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& ..

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:

: (4)

1 . (, )

x0 .

f (x ) > 0 (, x0) f (x) < 0 (x0 , ) ,

f f (x0).

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3 . [, ];

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3 . ,

1. x0

x0 .

2

2. f: f (x) = 0

x f

2

3. f 11

x0 x x

2

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fog x0

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5.

f .

2

z, w

z( z + 1) 2i Im(z) = 4 + z , (1) w = 2z + 3 4i

1 . z

(0, 0) 2

w

6

B2 . |z w|

6

3 . 2|z| + |w| 5

5

4 . z1 , z2 (1)

1 2

1 2

3z zi

z z

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2 1z z i

i

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f:[ 2,2]

(x2 4) [f (x) ex + e x] = ex + e x f(x), (1)

x[ 2,2].

1 .

f (x) = ex + e

x, x[ 2,2].

7

2 . f ,

.

6

3 .

e3 x

e2 x + ex = 0

.

4

4 .

ex + 2

+ 2xe 4e e x

2x 2e

7

f (0,+ )

f (x) = 3 + , x(0,+ ).

1 N f.

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2x

2

x

tf ( )

x dtx

3x 1

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g (x) = f (x) lnx, x(0,+ ).

2 N g (0,+ ).

4

3 N ()

h (x) =

k (x) =

x = x = .

8

4

F (x) = G (x) = , x(0,+ )

N

H (x) = F (x) G (x), x(0,+ )

(0,+ ).

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|

,

, ,

1

2

g (x)

x

2

g (x)

x

1

4

1

2

2x

x

g(t) dt

t3x

2x

g(t) dt

t

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