7/31/2019 Them Mat Kat c Hmer No 1206

1/4

1

1 4

() 28 2012

:

: (4)

A1. f . x

, f

0(x)f >

7

A2. f [, ];

4A3. f .

f x0A ;

4A4. ,

,

, ,

.

)

) f 1-1, y f(x)=y x

) = + , f(x)

7/31/2019 Them Mat Kat c Hmer No 1206

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2

2 4

) ,x

1)(x

2= x{x|x=0}

) ,(x)g(x)dxf[f(x)g(x)](x)dxgf(x)

+= g,f

[,] 10

z w

:4=+z+1z

221_ (1)

12=w5_w (2)

B1. z = 1

6

B2. z1, z2

z 2=zz 21_ , .zz 21 +

7

B3. w

14

y

9

x 22

=+ w

6

B4. z,w (1) (2) :

1 wz 4

6

7/31/2019 Them Mat Kat c Hmer No 1206

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3

3 4

f(x)=(x1) nl x1, x>0

1. f

1=(0,1] 2=[1,+). f

6

2. x>0 .

,ex 20131-x =

6

3. x1, x2 x10, x=exx

7

f :(0,+) , x>0 :

f(x) 0

e

xxf(t)dt

21xx

1

2

+

xx = nl f(x)edtf(t)

tnt

x

1

+

l

1. f .

10

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4

4 4

f(x) = ex( nl xx), x>0, :

2. : ( )( )( )

( )

+

xfxf

1xflim

2

0x

5

3. nl xx1, x>0,

( ) dt,f(t)xFx

= x>0, >0, ( 2).

:F(x) + F(3x) > 2F(2x), x>0 ( 4).

6

4. >0. (,2) :

F() + F(3) = 2F()

4 ( )1 . ( ,

) . .2.

. . .

3. .4. .

, .

5. .6. .7. : (3)

.8. : 10.30 . .