089

983089 sdot 983091 + 983089

983091 sdot 983093 + 983086983086983086983086983086 +

983089

983090 sdot 983092 + 983089

983092 sdot 983094 + 983086983086983086983086983086 minus 983105

= 983089983091 minus 983089

983089983089 +

983089983092 minus 983090

983089983090 minus 983105

= 983089

983090 + 983089

983092 minus 983105 = 983091

983092 minus 983105

36 22

983137983089 + 983137983090 + 983137983091 + 983086983086983086983086983086 + 983137983150 = 983150 983090983137983150 rarr 983155983150 = 983150 983090983137983150

983137983150 = 983155983150 minus 983155983150 minus 983089 rarr 983137983150 = 983150 983090983137983150 minus (983150 minus 983089)983090983137983150 minus 983089 rarr 983150 983090983137983150 minus 983137983150 = (983150 minus 983089)983090983137983150 minus 983089

(983150 983090 minus 983089)983137983150 = (983150 minus 983089)983090983137983150 minus983089 rarr (983150 minus 983089)(983150 + 983089)983137983150 = (983150 minus 983089)983090983137983150 minus 983089

983137983150 = (983150 minus 983089)(983150 + 983089) 983137983150 minus 983089

983137983090 = 983089983091 983137983089 = 983089983089 + 983090 983137983089

983137983091 = 983089

983090 983137983090 = 983089

983094983137983089 = 983089

983089 + 983090 + 983091983137983089

983137983092 = 983091

983093 983137983091 = 983089

983089983088983137983089 = 983089

983089 + 983090 + 983091 + 983092983137983089

983137983150 = 983089983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150

983137983089 = 983089983150 983090

(983150 + 983089) 983137983089 =

983090983137983089

983150 (983150 + 983089) = 983090983137983089

983150 983090 + 983150 = 983090983088983088

983150 983090 + 983150

there4983150 rarr infin

983148983145983149 983150 983090983137983150 =983150 rarr infin983148983145983149

983090983088983088983150 983090

983150 983090 + 983150 = 983090983088983088

37 22

ก 983137983150 = 983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150 983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) =

983150

983090(983150 + 983089)

983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) + 983089983090(983150 + 983090)(983150 + 983091)

there4 =983123infin 983089

983090

983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983089

983093 sdot 983094 + 983086983086983086983086983086

= 983089983090

983089983092 minus 983091

983089983091

= 983089

983094

5

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 617

กก

5 45

=983139983151983155983089983093 + 983156983137983150983094983088 983155983145983150983089983093 983139983151983155983089983093 + 983155983145983150983094983088983139983151983155983094983088 983155983145983150983089983093 = 983139983151983155983094983088 983139983151983155983089983093 + 983155983145983150983094983088 983155983145983150983089983093983139983151983155983094983088

= 983139983151983155 (983094983088 minus 983089983093 )983139983151983155 983094983088

= 983139983151983155983092983093

983139983151983155983094983088 =

983090

983090

983089983090

= 983090

9 47

983155983145983150983160 + 983139983151983155983160 = 983089983090

rarr (983155983145983150983160 + 983139983151983155 983160)983090 = 983089983092

rarr 983089 + 983090983155983145983150983160983139983151983155983160 = 983089983092 rarr 983155983145983150 983160 983139983151983155983160 = minus 983091

983096

there4 =983096(983155983145983150 983091983160 + 983139983151983155983091983160) 983096(983155983145983150983160 + 983139983151983155983160)(983155983145983150 983090983160 minus 983155983145983150983160983139983151983155983160 + 983139983151983155983090983160)

= 983096

983089983090

983089 minus

minus983091983096

= 983089983089

983090

11 48

983155983145983150983160 + 983139983151983155983160 = 983137 (983089) 983084 983155983145983150 983160 minus 983139983151983155 983160 = 983138 (983090)

(983089) + (983090) 983090983155983145983150983160 = 983137 + 983138 983084 (983089) minus (983090) 983090983139983151983155983160 = 983137 minus 983138

(1)(2) 983155983145983150 983090983160 minus 983139983151983155983090983160 = 983137983138 rarr 983139983151983155983090983160 minus 983155983145983150 983090983160 = minus 983137983138

=983155983145983150983092983160 983090983155983145983150983090983160983139983151983155983090983160 = 983090(983090983155983145983150983160983139983151983155983160)(983139983151983155983090983160 minus 983155983145983150 983090983160)

= (983090983155983145983150983160)(983090983139983151983155983160)[minus983137983138] = (983137 + 983138)(983137 minus 983138)(minus983137983138)

= (983137983090 minus 983138983090)(minus983137983138) = 983137983138983091 minus 983137983091983138

14 49

983089 + 983155983145983150983160983139983151983155 983160

983089 minus 983155983145983150983160983139983151983155 983160

= 983089 + 983105983139983151983155983160983155983145983150983160

983139983151983155983090983160 minus 983155983145983150 983090983160rarr 983139983151983155983160 + 983155983145983150983160

983139983151983155983160 minus 983155983145983150983160 = 983089 + 983105983139983151983155983160983155983145983150983160

(983139983151983155983160 minus 983155983145983150983160)(983139983151983155983160 + 983155983145983150 983160)

983089 + 983105983139983151983155983160983155983145983150983160 = (983139983151983155983160 + 983155983145983150983160)983090 = 983089 + 983090983139983151983155983160983155983145983150983160

ก 2 1983105 = 983090 rarr 983105983090983093983093983091 = 983090983090983093983093983091 983090983093983093983091

983092

16 50

983105 + 983106 = 983092983093 rarr 983156983137983150 (983105 + 983106) = 983156983137983150983092983093 rarr 983156983137983150983105 + 983156983137983150983106983089 minus 983156983137983150983105983156983137983150983106

= 983089

983156983137983150983105 + 983156983137983150983106 = 983089 minus 983156983137983150983105983156983137983150983106

983156983137983150983105 + 983156983137983150983106 + 983156983137983150983105983156983137983150983106 = 983089 rarr 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089

983089 + 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089 + 983089 rarr (983089 + 983156983137983150983105)(983089 + 983156983137983150 983106) = 983090

6

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 717

(983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 ) = 983090983084 (983089 + 983156983137983150983090 )(983089 + 983156983137983150 983092983091 ) = 983090983084 983086983086983086983086983086983086983086983086983086983086

983086983086983086983086983086983086983086983086983086983086983084 (983089 + 983156983137983150983090983090 )(983089 + 983156983137983150983090983091 ) = 983090

ก 983105 = (983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 )(983089 + 983156983137983150983090 )(983089 + 983156983137983150983092983091 ) 983086983086983086983086983086 (983089 + 983156983137983150983090983090 )

(983089 + 983156983137983150983090983091 )(983089 + 983156983137983150 983092983093 )

983105 = 983090983090983091

983148983151983143983105 = 983148983151983143983090983090983091 rarr 983148983151983143983105 = 983090983091983148983151983143983090 rarr 983148983151983143983105 = 983090983091(983088983086983091983088983089983088) = 983094983086983097983090983091

there4 A 7 ก (ก กก) 19 52

983155983145983150983160 + 983155983145983150983161 = 983089

983094 rarr 983090983155983145983150

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983094 (983089)

983139983151983155983160 + 983139983151983155 983161 = 983089

983091 rarr 983090983139983151983155

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983091 (983090)

(983089)(983090) 983084 983156983137983150

983160 + 983161

983090 = 983089983090

there4 983156983137983150 (983160 + 983161) = 983156983137983150983090

983160 + 983161

983090 =

983090983156983137983150 983160 + 983161

983090

983089 minus 983156983137983150 983090

983160 + 983161

983090

=983090

983089983090

983089 minus

983089983090

983090 = 983092

983091

20 52

983155983145983150983105 + 983155983145983150983106 = 983089 rarr 983090983155983145983150

983105 + 983106

983090 983139983151983155 983105 minus 983106

983090 = 983089 (983089)

983139983151983155983105 + 983139983151983155983106 = 983091

983090 rarr 983090983139983151983155

983105 + 983106

983090 983139983151983155

983105 minus 983106

983090 = 983091

983090 (983090)

(983089)(983090) 983084 983156983137983150

983105 + 983106

983090 = 983090

983091

there4 983139983151983155 (983105 + 983106) = 983139983151983155983090

983105 + 983106983090

=

983089 minus 983156983137983150 983090

983105 + 983106

983090

983089 + 983156983137983150 983090

983105 + 983106

983090

=983089 minus

983090

983091

983090

983089 +

983090983091

983090 = 983093

983089983091

21 53

=983150 = 983089

983092983092Σ 983139983151983155983150

983150 = 983089

983092983092Σ 983155983145983150983150

983139983151983155983089 + 983139983151983155983090 + 983139983151983155983091 + 983086983086983086983086983086 + 983139983151983155983092983091 + 983139983151983155983092983092

983155983145983150983089 + 983155983145983150 983090 + 983155983145983150983091 + 983086983086983086983086983086 + 983155983145983150983092983091 + 983155983145983150983092983092

= (983139983151983155 983092983092 + 983139983151983155983089 ) + (983139983151983155983092983091 + 983139983151983155 983090 ) + 983086983086983086983086983086 + (983139983151983155983090983091 + 983139983151983155 983090983090 )(983155983145983150983092983092 + 983155983145983150983089 ) + (983155983145983150983092983091 + 983155983145983150 983090 ) + 983086983086983086983086983086 + (983155983145983150983090983091 + 983155983145983150983090983090 )

= 983090983139983151983155

983092983093983090

983139983151983155 983092983091

983090 + 983090983139983151983155

983092983093983090

983139983151983155 983092983089

983090 + 983086983086983086983086983086 + 983090983139983151983155

983092983093983090

983139983151983155 983089

983090

983090983155983145983150 983092983093

983090 983139983151983155

983092983091983090

+ 983090983155983145983150 983092983093

983090 983139983151983155

983092983089983090

+ 983086983086983086983086983086 + 983090983155983145983150 983092983093

983090 983139983151983155

983089983090

7

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 817

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 917

26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1117

47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1217

ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 517

35 21

983150 = 983090

infinΣ 983089

983150 983092 minus 983150 983090 = 983105 rarr

983150 = 983090

infinΣ 983089

(983150 983090 minus 983089)983150 983090 = 983105 rarr

983150 = 983090

infinΣ

983089

983150 983090 minus 983089minus 983089

983150 983090 = 983105

983150 = 983090

infin

Σ 983089

983150 983090 = 983150 = 983090

infin

Σ 983089

983150 983090 minus 983089 minus 983105 = 983150 = 983090

infin

Σ 983089

(983150 minus 983089)(983150 + 983089) minus 983105

=

983089983089 sdot 983091

+ 983089983090 sdot 983092

+ 983089983091 sdot 983093

+ 983089983092 sdot 983094

+ 983086983086983086983086983086 minus 983105

= 983089

983089 sdot 983091 + 983089

983091 sdot 983093 + 983086983086983086983086983086 +

983089

983090 sdot 983092 + 983089

983092 sdot 983094 + 983086983086983086983086983086 minus 983105

= 983089983091 minus 983089

983089983089 +

983089983092 minus 983090

983089983090 minus 983105

= 983089

983090 + 983089

983092 minus 983105 = 983091

983092 minus 983105

36 22

983137983089 + 983137983090 + 983137983091 + 983086983086983086983086983086 + 983137983150 = 983150 983090983137983150 rarr 983155983150 = 983150 983090983137983150

983137983150 = 983155983150 minus 983155983150 minus 983089 rarr 983137983150 = 983150 983090983137983150 minus (983150 minus 983089)983090983137983150 minus 983089 rarr 983150 983090983137983150 minus 983137983150 = (983150 minus 983089)983090983137983150 minus 983089

(983150 983090 minus 983089)983137983150 = (983150 minus 983089)983090983137983150 minus983089 rarr (983150 minus 983089)(983150 + 983089)983137983150 = (983150 minus 983089)983090983137983150 minus 983089

983137983150 = (983150 minus 983089)(983150 + 983089) 983137983150 minus 983089

983137983090 = 983089983091 983137983089 = 983089983089 + 983090 983137983089

983137983091 = 983089

983090 983137983090 = 983089

983094983137983089 = 983089

983089 + 983090 + 983091983137983089

983137983092 = 983091

983093 983137983091 = 983089

983089983088983137983089 = 983089

983089 + 983090 + 983091 + 983092983137983089

983137983150 = 983089983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150

983137983089 = 983089983150 983090

(983150 + 983089) 983137983089 =

983090983137983089

983150 (983150 + 983089) = 983090983137983089

983150 983090 + 983150 = 983090983088983088

983150 983090 + 983150

there4983150 rarr infin

983148983145983149 983150 983090983137983150 =983150 rarr infin983148983145983149

983090983088983088983150 983090

983150 983090 + 983150 = 983090983088983088

37 22

ก 983137983150 = 983089 + 983090 + 983091 + 983086983086983086983086983086 + 983150 983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) =

983150

983090(983150 + 983089)

983150 (983150 + 983089)(983150 + 983090)(983150 + 983091) + 983089983090(983150 + 983090)(983150 + 983091)

there4 =983123infin 983089

983090

983089

983091 sdot 983092 + 983089

983092 sdot 983093 + 983089

983093 sdot 983094 + 983086983086983086983086983086

= 983089983090

983089983092 minus 983091

983089983091

= 983089

983094

5

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 617

กก

5 45

=983139983151983155983089983093 + 983156983137983150983094983088 983155983145983150983089983093 983139983151983155983089983093 + 983155983145983150983094983088983139983151983155983094983088 983155983145983150983089983093 = 983139983151983155983094983088 983139983151983155983089983093 + 983155983145983150983094983088 983155983145983150983089983093983139983151983155983094983088

= 983139983151983155 (983094983088 minus 983089983093 )983139983151983155 983094983088

= 983139983151983155983092983093

983139983151983155983094983088 =

983090

983090

983089983090

= 983090

9 47

983155983145983150983160 + 983139983151983155983160 = 983089983090

rarr (983155983145983150983160 + 983139983151983155 983160)983090 = 983089983092

rarr 983089 + 983090983155983145983150983160983139983151983155983160 = 983089983092 rarr 983155983145983150 983160 983139983151983155983160 = minus 983091

983096

there4 =983096(983155983145983150 983091983160 + 983139983151983155983091983160) 983096(983155983145983150983160 + 983139983151983155983160)(983155983145983150 983090983160 minus 983155983145983150983160983139983151983155983160 + 983139983151983155983090983160)

= 983096

983089983090

983089 minus

minus983091983096

= 983089983089

983090

11 48

983155983145983150983160 + 983139983151983155983160 = 983137 (983089) 983084 983155983145983150 983160 minus 983139983151983155 983160 = 983138 (983090)

(983089) + (983090) 983090983155983145983150983160 = 983137 + 983138 983084 (983089) minus (983090) 983090983139983151983155983160 = 983137 minus 983138

(1)(2) 983155983145983150 983090983160 minus 983139983151983155983090983160 = 983137983138 rarr 983139983151983155983090983160 minus 983155983145983150 983090983160 = minus 983137983138

=983155983145983150983092983160 983090983155983145983150983090983160983139983151983155983090983160 = 983090(983090983155983145983150983160983139983151983155983160)(983139983151983155983090983160 minus 983155983145983150 983090983160)

= (983090983155983145983150983160)(983090983139983151983155983160)[minus983137983138] = (983137 + 983138)(983137 minus 983138)(minus983137983138)

= (983137983090 minus 983138983090)(minus983137983138) = 983137983138983091 minus 983137983091983138

14 49

983089 + 983155983145983150983160983139983151983155 983160

983089 minus 983155983145983150983160983139983151983155 983160

= 983089 + 983105983139983151983155983160983155983145983150983160

983139983151983155983090983160 minus 983155983145983150 983090983160rarr 983139983151983155983160 + 983155983145983150983160

983139983151983155983160 minus 983155983145983150983160 = 983089 + 983105983139983151983155983160983155983145983150983160

(983139983151983155983160 minus 983155983145983150983160)(983139983151983155983160 + 983155983145983150 983160)

983089 + 983105983139983151983155983160983155983145983150983160 = (983139983151983155983160 + 983155983145983150983160)983090 = 983089 + 983090983139983151983155983160983155983145983150983160

ก 2 1983105 = 983090 rarr 983105983090983093983093983091 = 983090983090983093983093983091 983090983093983093983091

983092

16 50

983105 + 983106 = 983092983093 rarr 983156983137983150 (983105 + 983106) = 983156983137983150983092983093 rarr 983156983137983150983105 + 983156983137983150983106983089 minus 983156983137983150983105983156983137983150983106

= 983089

983156983137983150983105 + 983156983137983150983106 = 983089 minus 983156983137983150983105983156983137983150983106

983156983137983150983105 + 983156983137983150983106 + 983156983137983150983105983156983137983150983106 = 983089 rarr 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089

983089 + 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089 + 983089 rarr (983089 + 983156983137983150983105)(983089 + 983156983137983150 983106) = 983090

6

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 717

(983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 ) = 983090983084 (983089 + 983156983137983150983090 )(983089 + 983156983137983150 983092983091 ) = 983090983084 983086983086983086983086983086983086983086983086983086983086

983086983086983086983086983086983086983086983086983086983086983084 (983089 + 983156983137983150983090983090 )(983089 + 983156983137983150983090983091 ) = 983090

ก 983105 = (983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 )(983089 + 983156983137983150983090 )(983089 + 983156983137983150983092983091 ) 983086983086983086983086983086 (983089 + 983156983137983150983090983090 )

(983089 + 983156983137983150983090983091 )(983089 + 983156983137983150 983092983093 )

983105 = 983090983090983091

983148983151983143983105 = 983148983151983143983090983090983091 rarr 983148983151983143983105 = 983090983091983148983151983143983090 rarr 983148983151983143983105 = 983090983091(983088983086983091983088983089983088) = 983094983086983097983090983091

there4 A 7 ก (ก กก) 19 52

983155983145983150983160 + 983155983145983150983161 = 983089

983094 rarr 983090983155983145983150

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983094 (983089)

983139983151983155983160 + 983139983151983155 983161 = 983089

983091 rarr 983090983139983151983155

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983091 (983090)

(983089)(983090) 983084 983156983137983150

983160 + 983161

983090 = 983089983090

there4 983156983137983150 (983160 + 983161) = 983156983137983150983090

983160 + 983161

983090 =

983090983156983137983150 983160 + 983161

983090

983089 minus 983156983137983150 983090

983160 + 983161

983090

=983090

983089983090

983089 minus

983089983090

983090 = 983092

983091

20 52

983155983145983150983105 + 983155983145983150983106 = 983089 rarr 983090983155983145983150

983105 + 983106

983090 983139983151983155 983105 minus 983106

983090 = 983089 (983089)

983139983151983155983105 + 983139983151983155983106 = 983091

983090 rarr 983090983139983151983155

983105 + 983106

983090 983139983151983155

983105 minus 983106

983090 = 983091

983090 (983090)

(983089)(983090) 983084 983156983137983150

983105 + 983106

983090 = 983090

983091

there4 983139983151983155 (983105 + 983106) = 983139983151983155983090

983105 + 983106983090

=

983089 minus 983156983137983150 983090

983105 + 983106

983090

983089 + 983156983137983150 983090

983105 + 983106

983090

=983089 minus

983090

983091

983090

983089 +

983090983091

983090 = 983093

983089983091

21 53

=983150 = 983089

983092983092Σ 983139983151983155983150

983150 = 983089

983092983092Σ 983155983145983150983150

983139983151983155983089 + 983139983151983155983090 + 983139983151983155983091 + 983086983086983086983086983086 + 983139983151983155983092983091 + 983139983151983155983092983092

983155983145983150983089 + 983155983145983150 983090 + 983155983145983150983091 + 983086983086983086983086983086 + 983155983145983150983092983091 + 983155983145983150983092983092

= (983139983151983155 983092983092 + 983139983151983155983089 ) + (983139983151983155983092983091 + 983139983151983155 983090 ) + 983086983086983086983086983086 + (983139983151983155983090983091 + 983139983151983155 983090983090 )(983155983145983150983092983092 + 983155983145983150983089 ) + (983155983145983150983092983091 + 983155983145983150 983090 ) + 983086983086983086983086983086 + (983155983145983150983090983091 + 983155983145983150983090983090 )

= 983090983139983151983155

983092983093983090

983139983151983155 983092983091

983090 + 983090983139983151983155

983092983093983090

983139983151983155 983092983089

983090 + 983086983086983086983086983086 + 983090983139983151983155

983092983093983090

983139983151983155 983089

983090

983090983155983145983150 983092983093

983090 983139983151983155

983092983091983090

+ 983090983155983145983150 983092983093

983090 983139983151983155

983092983089983090

+ 983086983086983086983086983086 + 983090983155983145983150 983092983093

983090 983139983151983155

983089983090

7

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 817

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 917

26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1117

47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1217

ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 617

กก

5 45

=983139983151983155983089983093 + 983156983137983150983094983088 983155983145983150983089983093 983139983151983155983089983093 + 983155983145983150983094983088983139983151983155983094983088 983155983145983150983089983093 = 983139983151983155983094983088 983139983151983155983089983093 + 983155983145983150983094983088 983155983145983150983089983093983139983151983155983094983088

= 983139983151983155 (983094983088 minus 983089983093 )983139983151983155 983094983088

= 983139983151983155983092983093

983139983151983155983094983088 =

983090

983090

983089983090

= 983090

9 47

983155983145983150983160 + 983139983151983155983160 = 983089983090

rarr (983155983145983150983160 + 983139983151983155 983160)983090 = 983089983092

rarr 983089 + 983090983155983145983150983160983139983151983155983160 = 983089983092 rarr 983155983145983150 983160 983139983151983155983160 = minus 983091

983096

there4 =983096(983155983145983150 983091983160 + 983139983151983155983091983160) 983096(983155983145983150983160 + 983139983151983155983160)(983155983145983150 983090983160 minus 983155983145983150983160983139983151983155983160 + 983139983151983155983090983160)

= 983096

983089983090

983089 minus

minus983091983096

= 983089983089

983090

11 48

983155983145983150983160 + 983139983151983155983160 = 983137 (983089) 983084 983155983145983150 983160 minus 983139983151983155 983160 = 983138 (983090)

(983089) + (983090) 983090983155983145983150983160 = 983137 + 983138 983084 (983089) minus (983090) 983090983139983151983155983160 = 983137 minus 983138

(1)(2) 983155983145983150 983090983160 minus 983139983151983155983090983160 = 983137983138 rarr 983139983151983155983090983160 minus 983155983145983150 983090983160 = minus 983137983138

=983155983145983150983092983160 983090983155983145983150983090983160983139983151983155983090983160 = 983090(983090983155983145983150983160983139983151983155983160)(983139983151983155983090983160 minus 983155983145983150 983090983160)

= (983090983155983145983150983160)(983090983139983151983155983160)[minus983137983138] = (983137 + 983138)(983137 minus 983138)(minus983137983138)

= (983137983090 minus 983138983090)(minus983137983138) = 983137983138983091 minus 983137983091983138

14 49

983089 + 983155983145983150983160983139983151983155 983160

983089 minus 983155983145983150983160983139983151983155 983160

= 983089 + 983105983139983151983155983160983155983145983150983160

983139983151983155983090983160 minus 983155983145983150 983090983160rarr 983139983151983155983160 + 983155983145983150983160

983139983151983155983160 minus 983155983145983150983160 = 983089 + 983105983139983151983155983160983155983145983150983160

(983139983151983155983160 minus 983155983145983150983160)(983139983151983155983160 + 983155983145983150 983160)

983089 + 983105983139983151983155983160983155983145983150983160 = (983139983151983155983160 + 983155983145983150983160)983090 = 983089 + 983090983139983151983155983160983155983145983150983160

ก 2 1983105 = 983090 rarr 983105983090983093983093983091 = 983090983090983093983093983091 983090983093983093983091

983092

16 50

983105 + 983106 = 983092983093 rarr 983156983137983150 (983105 + 983106) = 983156983137983150983092983093 rarr 983156983137983150983105 + 983156983137983150983106983089 minus 983156983137983150983105983156983137983150983106

= 983089

983156983137983150983105 + 983156983137983150983106 = 983089 minus 983156983137983150983105983156983137983150983106

983156983137983150983105 + 983156983137983150983106 + 983156983137983150983105983156983137983150983106 = 983089 rarr 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089

983089 + 983156983137983150983105 + 983156983137983150983106(983089 + 983156983137983150983105) = 983089 + 983089 rarr (983089 + 983156983137983150983105)(983089 + 983156983137983150 983106) = 983090

6

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 717

(983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 ) = 983090983084 (983089 + 983156983137983150983090 )(983089 + 983156983137983150 983092983091 ) = 983090983084 983086983086983086983086983086983086983086983086983086983086

983086983086983086983086983086983086983086983086983086983086983084 (983089 + 983156983137983150983090983090 )(983089 + 983156983137983150983090983091 ) = 983090

ก 983105 = (983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 )(983089 + 983156983137983150983090 )(983089 + 983156983137983150983092983091 ) 983086983086983086983086983086 (983089 + 983156983137983150983090983090 )

(983089 + 983156983137983150983090983091 )(983089 + 983156983137983150 983092983093 )

983105 = 983090983090983091

983148983151983143983105 = 983148983151983143983090983090983091 rarr 983148983151983143983105 = 983090983091983148983151983143983090 rarr 983148983151983143983105 = 983090983091(983088983086983091983088983089983088) = 983094983086983097983090983091

there4 A 7 ก (ก กก) 19 52

983155983145983150983160 + 983155983145983150983161 = 983089

983094 rarr 983090983155983145983150

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983094 (983089)

983139983151983155983160 + 983139983151983155 983161 = 983089

983091 rarr 983090983139983151983155

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983091 (983090)

(983089)(983090) 983084 983156983137983150

983160 + 983161

983090 = 983089983090

there4 983156983137983150 (983160 + 983161) = 983156983137983150983090

983160 + 983161

983090 =

983090983156983137983150 983160 + 983161

983090

983089 minus 983156983137983150 983090

983160 + 983161

983090

=983090

983089983090

983089 minus

983089983090

983090 = 983092

983091

20 52

983155983145983150983105 + 983155983145983150983106 = 983089 rarr 983090983155983145983150

983105 + 983106

983090 983139983151983155 983105 minus 983106

983090 = 983089 (983089)

983139983151983155983105 + 983139983151983155983106 = 983091

983090 rarr 983090983139983151983155

983105 + 983106

983090 983139983151983155

983105 minus 983106

983090 = 983091

983090 (983090)

(983089)(983090) 983084 983156983137983150

983105 + 983106

983090 = 983090

983091

there4 983139983151983155 (983105 + 983106) = 983139983151983155983090

983105 + 983106983090

=

983089 minus 983156983137983150 983090

983105 + 983106

983090

983089 + 983156983137983150 983090

983105 + 983106

983090

=983089 minus

983090

983091

983090

983089 +

983090983091

983090 = 983093

983089983091

21 53

=983150 = 983089

983092983092Σ 983139983151983155983150

983150 = 983089

983092983092Σ 983155983145983150983150

983139983151983155983089 + 983139983151983155983090 + 983139983151983155983091 + 983086983086983086983086983086 + 983139983151983155983092983091 + 983139983151983155983092983092

983155983145983150983089 + 983155983145983150 983090 + 983155983145983150983091 + 983086983086983086983086983086 + 983155983145983150983092983091 + 983155983145983150983092983092

= (983139983151983155 983092983092 + 983139983151983155983089 ) + (983139983151983155983092983091 + 983139983151983155 983090 ) + 983086983086983086983086983086 + (983139983151983155983090983091 + 983139983151983155 983090983090 )(983155983145983150983092983092 + 983155983145983150983089 ) + (983155983145983150983092983091 + 983155983145983150 983090 ) + 983086983086983086983086983086 + (983155983145983150983090983091 + 983155983145983150983090983090 )

= 983090983139983151983155

983092983093983090

983139983151983155 983092983091

983090 + 983090983139983151983155

983092983093983090

983139983151983155 983092983089

983090 + 983086983086983086983086983086 + 983090983139983151983155

983092983093983090

983139983151983155 983089

983090

983090983155983145983150 983092983093

983090 983139983151983155

983092983091983090

+ 983090983155983145983150 983092983093

983090 983139983151983155

983092983089983090

+ 983086983086983086983086983086 + 983090983155983145983150 983092983093

983090 983139983151983155

983089983090

7

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 817

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 917

26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

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47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

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ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

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15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

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(983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 ) = 983090983084 (983089 + 983156983137983150983090 )(983089 + 983156983137983150 983092983091 ) = 983090983084 983086983086983086983086983086983086983086983086983086983086

983086983086983086983086983086983086983086983086983086983086983084 (983089 + 983156983137983150983090983090 )(983089 + 983156983137983150983090983091 ) = 983090

ก 983105 = (983089 + 983156983137983150983089 )(983089 + 983156983137983150983092983092 )(983089 + 983156983137983150983090 )(983089 + 983156983137983150983092983091 ) 983086983086983086983086983086 (983089 + 983156983137983150983090983090 )

(983089 + 983156983137983150983090983091 )(983089 + 983156983137983150 983092983093 )

983105 = 983090983090983091

983148983151983143983105 = 983148983151983143983090983090983091 rarr 983148983151983143983105 = 983090983091983148983151983143983090 rarr 983148983151983143983105 = 983090983091(983088983086983091983088983089983088) = 983094983086983097983090983091

there4 A 7 ก (ก กก) 19 52

983155983145983150983160 + 983155983145983150983161 = 983089

983094 rarr 983090983155983145983150

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983094 (983089)

983139983151983155983160 + 983139983151983155 983161 = 983089

983091 rarr 983090983139983151983155

983160 + 983161

983090 983139983151983155 983160 minus 983161

983090 = 983089

983091 (983090)

(983089)(983090) 983084 983156983137983150

983160 + 983161

983090 = 983089983090

there4 983156983137983150 (983160 + 983161) = 983156983137983150983090

983160 + 983161

983090 =

983090983156983137983150 983160 + 983161

983090

983089 minus 983156983137983150 983090

983160 + 983161

983090

=983090

983089983090

983089 minus

983089983090

983090 = 983092

983091

20 52

983155983145983150983105 + 983155983145983150983106 = 983089 rarr 983090983155983145983150

983105 + 983106

983090 983139983151983155 983105 minus 983106

983090 = 983089 (983089)

983139983151983155983105 + 983139983151983155983106 = 983091

983090 rarr 983090983139983151983155

983105 + 983106

983090 983139983151983155

983105 minus 983106

983090 = 983091

983090 (983090)

(983089)(983090) 983084 983156983137983150

983105 + 983106

983090 = 983090

983091

there4 983139983151983155 (983105 + 983106) = 983139983151983155983090

983105 + 983106983090

=

983089 minus 983156983137983150 983090

983105 + 983106

983090

983089 + 983156983137983150 983090

983105 + 983106

983090

=983089 minus

983090

983091

983090

983089 +

983090983091

983090 = 983093

983089983091

21 53

=983150 = 983089

983092983092Σ 983139983151983155983150

983150 = 983089

983092983092Σ 983155983145983150983150

983139983151983155983089 + 983139983151983155983090 + 983139983151983155983091 + 983086983086983086983086983086 + 983139983151983155983092983091 + 983139983151983155983092983092

983155983145983150983089 + 983155983145983150 983090 + 983155983145983150983091 + 983086983086983086983086983086 + 983155983145983150983092983091 + 983155983145983150983092983092

= (983139983151983155 983092983092 + 983139983151983155983089 ) + (983139983151983155983092983091 + 983139983151983155 983090 ) + 983086983086983086983086983086 + (983139983151983155983090983091 + 983139983151983155 983090983090 )(983155983145983150983092983092 + 983155983145983150983089 ) + (983155983145983150983092983091 + 983155983145983150 983090 ) + 983086983086983086983086983086 + (983155983145983150983090983091 + 983155983145983150983090983090 )

= 983090983139983151983155

983092983093983090

983139983151983155 983092983091

983090 + 983090983139983151983155

983092983093983090

983139983151983155 983092983089

983090 + 983086983086983086983086983086 + 983090983139983151983155

983092983093983090

983139983151983155 983089

983090

983090983155983145983150 983092983093

983090 983139983151983155

983092983091983090

+ 983090983155983145983150 983092983093

983090 983139983151983155

983092983089983090

+ 983086983086983086983086983086 + 983090983155983145983150 983092983093

983090 983139983151983155

983089983090

7

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 817

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 917

26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1117

47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1217

ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 817

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 917

26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1117

47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

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ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

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15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

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26 55

(983155983145983150983097983160 + 983155983145983150983095983160) + 983093(983155983145983150983095983160 + 983155983145983150983093983160) + 983089983090(983155983145983150983093983160+ 983155983145983150983091983160)983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983155983145983150983096983160983139983151983155983160 + 983093(983090983155983145983150983094983160983139983151983155983160) + 983089983090(983090983155983145983150983092983160983139983151983155983160)

983155983145983150983096983160 + 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160

= 983089

983090983139983151983155983160(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160)(983155983145983150983096983160+ 983093983155983145983150983094983160 + 983089983090983155983145983150983092983160) = 983089

there4 983139983151983155983160 = 983089

983090 rarr 983160 = 983094983088 983139983151983155983091983160 = 983139983151983155 983089983096983088 = minus 983089

27 56

983091983156983137983150983105 = 983156983137983150 (983105 + 983106) rarr 983156983137983150 (983105 + 983106)983156983137983150983105

= 983091 rarr 983155983145983150 (983105 + 983106)983139983151983155 (983105 + 983106)

983139983151983155983105

983155983145983150983105 = 983091

983090983155983145983150 (983105 + 983106)983139983151983155983105

983090983139983151983155 (983105 + 983106)983155983145983150983105

= 983091 rarr 983155983145983150 (983090983105 + 983106) + 983155983145983150 983106

983155983145983150 (983090983105 + 983106) minus 983155983145983150 983106

= 983091

983155983145983150 (983090983105 + 983106) + 983155983145983150 983106 = 983091983155983145983150 (983090983105 + 983106) minus 983091983155983145983150983106 rarr 983092 983155983145983150 983106 = 983090983155983145983150 (983090983105 + 983106)

there4 983155983145983150 (983090983105 + 983106)983155983145983150983106

= 983090

34 59

983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 = 983091983088 rarr 983137983154983139983139983151983155 983160 minus (983097983088 minus 983137983154983139983139983151983155 983160) = 983091983088

983137983154983139983139983151983155 983160 = 983094983088 rarr 983160 = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983139983151983155 983160 minus 983137983154983139983156983137983150 983090983160 = 983094983088 minus 983137983154983139983156983137983150 983090

983089983090

= 983094983088 minus 983137983154983139983156983137983150 983089 = 983094983088 minus 983092983093 = 983089983093 = π

983089983090

35 10

π983090983093983093983091

= 983137983154983139983139983151983155 983160 minus 983137983154983139983155983145983150 983160 rarr π983090983093983093983091

= 983097983088 minus 983137983154983139983155983145983150 983160 minus 983137983154983139983155983145983150 983160

983139983151983155 π983090983093983093983091

= 983139983151983155 (983097983088 minus 983090983137983154983139983155983145983150983160) rarr 983139983151983155 π983090983093983093983091

= 983155983145983150 (983090983137983154983139983155983145983150983160)

983105 = 983137983154983139983155983145983150 983160 rarr 983155983145983150983105 = 983160 rarr 983139983151983155983105 = 983089 minus 983160983090

983139983151983155 π983090983093983093983091

= 983155983145983150983090983105 = 983090983155983145983150983105983139983151983155983105 = 983090983160 983089 minus 983160983090

37 61

983156983137983150 983090θ minus 983092983156983137983150 θ + 983089 = 983088 rarr 983090(983090983156983137983150 θ) = 983089 + 983156983137983150 983090θ rarr 983090983156983137983150 θ983089 + 983156983137983150 983090θ

= 983089983090

983155983145983150983090θ = 983089983090

rarr 983090θ = 983091983088 rarr 983092θ = 983094983088 rarr 983139983151983155983092θ = 983139983151983155 983094983088 = 983089983090

there4 983137983154983139983155983145983150 (983139983151983155983092θ) = 983137983154983139983155983145983150 983089983090

= 983091983088 = π983094

9

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1017

42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1117

47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1217

ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

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42 63

983137983154983139983156983137983150 983089

983090 + 983137983154983139983156983137983150

983089

983091 = 983090983094983086983093 + 983089983096983086983093 = 983092983093

983137983154983139983156983137983150 983089

983092 + 983137983154983139983156983137983150

983089

983093 = 983137983154983139983156983137983150

983089

983092 + 983089

983093

983089 minus 983089983092 983089983093 = 983137983154983139983156983137983150

983097

983089983097

983156983137983150 983137983154983139983156983137983150 983089983090 + 983137983154983139983156983137983150

983089983091 + 983137983154983139983156983137983150

983089983092 + 983137983154983139983156983137983150

983089983093 = 983156983137983150 983092983093 + 983137983154983139983156983137983150

983097983089983097

983105 = 983137983154983139983156983137983150 983097

983089983097 rarr 983156983137983150983105 = 983097

983089983097

there4 =983156983137983150 983092983093 + 983137983154983139983156983137983150 983097983089983097 983156983137983150 (983092983093 + 983105) = 983156983137983150983092983093 + 983156983137983150983105

983089 minus 983156983137983150983092983093 983156983137983150983105

= 983089 + 983097

983089983097

983089 minus 983097

983089983097

= 983090983096

983089983088 = 983089983092

983093

43 64

983137983154983139983139983151983155 983139983151983155 983091π

983093 = 983091π983093

983137983154983139983155983145983150 983155983145983150 983092π

983093 = 983137983154983139983155983145983150 983155983145983150 π983093 = π

983093

983137983154983139983156983137983150 983156983137983150 983094π

983093 = 983137983154983139983156983137983150 983156983137983150 π983093 = π

983093

there4 983137983154983139983139983151983155 983139983151983155

983091π983093

+ 983137983154983139983155983145983150

983155983145983150 983092π

983093 + 983137983154983139983156983137983150

983156983137983150 983094π

983093 = 983091π

983093 + π

983093 + π

983093 = π

45 65

ก 983094

983155983145983150983094983088 = 983089

983155983145983150983106 rarr

983094

983091

983090

= 983089

983155983145983150983106

983155983145983150983106 = 983089

983090 983090

there4 983139983151983155 983090983106 = 983089 minus 983090983155983145983150 983090983106 = 983089 minus 983090 983089

983090 983090

983090

= 983089 minus 983089

983092 = 983091

983092

46 65

983094983155983145983150983105 = 983092983155983145983150983106 = 983091983155983145983150983107 rarr 983155983145983150983105983090

= 983155983145983150983106983091

= 983155983145983150983107983092

กก sine 983137 = 983090983084 983138 = 983091983084 983139 = 983092

กก 983139983151983155 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

983092983090 = 983090983090 + 983091983090 minus 983090(983090)(983091)983139983151983155983107

983139983151983155983107 = minus 983089

983092

there4 983139983151983155983090983107 = 983090983139983151983155983090983107 minus 983089 = 983090 minus983089983092 983090

minus 983089 = minus 983095983096

60

1

A B

C

6

10

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47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

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ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

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15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

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26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

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47 66

กก sine 983155983145983150983105983137 = 983155983145983150983106

983138 = 983155983145983150983107

983139 = 983147

983155983145983150983105 = 983137983147983084 983155983145983150983106 = 983138983147983084 983155983145983150983107 = 983139983147

ก (983155983145983150983105 + 983155983145983150983106 + 983155983145983150983107)(983155983145983150983105 + 983155983145983150983106 minus 983155983145983150983107) = 983091983155983145983150983105983155983145983150983106

983147 (983137 + 983138 + 983139)983147 (983137 + 983138 minus 983139) = 983091(983137983147 )(983138983147 )

(983137 + 983138)983090 minus 983139983090 = 983091983137983138

983137983090 + 983090983137983138 + 983138983090 minus 983139983090 = 983091983137983138

ก983139983090 = 983137983090 + 983138983090 minus 983137983138 983139983090 = 983137983090 + 983138983090 minus 983090983137983138983139983151983155983107

there4

983139983151983155983107 = 983089

983090 rarr 983107 = 983094983088 983156983137983150983107 = 983156983137983150983094983088 = 983091

50 67

กก = 983160

ก กก = 983161

ก ก = 983162

ก 983160983091983088983088

= 983139983151983156983094983088 rarr 983160 = 983089983088983088 983091

983161983091983088983088

= 983139983151983156983092983093 rarr 983161 = 983091983088983088

กก 983162983090 = 983160983090 + 983161983090

983162983090 = (983089983088983088 983091 )983090 + 983091983088983088983090

983162983090 = 983091(983089983088983088)983090 + (983091 sdot 983089983088983088)983090 = 983091(983089983088983088)983090 + 983097(983089983088983088)983090

983162983090 = 983089983090(983089983088983088)983090

there4 983162 = 983090 983091 (983089983088983088) = 983090983088983088 983091

N

300

60

45

x

y z

S

W E

P

P ก

ก

11

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ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

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15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

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18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

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19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

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26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

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33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

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ก

6 85

983162 = 983096 983139983145983155983096983088

983090 983139983145983155983093983094 = 983090983139983145983155983090983092 rarr 983162983093 = 983090983093983139983145983155 983089983090983088 = 983091983090(983139983151983155 983089983090983088 + 983145983155983145983150983089983090983088 )

there4 983162983093 = minus 983089983094 + 983089983094 983091 983145 983162983093 = minus 983089983094

7 86

= 983089

983090 +

983091

983090 983145

983090983088983088983094

(983139983151983155983094983088 + 983145983155983145983150983094983088 )983090983088983088983094 = (983139983145983155 π983091

)983090983088983088983094 = 983139983145983155 (983090983088983088983094π)

983091

= 983139983145983155 983094983094983096π + 983090π983091 = 983139983145983155

983090π983091

= 983139983145983155983089983090983088

= 983139983151983155 983089983090983088

+983145983155983145983150983089983090983088

= minus

983089

983090 +

983091

983090 983145

10 87 983162983091 = 983139983151983155983094983088 + 983145983155983145983150983094983088 = 983139983145983155983094983088 rarr 983162983091 = 983139983145983155 983094983088 rarr 983162 983091 = 983089

rarr 983162 983091983088 = 983089983089983088 = 983089

983162983089983096 = (983162983091)983094 = (983139983145983155983094983088 )983094 = 983139983145983155983091983094983088 = 983089

there4 983162983091983088

983162983089983096 + 983089= 983162 983091983088

983089 + 983089 = 983089

983090

11 88

983090

983090 +

983090

983090 983145

983150

= 983089 rarr (983139983151983155 983092983093 + 983145983155983145983150983092983093 )983150 = 983089 rarr 983139983145983155983092983093 (983150 ) = 983139983145983155 983091983094983088

983092983093 (983150 ) = 983091983094983088 rarr 983150 = 983096

( 983091 + 983145)983090983150 = ( 983091 + 983145)983089983094 = (983139983145983155983091983088 )983089983094 = 983139983145983155983092983096983088 = 983139983145983155983089983090983088

there4 2 ( 983091 + 983145)983090983150 θ = 983089983090983088

14 89

983090983137 + 983138983145

sdot 983091983092 + 983139

= 983090983090

sdot 983091983090

sdot (983090983090

)(983090 + 983145)

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983090 sdot 983091983090 sdot 983090983092 + 983090983145

983090983137 + 983138983145 sdot 983091983092 + 983139 = 983090983094 + 983090983145 sdot 983091983090

983137 + 983138983145 = 983094 + 983090983145 rarr 983137 = 983094983084 983138 = 983090

983092 + 983139 = 983090 rarr 983139 = minus 983090

983160 + 983161983145 = 983138 + 983139983145

983139 + 983137983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 rarr 983160 + 983161983145 = 983090 minus 983090983145

minus983090 + 983094983145 =

983096

983092983088

983160 + 983161983145 983090 = 983096983092983088 rarr 983160983090 + 983161983090 = 983089983093

12

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1317

15 90 983162 = 983091 + 983092983145 983084 983162 = 983091 minus 983092983145

(983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983162983094 + (983162)983094 = 983162983094 + (983162983094) = 983090983122983141(983162983094) = 983090983122983141(983162983094) + 983151983145

there4 (983091 + 983092983145)983094 + (983091 minus 983092983145)983094 = 983088

16 90983162983090 = 983090 + 983092983145 rarr 983162 983090 = 983090 + 983092983145 = 983090 983093 rarr 983162 = 983090 983093 = 983090 983092 983093

983162983090 + 983089 = 983091 + 983092983145 rarr 983162983090 + 983089 = 983091 + 983092983145 = 983093

there4 983162 + 983089983162 = 983162983090 + 983089

983162 = 983162983090 + 983089

983162 = 983093

983090 983092 983093= 983093

983091983092

983090=

983092 983093983091

983090983086

983090

983090=

983090 983092 983089983090983093

983090

17 91 กก 983162983089 = 983137 + 983138983145

983162983089 minus 983091983145 = 983090 rarr 983137 + 983138983145 minus 983091983145 = 983090 rarr 983137 + (983138 minus 983091)983145 = 983090 rarr 983137983090 + (983138 minus 983091)983090 = 983090

983137983090 + (983138 minus 983091)983090 = 983090983090 rarr 983137983090 + 983138983090 minus 983094983138 + 983097 = 983092 rarr 983137983090 + 983138983090 minus 983094983138 = minus 983093 (983089)

983162983089 minus 983094 = 983093 rarr 983137 + 983138983145 minus 983094 = 983093 rarr (983137 minus 983094) + 983138983145 = 983093 rarr (983137 minus 983094)983090 + 983138983090 = 983093

(983137 minus 983094)983090 + 983138983090 = 983093983090 rarr 983137983090 minus 983089983090983137 + 983091983094 + 983138983090 = 983090983093 rarr 983137983090 + 983138983090 minus 983089983090983137 = minus 983089983089 (983090)

983162983089 minus 983093 minus 983095983145 = 983093 rarr 983137 + 983138983145 minus 983093 minus 983095983145 = 983093 rarr (983137 minus 983093) + (983138 minus 983095)983145 = 983093

(983137 minus 983093)983090 + (983138 minus 983095)983090 = 983093 rarr (983137 minus 983093)983090 + (983138 minus 983095)983090 = 983090983093 rarr

983137983090 + 983138983090 minus 983089983088983137 minus 983089983092983138 = minus 983092983097 (983091)

(983090) minus (983089)983084 minus 983089983090983137 + 983094983138 = minus 983094 (983091)

(983091) minus (983090)983084 983090983137 minus 983089983092983138 = minus 983091983096 (983092)

(983092) times 983094983084 983089983090983137 minus 983096983092983138 = minus 983090983090983096 (983093)

(983091) + (983093)983084 minus 983095983096983138 = minus 983090983091983092 rarr 983138 = 983091

(3) 983138 = 983091 983137 = 983090 983162983089 = 983137 + 983138983145 = 983090 + 983091983145

there4 983162983089 = 983090 + 983091983145 = 983089983091

13

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httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1417

18 91 ก 983162983089 minus 983162983090 983162983089 983162983090

ก983162 + 983089 minus 983145 = 983089 rarr 983162 minus (minus983089 + 983145) = 983089 rarr 983162 minus (minus983089983084 983089) = 983089

(x y) ก 1 กกก ก(minus983089983084 983089) (minus983089983084 983089)

1 ก983159 + 983089 + 983145 = 983094 rarr 983159 minus (minus983089 minus 983145) = 983094 rarr 983159 minus (minus983089983084 minus983089) = 983094

(x y) ก 6 กกก ก(minus983089983084 minus983089) (minus983089983084 minus983089)

6 ก z w983162 minus 983159

กก xy ก

ก กก ก 9983162 minus 983159 (minus983089983084 983090) (minus983089983084 minus983095)

there4 983162 minus 983159 = 983097

(-1 1)(-1 2)

(-1 -7)

(-1 -1)

(-1 5)

y

x

14

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1517

19 92983162983091 + 983089 = 983088 rarr 983162983091 = minus983089 rarr 983162 = minus 983089983084

983089983090 +

983091

983090 983145983084

983089983090 minus

983091

983090 983145

983162983089 = 983089

983090

+ 983091

983090

983145983084 983162983089 = 983089

983090

minus 983091

983090

983145983084 983162983089 minus 983162983089 = 983091 983145

ก983162983089 983162983091 + 983089 = 983088

983162983089983091 + 983089 = 983088 rarr 983162983089

983091 = minus 983089 rarr 983162983089983089983096 = (minus983089)983094 = 983089

there4 983162983089 minus 983162983089

983162983089983089983096 + 983145

= 983091 983145

983089 + 983145 =

983091

983090= 983091

983090

20 92 983162 = 983137 + 983138983145

983162 minus 983089 = 983093 rarr 983137 + 983138983145 minus 983089 = 983093 rarr (983137 minus 983089) + 983138983145 = 983093 rarr (983137 minus 983089)983090 + 983138983090 = 983093

(983137 minus 983089)983090 + 983138983090 = 983093 rarr 983137983090 minus 983090983137 + 983089 + 983138983090 = 983093 rarr 983137983090 + 983138983090 minus 983090983137 = 983092 (983089)

983162 minus (983093 + 983092983145) = 983089983091 rarr 983137 + 983138983145 minus 983093 minus 983092983145 = 983089983091 rarr (983137 minus 983093) + (983138 minus 983092)983145 = 983089983091

(983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091 rarr (983137 minus 983093)983090 + (983138 minus 983092)983090 = 983089983091

rarr 983137983090 + 983138983090 minus 983089983088983137 minus 983096983138 = minus 983090983096 (983090)

(983089) minus (983090)983084 983096983137 + 983096983138 = 983091983090 rarr 983137 + 983138 = 983092 rarr 983138 = 983092 minus 983137 (983091) (3) (1) 983137983090 + (983092 minus 983137)983090 minus 983090983137 = 983092 rarr 983137983090 minus 983093983137 + 983094 = 983088

(983137 minus 983090)(983137 minus 983091) = 983088 rarr 983137 = 983090983084 983091

983137 = 983090983084 983138 = 983090 983162983089 = 983090 + 983090983145

983137 = 983091983084 983138 = 983089 983162983090 = 983091 + 983145

there4 983162983089 + 983162983090 = (983090 + 983090983145) + (983091 + 983145) = 983093 + 983091983145

22 93983162983089

minus983089 = 983091983093 minus 983092

983093983145 rarr 983089

983162983089 = 983091 minus 983092983145

983093 rarr 983162983089 = 983093

983091 minus 983092983145 = 983089983093 + 983090983088983145

983090983093 = 983091 + 983092983145

983093

983093983162983089 + 983090983162983090 = 983093 rarr 983093

983091 + 983092983145

983093 + 983090983162983090 = 983093 rarr 983162983090 = 983089 minus 983090983145

there4 983162983090 = 983089 + 983090983145

15

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1617

26 95983162 + 983089

983162 = 983089 = 983090983139983151983155983094983088

there4 983162983089983089 + 983089

983162

983089983089 = 983090983139983151983155983094983094983088 = 983090

983089983090

= 983089

983139983151983155983094983094983088 = 983139983151983155983094983088 = 983089983090

lowast

28 96983160983092 + (983147 minus 983092)983160983091 + (983091983096 minus 983092983147 )983160983090 + (983089983091983147 minus 983089983088983088)983160 + 983091983090983093 = 983088

ก 983090 + 983091983145983084 983090 minus 983091983145983084 983139983084983139

ก

(983090

+983091983145

)(983090

minus983091983145

)(983139)(983139)

= 983091983090983093

rarr (983089983091)983139983090

= 983091983090983093

rarr 983139983090

= 983090983093

rarr 983139

= 983093983084

minus983093

ก 1 983139 = 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + 983093 + 983093 = minus (983147 + 983092) rarr 983147 = minus 983089983088

ก 2 983139 = minus 983093

ก(983090 + 983091983145) + (983090 minus 983091983145) + (minus983093) + (minus983093) = minus (983147 + 983092) rarr 983147 = 983089983088

there4 k ก = 10 32 98

983142 (983160) = 983160983091 + 983091983160983090 + 983147983160 minus 983093

c ก f(x) 983142 (983139) = 983088 rarr 983139983091 + 983091983139983090 + 983139983147 minus 983093 = 983088

983139983147 = minus 983139983091 minus 983091983139983090 + 983093 rarr 983147 = minus 983139983090 minus 983091983139 + 983093983139

ก ก c 5

c ก 1 5ก 1 there4there4there4there4983139 = 983089983084 983147 = minus 983089983090 minus 983091(983089) + 983093

983089 = 983089 983147 + 983139 = 983089 + 983089 = 983090

ก 2 there4there4there4there4983139 = 983093983084 983147 = minus 983093983090 minus 983091(983093) + 983093983093

= minus 983091983097 983147 + 983139 = minus983091983097 + 983093 = 983091983092

16

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17

7212019

httpslidepdfcomreaderfull-56d6be111a28ab3016907edb 1717

33 99983162983089 =

983089983090 983139983145983155π

983091 983139983145983155 π983091

= 983090983139983145983155 983090π

983091 rarr 983162983089 = 983090

ก 983162983090983084 983162983091 983162

983090

minus 983090983162 + 983093 = 983088 983162983090983162983091 = 983093

there4 983162983089983162983090983162983091

= 983162983089

983162983090983162983091

= 983090983093

= 983088983086983092

34 99983160983090 + 983106983160 + 983090 = 983088 rarr 983160983090 + 983106983160 +

983106

983090

983090minus

983106

983090

983090+ 983090 = 983088 rarr

983160 + 983106

983090

983090minus 983106 983090

983092 + 983090 = 983088

ก minus983106983090

983092 + 983090 = 983088 rarr 983106983090 = 983096 rarr 983106 = 983096 983084 minus 983096

there4 983106 = 983096 minus 983096 + 983096 35 100

ก 983154983089983084 983154983090983084 983154983091983084 983154983092 983160983092 minus 983092983160983090 + 983090 = 983088

(983160 minus 983154983089)(983160 minus 983154983090)(983160 minus 983154983091)(983160 minus 983154983092) = 983160983092 minus 983092983160983090 + 983090

983160 = minus 983089

(minus983089 minus 983154983089)(minus983089 minus 983154983090)(minus983089 minus 983154983091)(minus983089 minus 983154983092) = (minus983089)983092 minus 983092(minus983089)983090 + 983090

(983089 + 983154983089)(983089 + 983154983090)(983089 + 983154983091)(983089 + 983154983092) = 983089 minus 983092 + 983090 = minus 983089

36 100983142 (983160) = 983160983092 + 983137983160983091 + 983138983160983090 + 983139983160 + 983140

983142 (983089) = 983089 + 983137 + 983138 + 983139 + 983140

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089

กก 983090983145983084 minus983090983145983084983090 + 983145983084 983090 minus 983145

983142 (983160) = (983160 minus 983090983145)(983160 + 983090983145)[983160 minus (983090 + 983145)][983160 minus (983090 minus 983145)]983142 (983089) = (983089 minus 983090983145)(983089 + 983090983145)(minus983089 minus 983145)(minus983089 + 983145) = (983093)(983090) = 983089983088

there4 983137 + 983138 + 983139 + 983140 = 983142 (983089) minus 983089 = 983089983088 minus 983089 = 983097

The Brain

17