**************************************

2 3 4-1-2-3-4

2

-1

-2

-3

0 1

1

x

y

2 3 4-1-2-3-4

2

-1

-2

-3

0 1

1

x

y

1028-1029

f '(C )

**************************************

****************

80028002

08

****************

1028-1029

9109

0

f

1 x² 5x 2

f (x)x² 4

2;2 2

x² 4x 3f (x)

(x 2)²

2

3 4x 8

f (x)x² 4x 5

1;5 4

1f (x) x 1

1 x

1

5x

f (x)x 1

;0 2, 6 x

f (x) 1x² 1

1 1,

13x 1

x² 3x 2lim

x 1

2

2

xlim (x x 1)

3x 2

x 1 1lim

x 2

5

xlim ( x² 4x 3 2x)

f1 f

(C )

5211x

0f'(x)

1

2

2019

f (x)

1ff

C

2f

3f (x) 0f (x)

4g1

g(x)f (x)

g

g

10

19

13

0 0

9109

9

x

y Cf

1

D ffD

C

C

f(x)

2gg(x) f (x)

g 1;

g1

g(0)g

ا3f

C

R(x) f ( x) H(x) f (x) K(x) f (x 1) 1 T(x) f ( x )P(x) f (x)

f 1;2x sin x

f (x)x 1

2x 1 2x 1

f (x)x 1 x 1

x 1;

xlim f (x)

x 0

sin xlim 1

x

x 0

f (x)lim 1

x

x 1

lim f (x)

f

1x 32x 3x2x

2

xlim( x 3x 4x)

2x 029x x 1 3x

2

xlim( 9x x 1 2x)

14

15

16

9109

3

f2f (x) x 5 f

C

12

x 2

x 5 3lim

x 2

2f

3f (x) 2x 1;2

f

f x ; x 1

f x ; x 1

x² 1

11

x

1f1f

2xlim f (x)

f*

2x² 3f (x) : x 2

x

f (x) x² 2x : x 2

f2

f ;2 2;

320x

0

2

4

1

f(x)

(C)

1f1

fx

1f (x)

2 2 ;3

2g31

g(x) ;x 2f (x)

g(2) 0

17

18

19

01

9109

4

g2

g3g

If3f (x) 2x 3x² 1

1f

2f

3f (x) 0 1;2110

4xf (x)

IIg4 31g(x) x x x

2

1xg'(x) f (x)g

21

g( ) ( ² 3)4

g( )

3g(x) 0

If

1f (x) 1

2f (x) 3

3]0; 4]f[0 ; [

g(C )g

13g(x) ax bx c

1g(0)g(1)g '(1)

abc

2g

33x 3x 4 0

2;2,25 g(x)

00

09

03

2 3 4-1

2

3

4

-1

-2

-3

-4

-5

-6

0 1

1

x

y

9109

5

Ig3g(x) 2x 4x² 7x 4

1xlim g(x)x

lim g(x)

g

2g(x) 00,7 0,8

xg(x)

IIf3x 2x 1

f (x)2x² 2x 1

f(C ) O, i , j

1xlim f (x)x

lim f (x)

2x1 1 3x

f (x) (x 1)2 2(2x² 2x 1)

f(C )( )

f(C )( )

3xx.g(x)

f '(x)(2x² 2x 1)²

f 'f

f '(x)xff ( ) 0,1

4f (1)f (x) 0

5( )f

(C )

6h3x 4x² 2x 1

h(x)2x² 2x 1

h(C )

xh(x) f (x) 2

h(C )

f(C )

h(C )

If I ; 1 1;0 4

f (x) xx 1

059119

049104

9109

6

2-1-2-3-4-5-6-7

2

3

4

5

6

7

-1

-2

-3

-4

-5

0 1

1

x

y

2-1

2

3

-1

-2

0 1

1

x

y

f(C )(O ;i ; j )

1fI

f

2g 0;4

g(x) xx 1

g(C )

g

g(C )( )

g

IIk 1 4

k(x) xx 1

1h 0

k(h) k(0)lim

h

h 0

k(h) k(0)lim

h

21

( )2

( )

0x 0

31

( )2

( )k

(C )

C)g

I 1; 3g(x) x 3x² 3x 1

1g

g(0)g(0,5)

0;0,5g( ) 0

g(x)I

2f 1;

3x 3x² 3x 2f (x)

(x 1)²

( )

x I3

g(x)f '(x)

(x 1)

x

f (x) f ( )lim

x

x 1

lim f x

xlim[f x (x 1)]

f

30,26 f ( )10-2

( )

069118

9109

7

Ig3g(x) x 6x 12

1g

2g(x) 0 1,48; 1,47

xg(x)

IIf3x 6

f (x)x² 2

f(C ) O, i , j

1xlim f (x)x

lim f (x)

xx.g(x)

f '(x)(x² 2)²

f

2( )y xf

(C ).

f

(C )( )

33

f ( )2

f ( )

4( )f(C )

f 1; 2

f (x) xx 1

f(C )f

1f

2f(C )(D)y x

f(C )(D)

3f(C )0

x0

1,3 x 1,4

( )f(C )f(C )

( )f(C )

4 g 1; g(x) f (x)g(C )g

g(C )f(C )

m2g(x) m

079107

089119

9109

8

f1

f (x) x 1x² 1

f

(C )

(O ;i ; j )

1f

2x2

1f '(x) 1

(x 1) x² 1

3f

4(T)f

(C )0

5f

(C )(T)f

(C )

6(D)y=x+1f

(C )

(D')

7(D)(D')f

(C )

8 g1

g(x) x 1x² 1

g

f(C )

g(C )

099101

9109

9

1f 1 1

f (x) 2x 3(x 1)²

C(O ;i ; j )

x 1 3

2(x 2)(x² x 1)f '(x)

(x 1)

f

C

C0

3 1x ;

8 4

C0

C

2mCm

x32x (7 m)x² 2(4 m)x 2 m 0

f 1 3x 2x²

f (x)(x 1)²

f(C )(O ;i ; j )

1،، x 1

f (x) x(x 1) (x 1)²

2f

3f(C )

f(C )

f(C )

4 f(C )1

5f(C )

910997

900997

9109

01

f2

x 2f (x) x

x 1

f

(C )

(O ;i ; j )

1xlim f (x)x

lim f (x)

2f2

2 2

x(x 1)(x x 4)f '(x)

(x 1)

3f

4(D) : y x f

(C )f

(C )(D)

5f

(C )1f ( 1.25)

6(D)f

(C )

7gg

(C )g

(C )f

(C )

1

1v g(x)

g(C )

f 2ax² bx c

f (x)x 2

f(C )

1abcf(C )y x 3

3

2f

3f(C )1

(D )2

(D )3

1M

2M

1(D )

2(D )

41

(D )2

(D )f(C )

5mf (x) 3x m 0

6 f 2;2 g(x) f ( x )

g0

g(C )gf(C )g(C )

99

93

9109

00

I g3g(x) x 3x 3 g

(C )

1 g

2g(x) 0 2,1;2,2g(x)

3xg( x) g(x)

IIf 1; 1 3

2

2x 3f (x)

x 1

f

(C )

1x 1; 1 2 2

2x.g(x)f (x)

(x 1)

2 f

3f ( ) 3 f ( )

4( )y 2xf

(C )

f(C )( )

5f

(C )( )

6f

(C )

7m3 22x mx m 3 0

IIIh 1; 1

3

2

2 x 3h(x)

x 1

1h

2h

(C )f

(C )

f 1;1 2

xf x | x 1|

x 1

fC

(O,i, j)

1

f x

2 f ' x

f

3( ) : y x 1 ( ) : y x 1 fC

94

95

9109

09

fC( )( )

fC

0,5;1 2; 1,5

fC

4 mDy mx 1 m

m mD

m2

x| x 1| mx 1

x 1

f 2

xf (x) 1

x 1

f(C ) O, i, j1cmi =2cmj =

1 xlimf (x) 2

xlimf (x) 0

2x2 2

1f (x)

(x 1) x 1

3f

4xf ( x) f (x)

5 f(C )0

6f(C )

f (x) yx

f(C )

7 f(C )

8m2

xmx

x 1

96

9109

03

I)g 1; 3g(x) ax 3x b

g(C )

1abg(C )y 6 1

2g g

33x 3x 4 0 2;2,25g(x)

IIf 1;1 1, x²(x 2)

f (x)x² 1

f

(C )

1f

2f 1;1 1, f '(x)

2

x.g(x)f '(x)

(x² 1)

f

323 10 8

f ( )2 4

f ( )

5xlim(f (x) (x 2))

f

(C )( )

6f

(C )( )

7( )f

(C )

I gCg

3g(x) x 3x 3

1

g( 1)g(1)g (0)g''(0)

g

2g(x) 0

2,2; 2,1 g(x)

IIf4 21f (x) ( x 6x 12x)

8

1x1

f (x) .g(x)2

f

223f ( ) ( 3 )

8 f ( )

2-1-2

2

3

4

5

-1

0 1

1

x

y

97

98

9109

04

2 3 4 5 6-1-2-3-4-5-6

2

3

4

5

6

-1

-2

-3

-4

-5

-6

0 1

1

x

y

IIIk4 21k(x) ( x 6x 12 x )

8

k(C )

1k

2k

3k0

اf

Cf

D 1;1 3 2

2

x x 1f x

x 1

1

(D)

2

3x(D)f (x)

f

4x(D)

f ( x) f (x)

ا5f

C

f

012x

00f'(x)

0

2

f(x)

f(x)c

f (x) ax bx 1

abc

1f '(x)

2f

a bc

99

31

9109

05

x 1

lim f (x)x 1

lim f (x)

1

2

3

4f

3a b c 1 )C( f

(O ;i ; j )

x( )( ))C( f( )y x 1

)C( f( )

( 1;0) )C( f

)C( f)C( f

Ig 3R 3x

1bax)x(g

abC

1ab

CA(2 ;1)

2)ba3;3(I C

IIf 3R 3x

7x5x)x(f

2

)C( f(O ;i ; j )

1x 3R f(x) = g(x)

2f

3 )2x()x(flimx

4)C( f)(

5)()C( f

6)C( f3

7)C( fmf(x)=3x+m

2

30

39

9109

06

2 3 4 5 6 7-1-2-3-4-5-6-7-8

2

3

4

5

6

7

8

9

-1

-2

-3

-4

-5

-6

0 1

1

x

y

( c )

0

g

x0 g(x) 1

g(x)x

9 f 2; f (x) g(x²)

f ( 2) xlimf (x)

f 2;

f ; 1 1; f (x) x x² 1

(C)(O;i; j)

1ff

2 xlim f (x) 2x 0

3f 1

4f 1; ; 1

5(C)2y 51 2

6(C)

33