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|

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?B ? s:1  ? ? 9 F5 
1
I )(xf
+
≤≤
2
)(0
ba
fxf  0
2
<
+
ba
x 
?s￥  ??
? i $f
1 μ yN
dx
ba
f
ba
xI
ba
a
+
+
≥
∫
+
22
2
1
 

  I
n -
?| · 
?￥? = ?s
:1 ?i
2
I?
+
≥
2
)(
ba
fxf 
0
2
>
+
ba
x ? ? ? ?μ
dx
ba
f
ba
xI
a
ba
+
+
≥
∫
+
22
2
2
        

 |]_ ??
T

MF 5μ
0
22
21
=
+
+
≥+=
∫
dx
ba
x
ba
fIII
b
a


 ?
^? ?
T
¤ ￡b
 
ZE 
ZE ? ￥ D ?i?
1
I
2
I
2
ba
x
+

?  s|
=s Y  ??|
7 ?? ? s?′ ? ?5μ)(xf
 )()(
8
1
2
)(
1
2
2
11
ξξ fabdx
ba
xfI
ba
a
=?
+
=
∫
+
)()(
8
1
2
)(
2
2
2
22
ξξ fabdx
ba
xfI
b
ba
=?
+
=
∫
+


+
2
,
1
ba
aξ 
+
∈ b
ba
,
2
2
ξ 
'μ
12
ξξ > ? ￥? ? ? 5μ)(xf )()(
12
ξξ ff ≥ ?
^
0))()(()(
8
1
12
2
21
≥=+= ξξ ffabIII    

6;
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￡
!·° Iù
T? www.tsinghuatutor.com è 82378805 12
2008
￡
!·° Iù￡?$? bê
ê]Z<? BV 609 è 62701055
è 
! ??)(xS
∫
=
x
dttxS
0
cos)(


 ? 1??
H
 On ππ )1( +≤≤ nxn
H
￡
ü )1(2)(2 +≤≤ nxSn 

 p
x
xS
x
)(
lim
+∞→

}3~ 
 0cos ≥x ? ππ )1( +≤≤ nxn
H 19f

[ )(xS

∫
πn
dtt
0
cos
∫
+
<≤
π)1(
0
cos)(
n
dttxS 
?i? xcos [ π1 ?
ù
∫
πn
dtt
0
cos ndttn 2cos
0
==
∫
π

∫
+ π)1(
0
cos
n
dtt )1(2cos)1(
0
+=+=
∫
ndttn
π
?
^¤? 
)1(2)(2 +≤≤ nxSn b

 ? ππ )1( +≤≤ nxn
H
ππ n
n
x
xS
n
n )1(2)(
)1(
2 +
≤≤
+

7 ?C / 5¤? ∞→n
π
2)(
lim =
+∞→
x
xS
x
b
è 
! )(xf [ ]ba,
 ?? 
= V? O),( ba 0)( >′ xf 
k￡
ü  
=i
B?
),( ba
ξ
P wL D)(xfy = )(ξfy =  ax =
??￥ m?

^? wL D
1
S )(xfy =
)(ξfy = 
??
ü
m? ￥ bx =
2
S
}3~ 
= |B? 5 ),( ba t
∫
==
t
a
dxxftftSS ))()(()(
11
 
∫
==
b
t
dxtfxftSS ))()(()(
22
7  =?=
∫
t
a
dxxftftStStF ))()(()(3)()(
21
∫
b
t
dxtfxf ))()((3
5o?￡
ü  μ O? μ B?
,?)(tF
),( ba
),,( ba∈ξ
P¤ 0)( =ξF b
?i?? ?
^ 
=? ?9F ? s′ ? ? V¤0)( >′ xf )(tf ),( ba
0)( <aF  O b
[ 
=à
 μ B?
,? b0))()(()( >?=
∫
b
a
dxxfbfbF )(tF ),( ba
6?  I3 
=￥? ? ?b0)( >′ xf )(tF ),( ba

6;
> ?
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!·° Iù
T? www.tsinghuatutor.com è 82378805 13
2008
￡
!·° Iù￡?$? bê
ê]Z<? BV 609 è 62701055
′?+=′ )()()()( tfattftF )()(3)()(3)( tftbxftbtf?+ 
 )]()()[(3)()( xftftbtfat+′?= 
0)()(3)()( >′?+′?= ξftbtfat 
? ),( xt∈ξ b?
^ 
=?? 9 FK μ B?
,? b)(tF ),( ba
8

s 
[  μB?
,?)(tF ),( ba ),,( ba∈ξ
P¤ 0)( =ξF b
è 
×ˉ

è 
!μ ???Ce
°?H1 | 
°b ?
￡ ? 
PB° ? D
￡
× 
6 B
°?H< ° _/ ù
° ?H? 1 è
H ??? Ce?
s
￡ a ?Kv $ 
!
￡￥
á 1 
pNK v a ?
l
}3~ [< °_/° ? H??1 U Se? < °_
Z _ 1 ày yx?
ü
D ??e

ü
M
ü?y ? US"
i
!
￡
ü°?H D<°_/ °?H￥HésY 1 a D 5μ 
|H
 °LZ? 1
ka
lkaa =+ kxy = 
,1Ce ?
s￥
￡a ?  |_ s é  V
U
)(kP xdy yka? 1
￡
' 
5 μ ± s1" 
 ?
^ dxxaxkdyykaxkdP )()()(
22
=?=
3
3232
0
22
)1(66
)()(
+
==?=
∫
k
lkak
dxxaxkkP
a
4
32
)1(6
)2(
)(
+
=′
k
lkk
kP 
3¤?  O  ?
5 2=k )(kP′
M| 5?a μ
 yNK va ?1
81
2
)2(
3
l
P = b


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