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 =

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- ..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 >

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- ..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 >

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- ..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 ()

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- ..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

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- ..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

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- ..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

=

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- ..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

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- ..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

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- ..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

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- ..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

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- ..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

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- ..45/1-5

b 23 1 , 0

( )1 , 0

x x bf x

x + =

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- ..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

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- ..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

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- ..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

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- ..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

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- ..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

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- ..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

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- ..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

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- ..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

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- ..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

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- ..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

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- ..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