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$?±s? c±sD'? ?#?¨
?y
 ± s D'? ? ￥
n1?
^ù? V?f
)(xfy = 
? ) |¤′ ￥ù5bf
 ) |¤′ ??
a
^ ? ′ii±4?

￥'
Y
L
^
)￥f
9

0
x
)(xfy =
0
xx=
0
xx=
)()()(
000
xfxxfxf+=?  ?í ?
a
§
1 ?| ' 1 ? 
1μb [ ) |¤ v′ f ? ?s
0
x
0
x )(xfy =  ?í

0
x ),(
0
δxN
#×
￥±4
?
?/

! ) V? ) |¤v ′')(xf
0
x
0
x ),(
0
δxN
= ￥ ?i )?μ
?N V?
x
)()(
0
xfxf ≤ 0)()(
0
≤?=? xfxff '  ),(
0
δxN
=
ê ?
Hf
|′Ml?
^ V? 
0
x )(xf
? 
0
xx> 0
)()(
0
00
≤
+
=
xx
xfxxf
x
f
b
? K￥ ?? L¤? 0lim
0
≤
+
→?
x
f
x
 b0)(
0
≤′
+
xf
? 5
0
xx< 0
)()(
0
0
≥
=
xx
xfxf
x
f
b 0lim
0
≥
→?
x
f
x
 0)(
0
≥′
xf
?
^ á
ìμ i O b?N? ?L
^n
? ?￥2
b 0)(
0
≥′ xf 0)(
0
≤′ xf 0)(
0
=′ xf
?n
? ? V[ °¤??
,?? ? i O V[ ? ?+ ?±sD '? ?b 
±s? ′? ?
? ? n
? ? 'FSNBU ? ? V?f
|¤′￥A1Hq


!
@ °

# ×)(xf ),(
0
δxN
=μ?l i O ),(
0
δxNx∈? μ 
  ° ) V? 5 b
)()(
0
xfxf ≤
))(
0
xf≥
0
x 0)(
0
=′ xf
è ￡
ü ?
,?? ?
 ?
,?? ?
!f

 V?i O)(xfy = ],[ ba 0)()( <′′
+
bfaf b5A
> ?
 
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),(
0
bax ∈? 
P¤  ) μ
￡
ü ML
b 0)(
0
=′ xf
0
x

±
^
?s| ?)(xf ′ ba,0)( <′
+
af ?  ?1??é 5  ·§
μ
P¤ y N ?
^ ￥ Kl′? 7
)(xf ax =
1
x )()(
1
afxf < )(af )(xf 0)( >′
bf ]" P
§μ
P¤
bx=
2
x )()(
2
afxf < ' 9 ?
^ ￥ K l ′?b yN V?f
Aμ K
l′ ? ?n
? ?' μ
)(bf )(xf )(xf
),(
0
bax ∈ 0)(
0
=′ xf b
}￡ ~
! O
6B f ? h? ??￡
ü
'μ 0)( <′
+
af 0)( >′
bf
0
)()(
lim)( <
=′
+
→
+
ax
afxf
af
ax

? K?l 0
1
>?ε  0
1
>?δ 
P?
1
0 δ<?< ax
Hμ 
11
)(
)()(
)( εε +′<
<?′
++
af
ax
afxf
af b
| 0)(
2
1
1
>′?=
+
afε 5 μ
0))((
2
1
)()( <?′<?
+
axafafxf 
' y N ?
^ 
 ￥Kl′ b)()( afxf < )(af )(xf ],[ ba
6? ?μ 50)( >′
bf 0
2
>?ε b 0
2
>?δ 
P?
2
0 δ<?< xb
HA μ
22
)(
)()(
)( εε +′<
<?′

bf
bx
bfxf
bf b
+Y | 0)(
2
1
2
>′=
bfε 5μ 
0))((
2
3
)()( <?′<?
bxbfbfxf 
' by N g?
^ 
￥Kl ′b )()( bfxf < )(bf )(xf ],[ ba
y1 
 V? 5A ? ??KvK l′? ?+YAμ
P¤ 1

 ￥Kl′ 7 O
)(xf ],[ ba )(
0
xf )(xf
],[ ba bxax ≠≠
00
,'i ),(
0
bax ∈ ?n
? ? Aμ b0)(
0
=′ xf
? ? 
:? ? 3P MMF

!f
)(xfy =
@  °
 ?? ],[ ba
> ?
 
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°
= V ?  ° b),( ba )()( bfaf =
5 ),( ba∈?ξ 
P¤ 0)( =′ξf ' ξ=x ) μ
￡
ü ML
b 
}￡ ~ 
 ?? 5A
 |¤KvK l′ y1)(xf ],[ ba )()( bfaf =  ? ￥K
vKl ′ 
? | ¤5
)(xf
],[ ba Cxf ≡)(  ],[ bax∈? (μ 0)( =′ xf b?5 ￥K
vK l′?à
 μ=?-B 
=? |¤ ?^
! 
)(xf
],[ ba
P¤ )(max)(
],[
xff
bax∈
=ξ ?y1  V?)(xf )(ξf A1
= ￥v′ ??),( ba
n
? ?¤? 0)( =′ξf b
?
:? ?# -
￥?
,?? ?￥
5?
T (1μ
￡
ü ML￥ sHqb?
@?

?? ?￥Hq
H 2
9 V
? ?b 
? ?  ? ì μ °±s?′? ? -BHSBOHF

!
@ )(xf
°
 ??  °
= V ?b],[ ba ),( ba
5 ),( ba∈?ξ
P¤ 
ab
afbf
f
=′
)()(
)(ξ 
}￡~
!? D? - W￥?1))(,( afaA ))(,( bfbB AB5
AB
K
ab
afbf
=
)()(
AB￥
°L Z?1 )(
)()(
)()( ax
ab
afbf
afxy?
=? 
|￡ ùf

)()()( xyxfxF?= )(
)()(
)()( ax
ab
afbf
afxf?
= 
5 

@
,? ?￥Hq  O)(xF ],[ ba 0)(,0)( == bFaF ?
^ ),( ba∈?ξ 
0)( =′ ξF '
ab
afbf
f
=′
)()(
)(ξ b
? ?ì μ ° ±s?′? ?
^
:? ? 3PMMF
￥éB??Z ￡
üZE
^YV? ? ￡ù
f
/
:? ?￥HqV7¤?2Tbi O 
T Vμ ?/?NVr
T
))(()()( abfafbf?′=? ξ )))((( ababaf+= θ  )10( <<θ   
> ?
 
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))(()()(
00
xxfxfxf?′+= ξ 
hfxfhxf )()()(
00
ξ′+=+ 
?±s?′? ?￥￡
ü
^ 5? ?￡ùf
[7 /?¨
,? ?￥Hq ?2
b
? ?±s?′ ? ? V°¤ ¤ ? w
?/ 
w
 ?μ),( bax∈? 0)( =′ xf 5 cxf =)(  ? 1 è
bc
w
 ? μ),( bax∈? )()( xgxf ′=′ 5 
=Aμ),( ba cxgxf += )()( b? O??

wL D)(xfy = )(xgy = μB?
? ),(),,(
000
baxyx ∈
Hμ b)()( xgxf =
w
 ? 
μ ?5
 ￥ ?i
? iè

P¤)(xf ′ ],[ ba ],[ ba
21
,xx 0>L
1212
)()( xxLxfxf?≤? 
? L? 1 ?
 Gè
b 
? éB?μ 10 << L 5 ?"￥ )(xfy =
@ a
ê?`e ?b
a
ê ?`e ??
?' [? 1 p￥
= ? 
w
 ?  5),( bax∈? 0)( ≥′ xf )(xfy = 
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9F O
H ?ì ?? 9F b7 ?
),( ba 0)( >′ xf
)(xfy = 0)( ≤′ xf
H 0)( <′ xf
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?? h
b
? ?ì μ °? ′? ?￥
 ?è¨×1 ?
^ 
 
? 
 )￥ |′?
 Vw? í
) ￥ |′?
 ^
^ B
Ho y
íp 
@? ? Hq￥  uW
μ
? ?  e?T ¨b
)(xfy =
1
x
1
x )(xf
)(xf ],[ ba
 
 ?ì μ °?′? ? ￥f
|′
9
D ?
|′ -Wq 
 B
V B
b 
)(xfy =
? ?  O?′? ? $BVDI Z
 ?T
@ 
> uW
 ?? 

 7 uW
= V ? O
)(xf )(xg ],[ ba
),( ba 0)( ),()( ≠′≠ xgagbg 5  7 u W
=à
 i B?),( ba
> ?
 
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ξ
P¤
)(
)(
)()(
)()(
ξ
ξ
g
f
agbg
afbf
′
′
=
 
±sD'? ?￥+il
 ±sD+?'? ?μ"
üA￥+il
3?t+il|μù?á
ìy ?A
1￥ °4?? a
Mb ? V[éB?
± I
@
I
1Hq
H
:? ?D ?ì μ °?
?? ￥
)(xf
ξ? μ· B?$?
@
I
1Hq
Hμ
?? ]￥
1
ξ D
2
ξ $
è 
! 11 ?
 5nm,
nm
xxxf )1()(?= )(xf ′  

=
,??
1 #
b
 "
b #
b $
b %
b
}3~? ?ê[1 #
b 
 ?
:? ? yNà
i B?0)1()0( == ff )1,0(∈ξ
P 0)( =′ξf ? 
11
)1()1()(

=′
nmnm
xnxxmxxf )()1(
11
nxmxmxx
nm
=

b
7 ?0)( =′ xf )1,0(∈x
H ¤0)1(
11
≠?
nm
xx )1,0(
0
∈
+
=
nm
m
x 
1· B?'
0
x=ξ 1 ￥·B
,?b )(xf ′
è 
!
^?
ù1 ￥?
ùf

= V? O)(xf ]1,0[,0)1( =f 
7 )(max
]1,0[
xfM
x∈
= 
k￡
üi ( )2,1∈ξ 
P¤ Mf 2)( ≥′ξ b
}￡ ~
n5y
^ ?
ù1 ￥?
ùf
5o?￡
ü)(xf
 (1,0
0
∈ )ξ
P¤ Mf 2)(
0
≥′ξ b
¨ -BHSBOHF?′? ?
? 
= V?5 A
= ?? ?y)(xf ]1,0[ ]1,0[,0)0()1( == ff 
5o
i
P¤),(10∈
M
x )(max)(
]1,0[
xfMxf
x
M
∈
== b

K vKl′? 
? |¤ 
 u W ),0(
M
x
M
xfM )(0
1
ξ′=?± 
 u W )1,(
M
x )1)((0
2 M
xfM?′=± ξ  ( )
M
x,0
1
∈ξ  ( )1,
2 M
x∈ξ 
> ?
 
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TsY | ' ′aMF ¤? 
)1)(()(2
21 MM
xfxfM?′+′= ξξ 
7 { })(,)(max)(
210
ξξξ fff ′′=′ 
5μ (1,0
0
∈ )ξ N
Hμ? ?
T )(2
0
ξfM ′≤ 
yN i (2,11
0
)∈+= ξξ 
P¤ Mf 2)( ≥′ξ 
 T 1
 h ?| ?ì μ °?′? ?￥  ?w
GQé?￡
ü?|μ ù??B×
1? ?￥ ?3D ?¨b
è 
! 
 μ=¨?
 O)(xf ]2,1[ 0)2()1( == ff  ￡
ü

P¤ b
±
^ 
)()1()(
2
xfxxF?=
)2,1(
0
∈?x 0)(
0
=′′ xF )(xF′ ?¨
:? ?b 
}￡ ~ ZE 

 
7)()1()()1(2)(
2
xfxxfxxF ′?+?=′ 1=x 5μ 0)1( =′F 
6?
?
:? ?0)2()2(,0)1( === fFF )2,1(
1
∈?ξ 
P¤ 0)(
1
=′ξF  )(xF′ ],[
1
1 ξ
? ¨
:? ? 5 )2,1(),1(
10
∈=? ξξ x 
P¤ 0)(
0
=′′ xF b
 ZE 

 Q ￡
! 5 ??
,? ? ?-w
V?0)( ≠′′ xF )(xF ′′  

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!
y N0)( >′′ xF )(xF′ 
1? ì??9f
b ]2,1[
 I
n? # 
[0)1( =′F )2,1(∈x 0)( >′ xF ' )()2,1( xFx ′∈? μ ?|￥2
b
?? ?
:? ? ?0)2()1( == FF )2,1(
1
∈?ξ 
P¤ 0)(
1
=′ξF ?D

?|
2
±?
^ eL
!?? ?'A
)(xF′
)2,1(
0
∈?x 
P¤ 0)(
0
=′′ xF b
è 
! )13)(12)(1()(?++= xxxxxg 
k ? ?Z? 0)( =′ xg  )0,1(?
= μ+?
L? b
±
^  X?f
V r
TX
^ y0e?
T ??¨ ??f
,?? ?#
:? ?8
)
￥
,?ù5 7??ü
)(xg
)(xg′ )(xg′ p ?)

,?b 
}3 ~f

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L?   )(xg ),( +∞?∞ )(xg 0
1
=x 1
2
=x
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2
1
3
=x 
3
1
4
=x ?
:? ? )(xg′ à
μ ?
,? )
3
1
,0(
1
∈ξ  )
2
1
,1(
2
∈ξ 
)0,
2
1
(
3
∈ξ b
? 1 Q[
T Kμ ?
L?y N)(xg′ )(xg′  )0,1(?
= μ ?
L?b 
è 
! ￡
ü ??
T 0>x
24
)1arctan(
22
2
x
x
xx
x
<?+<
++
π
b
}￡ ~
ZE  ? o 3￡
ü ??
T0>x
2
1
4
)1arctan(
22
1
2
<
+
<
++ x
x
xx
π

?i ?
4
1arctan
π
=  ?i ),0( ∞∈x
7 xxf arctan)( = 5μ 
1)1(
)1()(
4
)1arctan(
+
=
+
x
fxf
x
x
π


¨ -BHSBOHF?′? ? 5μ]1,1[ x+
)1,1(,
1
1
1)1(
4
)1arctan(
2
+∈
+
=
+
+
x
x
x
ξ
ξ
π

y
2
1
1
x+
1 ??hf
?
^
2
1
4
)1arctan(
22
1
2
<
+
<
++ x
x
xx
π
b

ZE 
7
xxxxxxxf?++?+++= )22(
4
)1arctan()22()(
22
π

0)0( =f

)22(
4
)1arctan()22()( +?++=′ xxxxf
π

0]
4
)1)[arctan(22( >?++=
π
xx 
> ?
 
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?
^ ?
H 'e P§??
T ? ?b0>x 0>)(xf
7 0)0(,
24
)1arctan()( =+=?
π
x
xx 
0)(,0
2
1
)1(1
1
)(
2
<?<?
++
=′ x
x
x ' e·§??
T? ?b 
è
! 
= V?  O]1,0[)( Cxf ∈ )1,0( 0)1()0( == ff ￡
ü i )1,0(∈ξ
P
0)(')(2 =+ ξξξ ff b
}￡ ~/  ? ^￡)()(
2
xfxxF =
]1,0[)( CxF ∈ O
= V? O)1,0( 0)1()0( == FF  ?¨
:? ?¤ )(xF
i 0)(')1,0( =∈ ξξ F
P ' 
H ]"0)(')(2
2
=+ ξξξξ ff 0≠ξ ?
^ e5¤￡b 
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7? ?ù5
#￥S?
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DK vKl′ù 5 wL￥ ?j?ù5 DvíLù 5[#
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T￥ ￡
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f
￥  ?′ù5 
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#×
=μ
0
x )()(
0
xfxf ≤  ))()(
0
xfxf ≥
5? 1f
￥B ?v l
′b )(
0
xf )(xf
  v ′al′ d?1′ 
Pf
| ′￥? ? 1′?b 
0
x
 B ? V?f
 ) | ¤ ′￥A 1H q
^
0
xx= 0)(
0
=′ xf ? ?
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? ?b
@ ￥? ?￥1 ￥ ?b0)(
0
=′ xf
0
x )(xf
 V +
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^
￡
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0
x
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￡
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? ?  ?B ? sHq

! 

#×
=μ ?l ? ) ￥9
)(xf
0
x
0
x )()()(
0
xfxfxf?=? 
 §?í
?M| 5 A1 ￥ ′?b i O
0
x
0
xx= )(xf 0)( ≥? xf
H 1 l′ ? 7
H
1 v′?b 
0
x 0)( ≤? xf
0
x
è  p xxf?= 1)( 
=￥ ′?b ]1,1[?
}3 ~ ?
≥?
<?
=
11
11
)(
xx
xx
xf 0)1( =f ¤ 
1<x  01)1(1 <?==? xfxf 
1>x  01)1(1 <?==? xfxf 

 §?í (μ ?|?1=x 0≤?f 1=x ) ? ?b 
? ?  ?= ? sHq


!
 ??
#×)(xf
0
x ()( )δδ +?
0000
,,xxxx U
= V±  ) ?? 5? 
§ M|
H 1 ￥ ′? i O 
0
x )(xf ′
0
x
0
x )(xf
 
? ()xxx,
0
δ?∈
H 7?0)( >′ xf ( )δ+∈
00
,xxx
H 0)( <′ xf  A
1 v′?b 
0
xx=
 
? ()xxx,
0
δ?∈
H 0)( <′ xf 7? ( )δ+∈
00
,xxx
H 0)( >′ xf  A
1 l′?b 
0
xx=
è 
! Z? )
03
3
=+? Axx A | ′
H 
 
Z?μ B?
L? 
 
Z?μ =??]
L? 
 
Z?μ ???]
L?b
}3~
! 5 1 ?Q[
T K μ ? ?
L?b ¨?
)
?f
￥ 9h uWD ′￥s? f ?b
Axxxf +?= 3)(
3
)(xf
> ?
 
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￡
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 )1)(1(333)(
2
+=?=′ xxxxf

7 3¤?0)( =′ xf 1
1
=x  1
2
=x i O
)1,(∞∈x
H 0)( >′ xf  ??9F  )(xf
)1,1(?∈x
H  ??h
  0)( <′ xf )(xf
),1( +∞∈x
H  ??9F b0)( >′ xf )(xf
 ?
^ V? 1
1
=x 1 ￥v′? 7)(xf 1
2
=x 1 ￥l′?b ￥v 
l′ sY1 
)(xf )(xf
 
 2)1( +=? Af 2)1(?= Af 
Kv Kl′ (v ?
, l?
,
H )(xfy =  ),1( +∞?
= í
,?? 
' V
= V |¤μ′ ? ??f
￥
,?? ?  V? ?
=
μB ?
,?b 
∞=
∞→
)(lim xf
x
)(xf )1,(∞ )(xf )1,(∞
0)2)(2()1()1( >?+= AAff 
?N V¤ A?
@ '04
2
>?A 2>A 
 
A ? ? ￥ KvKl′ μB?1
,
H'
H)(xf 04)1()1(
2
=?= Aff
)(xf μ
?
,? N
H 2=A b
 
? D |¤s|
H?i?)1(?f )1(f +∞=
+∞→
)(lim xf
x
?
^ μ ??
,? 
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bx
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→
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è ￡
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T )2,0(∈x 32ln4
2
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2
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n  

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0
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4
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2
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1
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x
x
x
x
x
xf +=+=′ 
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2
0
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 0lnlim
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+
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xx
x
# +∞=
+∞→
xx
x
lnlim 
> ?
 
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6; I
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!·° Iù￡?$? bê
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6; I
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!·° Iù￡?$? bê
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0)()(0)( >↓<′ xFxFxF 
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