1 3

( )

1. f (,),

0x , f .

f (x) 0 0(,x ) (x ,) , 0f(x )

f (,).

10

2. f .

f ;

5

3. (),

, (), :

1) *z i, , ,

1 1 1i

z .

2) 1 2z z z z z 1 2z ,z

.

3) f [,]. f()f()>0 ,

f(x)=0 (,).

4) f

1-1, 0x f

.

5) f [,],

f x x

x= x=

E() f(x) dx .

10

z1, z2 :

|z2|=1, |z1z2|=|z1| 2 1z z 1 2i ,

.

2 3

1. 1 21

Re(z z )2

.

6

2. N 1

2z

2 .

8

3. z1 z2 ,

. (

).

6

4. w ,

2

2

z iiw

z

,

.

5

f : :

x 1

f x+2 -5lim = 6

x-1

1. :

) f 3 =5 ) f 3 =6

6

2. x+2 - f(x)

lim(x-3)x 3

.

7

3. h(x) = xf(x)-3x-7x ,

x x x .

5

4. g : ,

3 3

g (x) f (3) , x . 6g(x) = x ,

1.

7

f : , :

f(0) =1

x u x

0 0 0

1 1f(t) dt du = x f(t) dt + f(x) - , x,u, t

2 2

.

1. 2- xf(x) = e , x .

7

2. f ,

.

5

3.

x

0

2 2t x- -e dt x e , x 0 .

4

4.

x

0

3x 0

f(x-t)dt - x

limx

.

4

5. (0,k), k >0 k 22

0

t dt--e k e .

5