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A

2-2

2-2

.

1.

f(x

x)

x

xx

yf(x)

lim

x

0

0

0

yf(x)xx

f

0

f(x

x)f(x)

0

x

f(x)=lim

x

0

0

0

2.

P

P

PT

.

,

n

P

P

xx

0

yf(x)

f(xn)f(x0)

xx

k

n

n

n

0

f(x)f(x)

k

klim

f(x)

0

n

0

xx

x

0

n

0

f(x)

f(x)

3.

x

x

y,

f(xx)f(x)

x

0

f(x)lim

x

.

:

f(x)c(c

f(x)sinx,

f(x)ax,

)

f(x)0

2

4

f(x)x

,

1

3

f(x)cosx

f(x)cosx,

f(x)ex,

f(x)axlna

5

6

A

2-2

(2)

(1)

f(x)

f(x)0

.

yf(x)

2.

.

x

0

:1

f(x)0,

yf(x)

f

x

2

2

;

f(x)0,

f(x)0,

f(x)

0

0

4.

()

yf(x)

1

yf

[a,b]

yf(x)

.

f(b)

f(a)

,

,

,

(

),

,

.

:

(1)

;

(2)

(3)

,

(

,

,

,

.

,

(4)

,

,

.

(

)

,

.

1.

2.

.

n

:A.

n=1

B.

n=k

0

A

2-2

(6)

1.

zabi,zcdi(a,b,c,dR)

1

2

zz(acbd)(ad

1zz(ac)(bd)i

2

1

2

1

2

z(acbd)(adbc)i(z0)

1

z

c2d2

2

2

2,

|zz||zz|2(|z||z|2)

zz|z|2|z|2

(1)

(2)

2

2

2

1

2

1

2

1

2

|z|2z2

3.

zmznzmn;(2)(zm)nzmn;(3)(zz)nzzn(m,nR)

n

(1)

4.

1

2

1

2

i

i21

i3i

i41

inin2in3i

1

2

3

2

x(

)

1

xx0

A

B

C

D

[

]D

[

]x

0

D.

x0

x

2

yf(x)

x)

xx0

Af(x0

Cf(x0)x

Bf(x0)x

Df(x0

x)f(x0)

A

2-2

f(x)x2

4

ABx1x1.3

AB

4

A2

C2.09

B2.3

D2.1

[

[

]B

]f(1)5f(1.3)5.69.

f(1.3)f(1)5.695

kAB

2.3

B.

1.31

f(x)

0.3

2

x

2x

f(x)22x

5

A2x

C2x

B

2x

2x

D(x)2

[

[

]B

]

22

(2x)

220

2

2(2x)

f(2)

f(2x)

2x(x)

2

f(2x)f(2)

2x2

2x

B.

yx2

1

(1,2)

(1x,2

6

A2

B2x

C2x

D2(x)2

[

[

]C

yf(1x)f(1)

]

x

x

[(1x)2

x

1]2

2x.

C.

S(t)t2

3

33.3

7

A

2-2

C

[

D

]B

1

[

]x0.3

k22x2.3

yxx1

yx

k1

3

x1

1

k3

1

x

10

.k3

y

x1

k4

k2k1

1x13

9

s

t

s

[t0t0

t]

(

)

t

t)s(t0)

Av0

B.s(t0

D.s(t)t

C.s(t0

t)s(t0)

t

[

[

]C

]

C

C.

1

2

yx

4

1

4

P1

Q

10

Q

(

)

1

1

4

A.1x(x)2

4

B.

D.

x

(x)2

1

1

4

C.1x(x1)2

4

x

(1x)2

[

[

]C

]

Q

1x

f(1x)

y

x

yx3

2

x2

________.

11

A

2-2

1

1

2

y2x

1

42x

2

9

[

]

.

x

x

1

x

2

_____

13

[

yxx1

]62

y1x1

]

1

1x1

A(2,3)B(2x,3y)

62.

[

x

x

yx2

1

x

14

________

x0.1

AB

________

[

[

]54.1

]

x1

AB

1221

22

y(2x)2

x

(21)

1

2

5.

k

1

x

x0.1

AB

y(20.1)2

12

2

1

4.1.

k

2

x

0.1

15

f(x)2x1g(x)

2x

[3

g(x)

[

]

f(x)[31]

f(1)f(3)[2(1)1][2(3)1]

2.

1(3)

2

f(x)[0,5]

f(5)f(0)

50

2.

A

2-2

2

2

(1x)2

2(x2)

72

25

.

x

(1x)2

yx2

x2

x123

17

[

]

f(1x)f(1)(1x)2

1

2x

4x

6x.

k1

k2

k3

x

x

x2

f(2x)f(2)(2x)2

2

2

x

x

x3

2

32

f(3x)f(3)(3x)

x

x

x

k1k2k3

x3

18

8m

y

1.6m

x

84m/min

C

(1)

(2)

[

10s

](1)

C

B

xmAB

ym

CDBE

ABBE

ACCD

y1.6

yx8

1

4

yf(x)

x.

(2)84m/min1.4m/s[0,10]

A

2-2

A

2-2

1

A

B

C

D

[

(

)

]C

]

y

x

[

f(x0)

x

0

s3t2

t03

2

A

A6

B18

D81

C54

[

[

]B

]

s(t)3t2

t03

t)s(t0)3(3t)233

s

ss(t0

2

18t3(t)

2

183t.

t

s

t

t0

18

B.

3yx2

x1

(

)

A2x

B2

D1

C2x

[

[

]B

f(x)x2

x1

f(1)(1x)

]

yf(1x)

2

2

12x(x)

2

A

2-2

s4(5t)2

345

t

2

3

404t

[

]

t

s

t

s(5)lim

t0

lim

(404t)40.

t0

D.

5

yf(x)

x)f(x0)

(

)

Ayf(x0

yf(x0

x)f(x0)

x

x0x0

x

B.

x

y

Cf(x)x0

Df(x)x0

f(x0)

[

]C

]

[

C

C.

y|xx0

(

)

6

f(x)xx0

x)f(x0)

Af(x0)f(x0

Bf(x0)lim[f(x0

x)f(x0)]

x0

f(x0

x)f(x0)

x

Cf(x0)

f(x0

x)f(x0)

x

Df(x0)lim

x0

[

]D

]

[

D

D.

yax2

bxc(a0abc

B2ab

D4ab

)x2

7

A4a

Cb

[

]D

ya(2x)2

b(2x)c4a2bc

A

2-2

A0

B3

C

[

2

D32t

]B

s3(0t)(0t)2

3t

[

]

t

t

s

t

s(0)lim

t0

3.

B.

1

x

f(x)f(a)

xa

lim

xa

(

)

10

A

f(x)

1

a

2

a

B.

1

a2

D.a12

C

[

]C

11

f(x)f(a)

xa

xa

xa

lim

xa

[

]lim

xa

ax

(xa)xa

1

axa

1

lim

xa

lim

xa

2.

11

11

yf(x)xx0

f(x0

x)f(x0)

x

________

lim

x

0

f(x)f(x)0

________.

lixmx0

x)

2(x0

11

2

[

[

]

11

f(x0

x)f(x0)

]lim

A

2-2

1

(x)2

x1

x

x1x1

y

x

x1

lim

x0

0.

xx1.y|x1

13

[

f(x)ax4

f(2)2

a

______

]2

]

ya(2x)42a4

a

[

x

x

y

x

f(1)lim

x0

a.a2.

f(x)f(x0)

f(x0)lixmx0

xx0

f(3)2f(3)

2

14

________

[

]8

2x3f(x)

x3

2x3f(x)3f(3)3f(3)

x3

lim

x3

[

]lim

x3

2x3f(3)

x3

3(f(3)f(x)).

lim

x3

lim

x3

x3

f(3)2

2(x3)

f(x)f(3)

x3

x3

3lim

23(2)8.

lim

x3

x3

15

[

f(x)x2

f(x0)f(1)f(2)

f(x0)

x)f(x0)

x

]

f(x0

lim

lim

x0

x)

2

x

2

0

x(2x0x)

(x0

lim

2x

A

2-2

s

t

1

2

lim

t0

limat0

at

at0

t0

a5.0105m/s2t01.610

at0800m/s.

3s

800m/s.

yf(x)x2

3

P(1,4)

(1

17

y

x

(1)

(2)f(1)

yf(1x)f(1)

[

](1)

x

x

(1x)2

31

2

3

2x.

x

f(1x)f(1)

x

(2)f(1)lim

x0

lim

x0

(2x)2.

0

18

[

f(x)|x|(1x)

x0

xx2

(x0)

(x<0)

]f(x)

xx

2

yf(0x)f(0)f(x)

x(x)2

(x>0)

(x<0)

x(x)

2

y

x

lim

x0

lim

x0

(1x)1

y

x

lim

x0

lim

x0

(1x)

y

1

y

y

A

2-2

1

yf(x)

(x0f(x0))

x2y30

Af(x0)0

Cf(x0)0

Bf(x0)0

Df(x0)

[

]B

1

2

1

2

f(x0)

(

0.

[

]

x2y30

k

1

2

3

2

yx2

2

1

)

2

A1

5

B.4

C.

4

D

4

[

[

]B

1

2

1

2

[(xx)2

2](

x

x2

2)

]

y

lim

x0

1

2

lim

x0

(x

x)x

ky|1.

x1

B.

4

yx2

(

)

3

4

A(0,0)

B(2,4)

C.11

416

D.11

24

[

]D

A

2-2

f(1)f(12x)

lim

2x

x0

1

5

f(x)

(

)

A2

C1

[

B

D

1

2

]B

f(1)f(12x)

2x

f(12x)f(1)

2x

lim

x0

[

]lim

x0

1

y|

1

x1

yf(x)

(1f(1))

1

B.

6

A

C

[

f(x0)0

yf(x)

(x0f(x0))

(

)

B

D

x

x

x

]B

]

[

B

B.

7

yf(x)x5

y

x8

f(5)

A3,3

B3

D

1

C

[

1,3

1

1

]B

]

[

f(5)

x2P

583f(5)

1B

y4x1

f(x)x3

8

A(1,0)(1

C(1,0)

4)

B(0,1)

D(1,4)

[

[

]A

f(x)x3

x2

xx

]

A

2-2

2

3

5

D.26

C.

[

[

]A

]

y

P(x0)

0

2

3

2

3

(xx)3

3(xx)

x

3

3x

f(x)lim

x0

x

3x

2

3

k3x

2

3

0

tan3x0

2

3

3.

2

23

0

.

A.

Cyx2

2x3

C

P

10

P

[0

4]

P

1

(

)

A[1

C[0,1]

]

B[1,0]

1

2

1]

D[

2

[

[

]A

]

y2x2

[0

4]

k

0k1

02x21

1

2

1x

.

3

f(x)(2f(2))

__

11

f(x)x

2

[

[

]4xy10

3x2

]

f(x)x2

0

A

2-2

1

xx

x

1

x

x

(xx)

f(x)lim

x0

1

x(xx)

1

.

lim1

x0

1

2

x

1

1

k1

2.

y2(x1)y2(x1)

P(x0y0)

13

C

l

l

C

[

[

]

]

l

P(x0y0)

yx3

3x

2

6x10

14

[

]3xy110

[

]

P(x0y0)

P(x0y0)

P(x0y0)

3

2

3x

0

6x0

P

P

k

1k

(1

14)

1

7

4

x

P4

1

15

y

x

1

(xxx)

x

xxx

[

]

y

lim

x0

x

x

xxx

x(xx)

lim

A

2-2

(2)

[

lyf(x)

P

yg(x)

(xx)3

3(xx)3x

x

3

3x

3x

2

3.

](1)y

P

lim

x0

P(1

2)

f(1)0

k1

y

2.

x

3

0

3x0)

(2)

(x0

l

l

l

k2f(x0)3x

2

3

0

y(x

3

3x0)(3x

2

0

3)(xx0)

0

P(1

2)

2(x0

3

3x0)(3x

2

0

3)(1x0)

x

3

3x02(3x0

2

3)(x01)

1

0

x01(

)x0

.

2

9

4

k3x

9

2

0

3

91

44

y(2)

(x1)

y

x.

4

1

x

1.

17

[

yx

f(xx)f(x)

x

]y

lim

x0

1

xx

1

x

xx

x

lim

x0

x

xx(xx)x

(xx)xx

lim

x0

A

2-2

(1x)2

(1x)2(1

2

12)

lim

x0

3

x

y3(x1)

x2

l1

y3x3.

B(bbb2)

b2)

l2

yx

2

2

(bx)2

(bx)2(b

x

2

lim

y|

xb

x0

2b1

l2

y(b

2

b2)(2b1)(xb)

2

l1l2

3(2b1)

1

b

l2

3

1

6

y3x3

x

(2)

122

5

2

y

x

39

y

1

6

5

.

l1l2

2

22

3

l1l2x

(1,0)

0.

1

2

5

2

22125

.

S

1

3

12

A

2-2

1

(

)

A

B

C

y0

y5x

yx

y

0

y

5

1

2

x

y

[

]D

1

3

7

3

2.

y

x3

2

1

(

)

A30

B45

D60

C135

[

]B

1

45.

[

]y|x

1

3.

y(x1)2(x1)x1

(

)

A1

B2

D4

C3

[

[

]D

]y

[(x1)2](x1)(x1)2(x1)

2x1

2(x1)(x1)(x1)

2

3x

2

A

2-2

5

A

B

C

D

[

f(x)

x

(

)

0

f(x)>0

f(x)>0

f(x)<0

f(x)<0

f(x)<0

f(x)>0

f(x

)

0

x

0

f(x

x

)

0

0

f(x

x

)

0

0

]C

]

[

0

f(x)x3

C

f(x)

f(x)

A

C.

6.

A

C

[

yf(x)

[ab]

M

0

m

M

0

0

B

D

]A

[

]

Mm

yf(x)

A.

f(x)0

7.

R

(

)

AR

4

B2R

3

C.R

3

D.R

4

[

[

]C

R2

(Rh)

2

r

2

r

]

h

r

1

3

2

3

V

r2h3h(2Rhh2)

Rhh2.V

Rh2

3h3

4

3

4

0hR.

3

V

A

2-2

[

[

]C

5

1)(y11)(y21)(y31)(y41)(y51

]

(yi

i1

5

C.

9

A

C

[

f(x)[ab]

f(x)dxf(t)dt

(

)

B

D

]B

[

]f(x)dxf(t)dt

yf(x)xaxby0

0.

2

x

(0x<1)

f(x)dx

(

)

10.

f(x)

2x(1x2)

3

A.

4

4

5

B.

5

C.

6

D

[

[

]C

]f(x)dxx2dx(2x)dx

1

3

1

2

F1(x)xF2(x)2xx

3

2

F

1(x)x2

F

2(x)2x

f(x)dxF1(1)F1(0)F2(2)F2(1)

1

3

1

2

1

2

5

6

022

2

2

21

1

(

2

.

C.

11.

)

A

2-2

B2

C

D

[

]B

f(x)x3

x

f(x)

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