Асимптотические оценки. Мицик М.Ф. - 4 стр.

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
.
5
.  
( )
)( xSxf
  
Rba
⊂
];[
, 
( )
0≡xf
,
constxS
≡
)(
.    
0
>
λ
,
(
)
+∞
→
λ
.

( ) ( )
( )
dxexfF
xS
b
a
λ
λ
∫
=
(6)
.
 1.
)(xS

Rba
⊂
];[
, .
[ ]
baxMxS ;,)( ∈≤
.    (6)   

0
λ
. 
0
λ

( )
λ
λ
M
eF =
, (7)

−
.
.

)(xS
, 
( )
[ ]
baxeCe
M
xS
;,
0
)(
0
∈≤
−
λ
λλ
, 
( )
.
00
0
)( MxS
eCe
λλλ −−
=≤
,
( ) ( )
( ) ( ) ( )
( )
( )
dxexfedxeexfF
xS
b
a
M
xSxS
b
a
000
0
λ
λ
λλλ
λ
∫∫
≤=
−
 (7) .
 1. 
( )
)( xSxf
  
 [a;b],     
0
=
x
,  
)(xS
  :
( ) ( )
,aSxS
<

a
x
≠

( )
.0
≠
′
aS

( )
( )
( )
( )
( )
.,
1
∞→
+
′
−
=
∫
λ
λλ
λ
λ
Oaf
aS
e
dxexf
aS
xS
b
a
(8)
.

( )
0
≠
′
aS
, 
0
>
δ
, 
( )
δ
+
≤
≤
≠
′
axa0aS
.  (6) :
( ) ( )
( )
( )
( )
( ) ( )
λλλ
λ
δ
λ
δ
21
FFdxexfdxexfF
xS
b
a
xS
a
a
+=+=
∫∫
+
+
. (9)




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