~ ?yvD ?Dy
???
a)
¥
ü à)
~ ?yvD ?Dy
Ba
a)
¥
}

?é
(1) FhE
∑∑

=

=
±
00 n
n
n
n
n
n
xbxa,
0


=
=
n
n
n
xc
( ?
{ }
21
,min RRR=
)
nnn
bac ±=
( )RRx,?∈
,
21
00
RRxbxa
n
n
n
n
n
n
¥
l ???ò1
!
∑∑

=

=
~ ?yvD ?Dy
(2) eE
)()(
00
∑∑

=

=
n
n
n
n
n
n
xbxa,
0


=
=
n
n
n
xc ( )
RRx,?∈
( ?
)
0110
bababac
nnnn
++?+?=
L
00
ba
10
ba
20
ba
30
ba
01
ba
11
ba
21
ba
31
ba
02
ba
12
ba
22
ba
32
ba
03
ba
13
ba
23
ba
33
ba
L
L
LLLL
L
L
L
O

e

L
32
1 xxx
~ ?yvD ?Dy
(3) "E



=

=
0
0
n
n
n
n
n
n
xb
xa
.
0


=
=
n
n
n
xc
)0(
0



=n
n
n
xb
l ?×
=
(M"a¥
l ? uW1e ?
)
¥
l ? uWl¤ )
f
¥s
?é
(1)
a)


=0n
n
n
xa ¥f
)(xs 
l ? uW
),( RR?
= ??,
?
l ?,5
??§ ??,
~ ?yvD ?Dy
(2)
a)


=0n
n
n
xa ¥f
)(xs 
l ? uW
),( RR?
= V, O ),( RRx?∈? V?[s,




=
=
x
n
n
n
x
dxxadxxs
0
0
0
)()('



=
=
0
0
n
x
n
n
dxxa,
1
1
0
+

=

+
=
n
n
n
x
n
a
(
l ????M )
~ ?yvD ?Dy
(3)
a)


=0n
n
n
xa ¥f
)(xs 
l ? uW
),( RR?
= V?,i V?[ p? ?iQ,


=

=

0
)()(
n
n
n
xaxs'


=

=
0
)(
n
n
n
xa
.
1
1


=
=
n
n
n
xna
(
l ????M )
~ ?yvD ?Dy
è p)


=
1
1
)1(
n
n
n
n
x
¥f
,
3
,)1()(
1
1


=
=
n
n
n
n
x
xsQ,0)0( =sA ?
Hs¤
)1ln()(
0
xdtts
x
+=


L?+?=

2
1)( xxxs,
1
1
x+
= )11( <<? x
~ ?yvD ?Dy
,1
H? =x,
1
)1(
1
1
l ?


=
n
n
n
).1ln()1(
1
1
x
n
x
n
n
n
+=?∴


=
)11( ≤<? x
),1ln()( xxs +=∴
)1ln()0()( xsxs +=?'
~ ?yvD ?Dy
è p
a)


=
+
0
)12(
n
n
xn ¥f
,
3


=
+=
0
)12()(
n
n
xnxs
!
∑∑

=

=
+=
00
2
n
n
n
n
xnx
,22
1
1
0
∑∑

=

=
=
n
n
n
n
nxxnxQ
,)(
1
1


=
=
n
n
nxxA
!
dxxndxxA
n
x
n
x

∫∫

=
=
1
0
1
0
)(


=
=
1n
n
x
,
1 x
x
=
1|| <x
~ ?yvD ?Dy

=∴
x
x
xA
1
)(
,
)1(
1
2
x?
=
,
)1(
2
2
2
0
x
x
nx
n
n
=∴


=
1||,
1
1
0
<
=


=
x
x
x
n
n
Q
=+=∴


=0
)12()(
n
n
xnxs +
2
)1(
2
x
x
x?1
1
1||.
)1(
1
2
<
+
= x
x
x
~ ?yvD ?Dy
è p


=
+
1
2
)1(
n
n
nn
¥,
3
,)1(
1
n
n
xnn


=
+ I
n)
l ? uW (-1,1),


=
+=
1
)1()(
n
n
xnnxs5 )(
1
1
′′
=


=
+
n
n
xx
)
1
(
2
′′
=
x
x
x,
)1(
2
3
x
x
=


=
+
1
2
)1(
n
n
nn
#
)
2
1
(s=
.8=
~ ?yvD ?Dy
è¨X?f
¥
a);
1
1
)1(
0
x
x
n
n
=


=;
1
1
)1()2(
2
0
2
x
x
n
nn
+
=?


=;
1
)3(
2
0
2
x
a
ax
n
n
=


=;
!
)4(
0
x
n
n
e
n
x
=


=
);1ln(
1
)1()6(
0
1
x
n
x
n
n
n
+=
+


=
+;sin
)!12(
)1()5(
1
12
1
x
n
x
n
n
n
=


=
~ ?yvD ?Dy
=a
ü à)
? è5 )11()1ln()1(
1
1
≤<?+=?


=
xx
n
x
n
n
n
n
n
n
xxaxf )()(
0
0
=


=
i
a)
 
l ?

=[ f(x)1f
ù5,1. ?T
Z 7,
^
I
1?
n
a
2.Z 7
T
^?·B?
3.
I
1Hq/?
Z 7?
a)

~ ?yvD ?Dy
£
ü
'
=
l ?? ),(),()(
00
0
xfxuxxa
n
n
n
δ?


=
Q
LL +?++?+=
n
n
xxaxxaaxf )()()(
0010
? ?  ?Tf
)(xf  ),(
0
δxU
= μ ?i¨?

 O ),(
0
δxU
=
Z 7? )(
0
xx? ¥
a)


'
n
n
n
xxaxf )()(
0
0
=


=

5 "
 ),2,1,0()(
!
1
0
)(
L== nxf
n
a
n
n

OZ 7
T
^·B¥
~ ?yvD ?Dy
LL +++=
+
)(23)1(!)(
01
)(
xxannanxf
nn
n
'¤
7,
0
xx =
),2,1,0()(
!
1
0
)(
L== nxf
n
a
n
n
ü à"
^·B¥,
.)( ¥Z 7
T
^·B¥xf∴
LL +?++?+=

1
0021
)()(2)(
n
n
xxnaxxaaxf
?[ p? ?iQ,¤
LL
ü à"
~ ?yvD ?Dy
?T )(xf ?
0
x ) ?i¨ V?
5
a)
n
n
n
xx
n
xf
)(
!
)(
0
0
0
)(


=
?1 )(xf ?
0
x ¥
ü à)

n
n
n
x
n
f


=0
)(
!
)0(
?1 )(xf ? 0
0
=x ¥
X ?
)

ù5
n
n
n
xx
n
xf
xf )(
!
)(
)(
0
0
0
)(


=
==
?l
ü à)

l ? uW
^?
l ?? f(x)?
?B?,
~ ?yvD ?Dy
=

=
0,0
0,
)(
2
1
x
xe
xf
x
è ?
),2,1,0(0)0(
)(
L== nf
n
O


=

0
0)(
n
n
xxf ¥
f)
1
.0)(),( ≡+∞?∞ xs
=f
?)
 Vn
).()(,0 xfxfx ?¥
f)
))?
l ??" =
 x=0? ?i V?,
~ ?yvD ?Dy
? ?  )(xf ?
0
x ¥
ü à)

 ),(
0
δxU
=
l
?? )(xf? ),(
0
δxU
= 0)(lim =
∞→
xR
n
n

£
ü A1?
)()(
!
)(
)(
0
0
0
)(
xRxx
i
xf
xf
n
i
n
i
i
+?=

=
Q
),()()(
1
xsxfxR
nn +
=∴
,)(
Z 71
ü à)
! xf
)()(lim
1
xfxs
n
n
=
+
∞→
Q
=∴
∞→
)(lim xR
n
n
)]()([lim
1
xsxf
n
n
+
∞→;0=
~ ?yvD ?Dy
 s? ),()()(
1
xRxsxf
nn
=?
+
Q
)]()([lim
1
xsxf
n
n
+
∞→
∴ )(lim xR
n
n ∞→
=
,0=
),()(lim
1
xfxs
n
n
=
+
∞→
'
).()( xfxf ¥
ü à)
l ??∴
? ? 
! )(xf  )(
0
xU
μ?l
0>?M

),(
00
RxRxx +?∈?
μ Mxf
n
≤)(
)(
),2,1,0( L=n
5 )(xf  ),(
00
RxRx +?
= VZ
7??
0
x ¥
ü à)

~ ?yvD ?Dy
£
ü
1
0
)1(
)(
)!1(
)(
)(
+
+
+
=
n
n
n
xx
n
f
xR
ξ
Q
,
)!1(
1
0
+

+
n
xx
M
n
),(
00
RxRxx +?∈
,),(
)!1(
0
1
0
l ? +∞?∞
+


=
+
n
n
n
xx
Q
,0
)!1(
lim
1
0
=
+

+
∞→
n
xx
n
n
,0)(lim =
∞→
xR
n
n
#
.
0
¥
ü à)
VZ?? x∴
),(
00
RxRxx +?∈
~ ?yvD ?Dy
?al2
1.
a)
¥
,
s
?é
2. ? pf
¥
ü à);
3.
ü à)
l ??f
¥Hq,
~ ?yvD ?Dy
± I5
a)
?[ p?a
l ????M
*
1
¥
l ?×
^?9?M$
~ ?yvD ?Dy
± I53s
?B?,
è
,)(
1
2


=
=
n
n
n
x
xf,)(
1
1


=
=

n
n
n
x
xf
,
)1(
)(
2
2


=
=
′′
n
n
n
xn
xf
ì¥
l ????
^ 1,
?
ì¥
l ?×ò
^ )1,1(),1,1[],1,1[
~ ?yvD ?Dy
Ba p/

a)
¥
l ? uW
a L
L
L +

++
+
)2(42422
2
n
xxx
n

a LL +
+
+++
n
n
x
n
xx
1
2
5
2
2
2
2
2
2

a


=
1
22
2
12
n
n
n
x
n

a )0,0(
1
>>
+


=
ba
ba
x
n
nn
n

5
~ ?yvD ?Dy
=a ?¨?[ p??[s
p/
)
¥f

a


=
1
1
n
n
nx 
a LL +
++++
1253
1253
n
xxx
x
n

~ ?yvD ?Dy
5s?
Baa ),( +∞?∞ 
a ]
2
1
,
2
1
[? 
a )2,2(? 
a ),( cc?
? {}0,max >= bac 
=aa )11(
)1(
1
2
<<?
x
x

a )11(
1
1
ln
2
1
<<?
+
x
x
x