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www.TewLek.com 1
.6
A-Net .. 51 2 9
f 2
3
; 0( )
1 ; 0ax b x
f xx x
+ = +
www.TewLek.com 2
A-Net .. 50 2 5
21
1 1lim1 2 3x x x x +
1 - ..48/2-16
1( )0
f x =
.
0lim( )( ) 0x
fof x = . 0lim( )( ) 1x fof x+ = 1. 2. 3. 4.
1
0x 0x >
www.TewLek.com 3
- ..46/2-17 2 2
30
1lim [ 1 1 (1 )(1 ) (1 )(1 ]x
x x x x x xx
+ + +
1. 0 2. 14
3. 12
4. 1
3 - ..46/2-18 f g 4x =
2
4( )( ) 2
4
xf xg x x
kx
=
k f 1y x= + 4x = k 1. ( 3, 1) 2. ( 2, 0) 3. ( 1, 1) 4. (0, 2)
2
4x 4x =
www.TewLek.com 4
- ..45/2-20 0a >
2( )1
xxf xxx
+= +
2( )g x x= 11lim ( )( ) lim ( )( )
( 2)x a x afog x gof x
a a+ = +
a 1. 1 2. 3 3. 5 4. 9
2 - ..45/2-20
2
( 4)( 2)2
1( )
x x ax
f x
x b
+ =
,a b
f 4x = 16bf a +
1. 16 2. 14 3. 14 4. 16
2
x a<
x a
4x >
4x =
4x <
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- ..44/2-19
1
( ) 12
f x x=
3( ) 2g x x x= + ( ) ( ) ( )h x f x g x= 1. h 1x =
1lim ( ) 0x
h x = 2. h 1x = 1lim ( ) 4x h x = 3. h 1x =
1lim ( ) 0x
h x = 3. h 1x = 1lim ( ) 4x h x = 4
- ..44/1-4
2
1
3 2lim1x
xx+
0.5
1x 1x =
www.TewLek.com 6
- ..43/1-22 3 2( ) 4 1f x ax x= + a
( )( ) ( )
0
f xg x f x
=
( )g x 1 a
1. 0 2. 52
3. 83
4. 3
2 - ..43/3-26
2
( ) 10
xf x x
=
20 1
( 1)lim ( ) lim2x x
f xf xx +
+ +
1. 43
2. 1 3. 0 4. 13
1
1x > 1x < 1x =
0 1x< 0x
1x >
www.TewLek.com 7
- ..42/2-18 f
3 2
2
4 4( )4
x x xf xx
+= 2x (2) , ( 2)f a f b= = a b 1. 1, 3a b= = 2. 1, 3a b= = 3. 1, 3a b= = 3. 1, 3a b= =
4 - ..42/2-16
2
32
2 1( )2( 1)
11
x xf xx
xx
+ = +
. f 1x = . f 1x = 1. . . 2. . . 3. . . 4. . .
1
1x
1 1x <
1x >
www.TewLek.com 8
- ..41/2-15
13 1
( ) 1
2 51
xf x
xx
+=
.
1 1lim ( ) lim ( )x x
f x f x + = . f 1x = 1. 2. 3. 4.
2 A-Net .. 51 1 19
f (0, ) (2) 2 (1)f f= 21( ) 27f x x x = L ( )y f x= ( )1, (1)f L 1) (2, 64) 2) (2, 66) 3) (3, 94) 4) (3, 96)
2
0 1x< < 1x = 1x >
www.TewLek.com 9
A-Net .. 51 1 20 f [ 2, 2] (0) 1, (1) 0f f= = f 1x = 1x = . ( 2) ( )f f x [ 2, 2]x . (2) ( )f f x [ 2, 2]x 1) . . 2) . . 3) . . 4) . .
1 A-Net .. 51 2 10
33 ; 1
( )2 ; 1x x
f xx x+ < =
f [ 4, 0] 3
www.TewLek.com 10
A-Net .. 50 1 21
( ) 1 af xx
= + 2( )g x x b= + 1(0)2
fog = ( 1) 2f =
( )f a bg
+
1. 13
2. 14
3. 14
4. 13
4 A-Net .. 50 1 22 3 22 2y x x x= + X 0x = 4x = 1. 16 2. 16.25 3. 16.5 4. 17
37.3 ()
www.TewLek.com 11
- ..48/2-4
. f g
0 0
( ) ( ) ( ) ( )lim lim ( )h h
f x h f x f x h f x g xh h+
+ + = = ( ) ( )g x f x= . f ( ) 0f x > x ( ) 0f a 1
( )y
f x= a 1
( )f a 1. 2. 3. 4.
2 - ..48/2-17 ( )y f x= ( , )x y 2 4x f 10 ( )y f x= X 0x = 3x = 1. 33 2. 36 3. 39 4. 42
1
www.TewLek.com 12
- ..47/2-5 ( )f x ( )g x
1( ( ))( )
f g xg x
= ( (0)) 5f g = ( (2))f g 1. 1 2. 3 3. 5 4. 7
4 - ..47/2-17 ( )y f x= 3 2x = 3 7 0x y+ = (1, 4) 2( ) ( )g x x f x=
2
1
( )g x dx 1. 5 2. 7 3. 8 4. 10
2
www.TewLek.com 13
- ..47/1-7
( ) 3 1f x x= + 2( ) ( ) 3 1fog x x = + (0) 1g = 1
0
( )g x dx 1.25
- ..47/2-18
1
( )1
f x x=
. fog 0x = . 1 1
2 2f g =
1. 2. 3. 4.
1
0x 0x =
1( )1
g xx
=
www.TewLek.com 14
- ..47/2-19
4 3 21 2 1 1( ) 24 3 2 3
f x x x x x= + f ( , ( ))c f c 0c > a f X b 1. 1, 2a b= = 2. 1, 4a b= = 3. 2, 2a b= = 4. 2, 4a b= =
3 - ..47/2-20 f 3( ) 1h x x= + a ( )( ) 9, ( ) ( ) 0hof a hof a= = ( ) ( ) 1hof a = 1. f a 1 2. f a 2 3. f a 1 4. f a 2
2
www.TewLek.com 15
- ..47/2-21 f (0) 1 (1)f f= = (0) 1f =
1
1
( ) 6f x dx
= ( 1)f 1. 7 2. 1 3. 13 4. 15
3 - ..46/2-20 g ( ) ( )f x x g x= 3 2( ) 4 9f x x x = + (0) 0f = ( )
( 1)d f xdx g x
+ 2x =
1. 4 2. 2 3. 2 4. 4 1
www.TewLek.com 16
- ..46/2-21 ,a b
3 2( ) 1f x x ax bx= + + + (1) 15f =
1
0
55( )12
f x dx = (1)f 1. 9 2. 10 3. 11 4. 12
2 - ..46/2-22 2( ) 1f x x=
. 1
1
4( )3
f x dx
= . ( )y f x= 1x = 1x = 4
3
1. 2. 3. 4.
3
www.TewLek.com 17
- ..46/2-19
f ( ) 2 1f x x = + f 12
1x = f
1. 1 2. 13
3. 0 4. 13
4 - ..46/2-20 50 51 2 52 4 53 6 90 100 1. 16,000 2. 16, 200 3. 16, 400 4. 16,600
1
www.TewLek.com 18
- ..46/2-21
( )y f x= ( , )x y 2 3 2x x + 2
0
( ) 4f x dx = ( , )x y ( )y f x= 1. 40,
3 2.
40,3
3. 131,4
4. 131,4
1
- ..46/2-22 A XY 2 7y x= X 0x = x a= a A X A X 2a a 1. 2 3 2. 3 3 3. 5 4. 7
2
www.TewLek.com 19
- ..45/1-5
b 23 1 , 0
( )1 , 0
x x bf x
x + =
www.TewLek.com 20
- ..45/2-22 2( ) 2f x x x= 2( ) 1g x x= + ( ) ( 3) ( ) (3)gof fog + 1. 132 2. 84 3. 84 4. 132
3 - ..45/2-23 ( )f x ax = a 2 6 0x y+ = f (1, 4) (0) 8f =
1
0
( )f x dx 1. 22
4 2. 23
4 3. 42
4 4. 43
4
2
www.TewLek.com 21
- ..45/1-5 a
2 2 4 10y a x ax= + + 0x = 1x =
7 - ..45/2-21 ( ) 3 1f x x= + g 2( )( ) 1fog x x= + x R (1) (1)f g +
1. 4112
2. 3512
3. 334
4. 394
1
www.TewLek.com 22
- ..45/2-22 2( ) ( )g x x f x= ( ) 2 3f x x = + (1) 0g = (4)f 1. 0 2. 11 3. 13 4. 28
3 - ..45/2-23 ( )y f x= X ( , )x y 6 2x b+ b 0x =
2x = 0x = 1x = f x 1. 2x = 2. 1x = 3. 0x = 4. 1x =
2
www.TewLek.com 23
- ..44/1-6 x a= 2y x= 0x = 8x = 3a
128 - ..44/2-20 g 0x > (3) 3g = n
3 2( 2 ) 4 6 31ng x x x x+ = + + 1. 5 2. 6 3. 7 4. 8
2
www.TewLek.com 24
- ..44/2-21 f (0) 2f = f 1x = 1x = (4)f 1. 28 2. 24 3. 24 4. 28
4 - ..44/2-22
( )y f x= (1, 0) ( , )x y 2 223 4x x x + ( , )a b 2 0x = a b+ 1. 3
2 2. 2 3. 7
2 4. 4
4
www.TewLek.com 25
- ..44/2-21 3( )f x ax bx= + a b f 2
1x = 3( ) ( )g x x f x= + g 1. (0, 2) 2. ( 3, 1) 3. ( 1, 1) 4. ( 2, 0)
4 - ..44/2-22 3 2( ) 2 2f x ax bx x= + + ,a b (1) 5f = (0) 12f = ( ( ) ( ))f x f x dx + 1. 3 25 9 10x x x c+ + 2. 3 25 9 10x x x c+ + + 3. 3 25 9 10x x x c + + 4. 3 25 9 10x x x c +
1
www.TewLek.com 26
- ..44/2-23
f f [0, 1] 4( )( )
1f xg xx
= +
(1) (1) 1f f = = (0) (0) 2f f = = 1
0
( )g x dx 1. 5
2 2. 1
2 3. 3
2 4. 7
2
3 - ..43/1-23 ( )y f x= (0, 1) (4, )c c ( , )x y 1x c 1. 4
3 2. 7
3 3. 8 4. 9
2
www.TewLek.com 27
- ..43/2-5 2( )f x x c= c 4c ( )y f x=
2x = 1x = 24 c 9
- ..43/2-19 3 2( ) 9f x x cx x= + c f 1 f 1. ( 3, 1) 2. ( , 3) (1, ) 3. ( 1, 4) 4. ( , 1) (4, )
1
www.TewLek.com 28
- ..43/2-20 F f 2( ) 3 6 3f x x x= + (0) 1F = F [0, 2] x c= ( )F c 1. 1 2. 0 3. 1 4. 2
3 - ..43/2-21 f ( ) ( 1) ( )g x x f x= + 2( )g x dx x x c= + (1)f 1. 3
4 2. 5
4 3. 3
2 4. 5
2
1
www.TewLek.com 29
- ..42/1-5 u v x 2( ) 2v x x x= ( )( )
( )u xf xv x
= (3) 9, (3) 3u u= = (3)f 5
- ..42/2-19 f (0, 2) 2( ) 3 12 9f x x x = + f 1. 2 2. 3 3. 6 4. 8
3
www.TewLek.com 30
- ..42/3-25 ( ) ( ( ))F x f g x= 3( ) 2 2g x x x= + + 3( ) 5 2F x dx x x c= + + (5)f 1. 6 2. 5 3. 4 4. 3
1 - ..42/1-6
f (3) 2, (3) 5f f = = 2( )( ) 1f xg xx
= + (3)g
0.62
www.TewLek.com 31
- ..42/2-17 , , ,a b c d 3 2( )f x ax bx cx d= + + + f 2 1x = (1) 4f = (0) 1f = f 1. 3x = 2. 1
3x = 3. 1
3x = 4. 3x =
2 - ..41/2-16 f 3( ) ( ( )) 15F x f x= + (1) (1) 4F f = = (1)F 1. 1
2 2. 3
2 3. 8 4. 24
2
www.TewLek.com 32
- ..41/2-17 2 3 2y x x= + 0x = 2x = x
1. 32
2. 16
3. 23
4. 56
4 - ..41/2-18 f (2) 1, (1) 3f f = = ( ) 3f x = x (0)f 1. 5 2. 6 3. 12 4. 15
1