: . .

: ", 3102 : 608530, 613

5

. : .

. : .

3 33 1

3 61 2 2#

3 33 1

3 61 2 2#

3 33 1

3 61 2 2#

" 001

. :

(1) . .

.

(2) ().

. :

(1) ; .

(2) . ,

.

, , .

.

(3) .

.

.

!/ /

- 2 - , ", ' 608530, 613

1

- 2 - , ", ' 608530, 613 +

! , , .

.

3 33 )1

(

3 61 ). 1-3 ( 2

! , .

1. I II . .

I II . %05 ,

51 I .2

. I II .

. 003 . 6 . I ?

2. na . n : - + + + + + - =2 n2 4 01 6 2 5n n n S]) ( ... [

. na .

. , 201 .

( ).

/ 3/

1.

()

( 1 )

"

x I : x11

.

x5 1

.

x15 1

y II: y11

.

y5 1

.

y15 1

I II :tt

11

T T11

/ 3/

- 3 - , ", ' 608530, 613

1.

x y t & = +1 ty tx .I yx

+ =

& = +: :5 1 5 1T y T x1 . . .II x y T) ( .

yx+ =5 1

51x T t .III 2

= -

I II III :x y) ( .

yxx yyx

51 5 1x2

= + - +

0

y. x ( !0 x): =5 1 x

= +1 6 6y x .I .

=5 1 xy. .II

I II : 51 = x

I 003 51 , 51 003

I : 02 =

/ 4/

- 4 - , ", ' 608530, 613

2

- 2 - , ", ' 608530, 613 +

! , , .

.

3 33 )1

(

3 61 ). 1-3 ( 2

! , .

1. I II . .

I II . %05 ,

51 I .2

. I II .

. 003 . 6 . I ?

2. na . n : - + + + + + - =2 n2 4 01 6 2 5n n n S]) ( ... [

. na .

. , 201 .

( ).

2 / 3/ . - + + + +2 4 01 6 2n) ( ...

n - = - + + - =:2 2 n2n n n n n n S5 3 ))1 (4 2 2( 5 4 2 , :

0

21 n : -- - - =2 1 n1 5 1 3n n S) ( ) (

- - =1 n n nS S a

0

- =n8 6n a

- =n8 6n a

$1-= - - =1 12 8 6 8 6n a= -= - =: :2 1 5 1 3 S, 1 = n :

0

- =n8 6n a n

/ 5/

- 5 - , ", ' 608530, 613

2.

1n201 a .

0

-1201 8 6n

0

3 81 n 1

1

0

81 = n 201:

1n0 a :

0

6 n 8

1

0

1 = n

-= - =12 8 6 a :

= + - = - = + + +: :2 1 81 81 3 2488 2 81 5 81 3 a S a a a... :

/ 6/

- 6 - , ", ' 608530, 613

- 3 - , ", ' 608530, 613 + 3

3. " " '

: ' '.

' .

.

'

.

2 .

. '

' . ' 5.0 .

. , ',

? .

. .

, ' ,

8.0 .

' .

/ 4/

3x = )' (P = )' (P , 5.0 = )' (P. :

(P+ )' +' +' (P+)' +' +' (P + )' +' +' (P =) 2

)' +' +' ( P +

0

(P ) 2

+ - + - + =: : : : : : : :5 0 5 0 1 5 0 1 5 0x x x x x x x x. . ) ( . ) ( .

0

(P x = ) 2

0

(P )' (P = ) 2

/ 7/

- 7 - , ", ' 608530, 613

3.

)' +' +' (P+)' +' +' (P + )' +' +' (P =( 2 /' (P. ) 2 (P

0

( 2 /' (P x. . . ) ( . =

+ - +2 : : : : :8 0 5 0 5 0 1 5 0x x x x x x

0

26 0 x.

": # 11 6 0x .

/ 8/

- 8 - , ", ' 608530, 613

4

- 4 - , ", ' 608530, 613 +

3 33 )1

(3 61 ).

4-6 ( 2 ! , .

4. . , .

. CBA L , M , K BC , AC BA .

P ,

L , M C ( ). MB = LA .

(1) =MCA B .

(2) MA = KA .

5. MLKA . MA . F

( ).

: 03 " = LM , a " = LF KLA 3

MLA. . AL

KLA . . a FK .

. +T TLFK MFA .

. : 5.24 " = FA , 2LMa . a .

/ 5/

B A

C

P

K

ML

A

M

L

K

F

4

2MB LA CB LB CA MA, ,1

21

. : = = =

": =CB CA

2:1 ,

,

MB PB LA PA

MB MP LA LP

32

32

31

31

= =

= =

Z

[

\

]]

]]

: MB = LA

: MP = LP , PB = PA

=B BLPB MPA

: T,T MPALPB ..

0

LB = MA

2CA MA1

2CB LB , =1

: =

0

CB = CA / 9/

B A

C

P

ML

- 9 - , ", ' 608530, 613

4.

.(1) I CB = CA ,

0

CL = CM M L

KC K CB 0

KC BBCA 0

PC LMC 0

PC TLMC 0

=CM MP o09

II CB = CA ,

0

CL = CM M L

MP = LP

PC 0

3,3 PMCPLC . . .

0

=B BPLC PMC .I

+= B Bo081 PLC PMC .II o081

I II : = Bo09 PMC

/ 01/

- 01 - , ", ' 608530, 613

4.

(2) (1): MB CA 0

CB = BA ,

(1): CB = CA

: BA = CA

2CA MA BA KA,1

21

: = =

: MA = KA

/ 11/

- 11 - , ", ' 608530, 613

5

- 4 - , ", ' 608530, 613 +

3 33 )1

(3 61 ).

4-6 ( 2 ! , .

4. . , .

. CBA L , M , K BC , AC BA .

P ,

L , M C ( ). MB = LA .

(1) =MCA B .

(2) MA = KA .

5. MLKA . MA . F

( ).

: 03 " = LM , a " = LF KLA 3

MLA. . AL

KLA . . a FK .

. +T TLFK MFA .

. : 5.24 " = FA , 2LMa . a .

/ 5/

B A

C

P

K

ML

A

M

L

K

F

5

. = Bo09 MLA

0

2LA S T=: : MLA03 1

3S S1

: T T=MLA KLA

0

2LA LA h03 ( h AL)1

31

21

=: : : : :

0

01 " = h

/ 21/

- 21 - , ", ' 608530, 613

5.

A

M

L

K01

03

aE F

.

=B BLKFE MF

= =B Bo09 FLM FEK

0

T+T MFLKFE ..

0

a EF03 01 =3a EF & =

3 01 3a a FK) ( KFE : + = + =2 2 2009 1

. =B BAFM KFL

=B BFMA FKL

0

+T TAFM KFL ..

MF FKa .I . :FA

=

3a FK .II :+ =2009 1

+ =2 203 a MF .III MFL :

5.24 " = FA .VI :

= + -20 009 5 721a a. I , II , III VI : 0

/ 31/5.7 " = a

- 31 - , ", ' 608530, 613

6- 5 - , ", ' 608530, 613 +

6. O CBA .

OA CB E .

OC BA F

( ).

: =a BCAB , =b BCBA .

FC .EA

. a b

FC , =bo06 .EA

21

. : =

2CB .1

BCA

,

,

3 33 )1

(

3 61 ). 7-9 ( 2

! , .

3 0x .7

3x x gnis) ( ) ( r # #r2

7. - =

. )x(g .

. )x(g

=x x fnis ) ( .

. A )x(g B )x(f

BA y .

(1) BA .

(2) BA ? ./ 6/

A

C

B

F

E

O

6

B B2 EAB EAC a

. = =

2 09 FCB FCA B Bo

b a- = =

+

nis nis) ( ) ( EAC :EA AC

2a

+b a b=

+) ( &

) (nis

AC EAnis

2a

b

b a=

+

+

AFC:nis nis) (

AC FC2 09

bb a ao=

- ++

& nis) (

AC FCnis2 09

o

aa b

=+

-

) ( :) ( ) (

nisnis

nissoc

FCEA

2

2a:

b

b aa

a b

=+

+-

/ 41/

316 ,035806 ' ," , - 14 -

.6

: . ( )( 60 ) (30 )sin sin

sin cos21

2 602

o

o o

:

:

aa

aa

=+

+ -

0

( )( 60 ) (30 )cos sin

sin cos21

30 22

o

o o

:

:

aa

aa

=-

+ - : ( )sin cos2 60 90 2 60o o o

a a+ = - +a k9 C

0

( )sin

sin21 60o

aa

=+

0

)60+(asin o

: sin sin cos cos sin2 60 2 60o oa a a= +

0

cos 0a= & 90oa=

0

ABC BC

0

BC21

=

/15 /

- 51 - , ", ' 608530, 613

7

- 5 - , ", ' 608530, 613 +

6. O CBA .

OA CB E .

OC BA F

( ).

: =a BCAB , =b BCBA .

FC .EA

. a b

FC , =bo06 .EA

21

. : =

2CB .1

BCA

,

,

3 33 )1

(

3 61 ). 7-9 ( 2

! , .

3 0x .7

3x x gnis) ( ) ( r # #r2

7. - =

. )x(g .

. )x(g

=x x fnis ) ( .

. A )x(g B )x(f

BA y .

(1) BA .

(2) BA ? ./ 6/

A

C

B

F

E

O

7

2 0 g) ( & 0 = x . y:3

2 0) , ( & =3

3k x & 0 = )x(g x:r2

(k ) = -r

0

3k x r2

- =r

0

3x x, 2

3r r5

= =

0

3) , ( , ) , ( 3 0 2

r r0 5

/ 61/

- 61 - , ", ' 608530, 613

7.

3x xnis nis) ( . r2= -

0

0 3 3 xsoc nis) (r r

: = -

0 3 x nis) ( r

3k x & = -r

+ =r

0

3 3x x x, , 4

3r r r7

= = =

0

2 3) , ( , ) , ( , ) , ( :3

34

23

37

2r r r3

-

- = =x g x f x d BA) ( ) ( ) ( . (1)

3 3x :4

# #r r

3x x x x d BAnis nis nis) ( ) ( ) ( 2

3r r

- = - - = =

3 dx xsoc ') ( ) ( r

- =

0 3 x soc) ( & = dx '0 ) ( r

6k x & = -r5

6 x & + =rr5

=

3 x x dnis '') ( ) ( :

r6 d''0 ) ( & - -=

51 3

r r-

# #3 0x :r

7

3x4

# #3r r

3x x x x d BAnis nis nis) ( ) ( ) ( 2

3r r

- = - - = =

3 dx xsoc ') ( ) ( r

-- =

6 x & = dx '0 ) ( r11

=

6 3 3d x x dnis'' ''0 ) ( ) ( ) ( :11

1 &r r r

- - -=

6d d) ( ) ( BA:5

6= =r r1 11

2 BA , =0 BA . ) ( =0 x =11 3

6 x .r11

6 x =r5

(2) (1), , =

/ 71/

- 71 - , ", ' 608530, 613

8- 6 - , ", ' 608530, 613 +

8. : + + =24b x x x f) ( + - =2c x x g) (

b c 0. P .

. b ( ) P . . )x(f

)x(g , 24 b .

a = x D , )x(f A )x(g B (D , A B ).

. DP BAP . . )x(f ,

=a x - =a x , S . S )x(f , )x(g

=a x - =a x .

/ 7/

8

.

)x('g = )x('f P , : 0

-= +2 4 2x x

0 -=1 x x P:

- = -3 1b f) ( y P:

- -3 1b P) , ( :

/ 81/

- 81 - , ", ' 608530, 613

8.

x

. y

( )x(f - -4 2b) , ( y . )x(g 0 = x . x -1 .)

= - = -g f'2 )1 ( )1 ( ' . - -3 1b P) , ( :- + =1 2b x y P:

0

- + =D1 2b a y y D:

+ + = =2 A4b a a a f y) ( y A:

- = -1 1g f) ( ) (

0 - =2 b c c:

0

- + -= =2 B2 b a a g y) ( y B :

D A1 2a a y y DA + + = - =2

B D1 2a a y y BD + + = - =2

0

DB = DA DP BAP .

1 2 1 2xd x x xd b x x f S) ( ]) ( ) ( [ .I . a

a

a

a+ + = - + - =2

--

##

1 2 2xd x x xd x g x f) ( ]) ( ) ( [ S .II :a

a

a

a2

+ + = - =:

--

##

=:S 2 S I II :

/ 91/

- 91 - , ", ' 608530, 613

- 7 - , ", ' 608530, 613 + 9

!

9. + + - =2 8c xb xa x f) ( -# #2 2x .

a , b c , 20 c. . a b .

a b , -. . )x(f =2 x ,

- =2 x .

2 .2 94

x c .

. -# #2 2x )x(g : - =x f x g) ( ) ( . )x(g =2 x ,

- =2 x .

)x(f )x(g ? .

9.

: + -$20 8xb xa -# #2 2x

= + -: :2 b a0 2 2 8 .I :

= + +: :20 2 2 8b a .II

I II : -=2 b , 0 = a

/ 02/

- 02 - , ", ' 608530, 613

9.

+ - =2 2 8c x x f) ( .

0

x f) ( ' x

x

2 82

- =2

-

0

= -2 2 f) ( ' , -=2 2 f) ( ' :

+ = = -2 2 2c f f) ( ) ( y :

+ + -=4 2c x y +2 2c A) , ( :

c x A x:2

4=

+

+ + =4 2c x y + -2 2c B) , ( :

c x B x :2

4-=

+

C )c + 4 , 0( ( ) :

CBA 20 c 2BA y S ( ) :

1=:C

0

2c c c S) ( 4 1

24

24

+ =::+

+m c+

0

) (

,

cc

24

20 2 94

22

+=

0

3 = c

/ 12/

y

BOAx

C

- 12 - , ", ' 608530, 613

9.

-=x f x g) ( ) ( .

0

-=fx x g' ') ( ) ( 0

=2 2 g') (

-= -2 2 g') (

)x(g =2 x )x(f -=x2 , )x(g -=2 x )x(f =2 x ,

.

A B ( ). A , B C , , AC = BC , .