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T< ps
1
2
1
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T< 20
!,[0,2]f →\=Q ?? V? O () 1fx≤ # () 1fx′′ ≤

[0,2]x?∈ b￡
ü [0,2]x?∈ μ () 2fx′ ≤ b
￡ ? Taylor ?
21
()
(0) ( ) ( )(0 ) (0 )
2
f
f fx f x x x
ξ′′
′=+?+?
22
()
(2) ( ) ( )(2 ) (2 )
2
f
f fx f x x x
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12
11
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?
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12
11
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2
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1
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 ?? V?￡
ü
1
max ( ) ( ) ( )
bb
aa
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f xfxdfxd
ba≤≤
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b
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1
()
b
a
f xdx
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∫
3
?
^
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xx
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′′=+ ≤+
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aa
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1
! [0,1]fC∈  O (0) 0f =  0()1fx′< ≤ b￡
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3
11
2
00
[()] [()]f tdt ft dt≥
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7
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2
00
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xx
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2
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Bá ??i O ()
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l ?5
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x
fx
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=
(2) ?|5
"?￥HqBá ???1 ??i OFHqo f dμp2
?$
￡ L
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fx
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0
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P 0>  x
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0
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0
0
2
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00
0
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22
fx fx fx fx fx fx fx
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ε

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]|?5
0
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0
()
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22
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f x dx dx
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++
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00
()
22
xx
f x dx dx
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∫∫
b
[

0
0
2
ε δ
>  0>  xxδ

+> >?
P¤
0
()
2
x
x
fxdx
δ
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+
≥
∫
b
4
? Cauchy
l ?e ?? ()
a
f xdx
+∞
∫
? ?b?DX?Hq
±b
[ lim ( ) 0.
x
fx
→+∞
=

2?bQ è ?/
4
3
4
333
3
0,[0,1]
1
4( ),[,]
2
()
111
4( ),[,]
2
1
0,[,1]
x
nxnx nn
n
fx
nxn x n n
nn
xn n
n
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=
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A ? () 0fx≥  f  [,)a +∞
 ?? O
32
0
11
11 1
0() 2
2
nn
fxdx n
nn
∞∞
+∞
==
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∑∑
∫
[
0
()f xdx
+∞
∫
l ?b?
^
3
1
lim ( ) lim 2
2
nn
fn n
n
→+∞ →+∞
+= =+∞# lim ( ) 0
x
fx
→+∞
≠ b