~ ?yvD ?Dy
? 6 ?
±s# ?¨
~ ?yvD ?Dy
Baù5¥4
L è ?Z?á

s £a
¥?M
,
2
0
xA=
0
x
0
x
,
00
xxx?+M?
!Hé?
,
2
0
xA=?Z?
Q
2
0
2
0
)( xxxA+=?∴
.)(2
2
0
xxx?+=
)1( )2(;,¥?1?s O1¥L?f
Ax
.,l
H V-
{?¥ú¨í kl xx
:)1(
:)2(
x?
x?
2
)( x?
xx?
0
xx?
0
~ ?yvD ?Dy
 è ?,
.,
0
3
yx
xxy

=
pf
¥?M

H1
)¥?M
?
!f
3
0
3
0
)( xxxy+=?
.)()(33
32
0
2
0
xxxxx?++=
)1( )2(
,l
H? x?
.3
2
0
xxy≈?∴
),()2( xox ¥ú¨í kl
^
; ?^9
?
^?z¥í
′
ù5 ??L?f
(?M
¥?1?s )
^?
μf
¥?M
?μ?
^
I
1? ? p?
~ ?yvD ?Dy
=a±s¥?l
?l
.),(
,)(
,)(
),(
)()()(
,
,)(
00
0
0
0
00
00
xAdyxdfdy
xxxfy
xAxxfy
xA
xoxAxfxxfy
xxx
xfy
xxxx
=
=
=
+=+=?
+
=
==
':T
¥±sM??1M
9
?
1f
i O? V±?
5?f
í1¥è
^D ?? ?
?T? uW
=#

 uW
=μ?l
!f
.¥L????Sf
9
±s ydy? ±s¥
Lé
~ ?yvD ?Dy
??l?;)1( ¥L?f
^1M
¥?M
 xdy?;)()2( ú¨í kl
^1 xxodyy=;,0)3(
^?Ní klD
H? ydyA?≠
dy
y?
Q
xA
xo

+=
)(
1 ).0(1 →?→ x;)(,)4(
0
μ1?Dí1¥è
^D xxfxA?
).(,)5( L???l
H? dyyx ≈
~ ?yvD ?Dy
?a V±¥Hq
).(,)(
)(
00
0
xfAxxf
xxf

= O) V??
V±¥ 1Hq
^f?f
? ?
£
(1) A1?
,)(
0
V±? xxfQ
),( xoxAy?+=?∴,
)(
x
xo
A
x
y
+=

x
xo
A
x
y
xx
+=
→?→?
)(
limlim
00
5,A=
).(,)(
00
xfAxxf

= O V??'f
~ ?yvD ?Dy
(2)  s?
),()(
0
xxxfyα+

=?V7
,)(
0
α+

=
xf
x
y
'
,)(
0
V??f
xxfQ
),(lim
0
0
xf
x
y
x

=

→?
),0(0 →?→α xQ
),()(
0
xoxxf?+

=
.)(,)(
00
Axfxxf =

O V±?f
Q
).(.
0
xfA

=?∴ V± V?
.)(),(,
,)(
xxfdyxdfdy
xxfy

=
=
':T±s
?1f
¥¥±s ?i?f
~ ?yvD ?Dy
è
3
.02.0,2
3
H¥±s? pf
=?== xxxy
xxdy?

= )(
3
Q,3
2
xx?=
02.0
2
2
02.0
2
3
=?
=
=?
=
=∴
x
x
x
x
xxdy
.24.0=
.,
,
xdxdx
xx
=
':T
?11M
¥±s¥9
Yèü1M

.)( dxxfdy

=∴ ).(xf
dx
dy

=
".",±
?
9??f
¥?
-
??D1M
¥±s'f
¥±s dxdy
~ ?yvD ?Dy
è
)(
,
)(
,),sin(
32
2
xd
dy
xd
dy
dx
dy
xy p
! =
3
dx
xdx
dx
xd
dx
dy )(cos)][sin(
222
==
2
2
22
2
2
2
cos
)(
)(cos
)(
)][sin(
)(
x
xd
xdx
xd
xd
xd
dy
===
)(
)(cos
)(
)][sin(
)(
3
22
3
2
3
xd
xdx
xd
xd
xd
dy
==
2
2
2
cos
3
2
3
2cos
x
x
dxx
xdxx
=
=
2
2
cos2
2cos
xx
dx
xdxx
=
=
~ ?yvD ?Dy
1a±s¥+il
)(xfy =
0
x
M
N
T
dy
y?
)( xo?

x
y
o
α
x?
+il  ?m
.
,
?¥9


^ ML:US
US9

H
^ wL¥:?
dy
y?
xx?+
0
P
.
,,
MNMP
Mx
Ví
}9 wL
ML
¥?í?l
H
~ ?yvD ?Dy
?a±s¥ pE
dxxfdy )(

=
pE 9
f
¥?
,e[1M
¥±s,
1.'?f
¥±s
T
0)( =Cd
dxxxd
1
)(
=
μμ
μ
xdxxd cos)(sin = xdxxd sin)(cos?=
xdxxd
2
sec)(tan = xdxxd
2
csc)(cot?=
xdxxxd tansec)(sec =
xdxxxd cotcsc)(csc?=
adxaad
xx
ln)( =
dxeed
xx
=)(
~ ?yvD ?Dy
2,f
aμaa
¥±sE5
dx
ax
xd
a
ln
1
)(log = dx
x
xd
1
)(ln =
dx
x
xd
2
1
1
)(arcsin
=
dx
x
xd
2
1
1
)(arccos
=
dx
x
xd
2
1
1
)(arctan
+
=
dx
x
xarcd
2
1
1
)cot(
+
=
dvduvud ±=± )(
CduCud =)(
udvvduuvd +=)(
2
)(
v
udvvdu
v
u
d
=
3,ˉf
¥±sE5
dxxufdxyxdfdyxfy
x
)()()]([)]([
′′
=

=== 5
~ ?yvD ?Dy
è
3
.),ln(
2
dyexy
x
p
! +=
,
21
2
2
x
x
ex
xe
y
+
+
=

Q,
21
2
2
dx
ex
xe
dy
x
x
+
+
=∴
è
3
.,cos
31
dyxey
x
p
!
=
)(cos)(cos
3131
xdeedxdy
xx
+?=

.sin)(cos,3)(
3131
xxee
xx
=

=


Q
dxxedxexdy
xx
)sin()3(cos
3131
+=∴

.)sincos3(
31
dxxxe
x
+?=
~ ?yvD ?Dy
Ba±s?
T¥?M?;)(,)1( dxxfdyx

=
^1M

H ?
5±f
¥ V'
6BM

^?WM

H ?
),(
,)2(
tx
tx
=
),()( xfxfy

= μ?
!f
dttxfdy )()(?
′′
=
,)( dxdtt =?

Q,)( dxxfdy

=∴
2

¥±s?
T9
^
f
^1M

^?WM
í
)(
,
xfy
x
=
±s?
T¥?M?
dxxfdy )(

=
~ ?yvD ?Dy
è
3
.,sin dybxey
ax
p
!
=
)(sin)(cos axdebxbxbxdedy
axax
+?=

dxaebxbdxbxe
axax
)(sincos+=

.)sincos( dxbxabxbe
ax
=
è
3
.),12sin( dyxy p
! +=
.12,sin +== xuuyQ
ududy cos=∴ )12()12cos( ++= xdx
dxx 2)12cos(?+=,)12cos(2 dxx+=
~ ?yvD ?Dy
è
3
/
?
TP
¥ ?|?A ?
a?¥f
,
P
?
T? ?,
).()()(sin)2(;cos)()1(
2
xdxdtdtd =ω=
,cos)(sin)1( tdttd ωω=ωQ
)(sin
1
cos tdtdt ω
ω
=ω∴
.cos)sin
1
( tdtCtd ω=+ω
ω

);sin
1
( td ω
ω
=
dx
x
dxxx
xd
xd
2
1
cos2
)(
)(sin
)2(
22
=Q
,cos4
2
xxx=
).()cos4()(sin
22
xdxxxxd =∴
~ ?yvD ?Dy
taú¨±s
?f
 ?
?ú¨?
á
ì9?l
ú¨±sb
)(xfy =
.
),(
2
yd
dydy
:1
¥±s¥±s'=¨±s?l1
.
1
1
ydn
yydny
n
n
¨±s:1
¥¥±s?1¨±s¥B?1
nnn
dxxfyd ))((
)(
=B?1á
ìμ
nnn
nn
dxxfydnxfy
dxdx
)()(
,)(
)(
==
=
¨±s V:1¥
V71

ZLYè:
~ ?yvD ?Dy
a9
f
9
¥í
′
,
,0)()(
00
l
H
O)¥?
? ?
x
xfxxfy


=
è
,05.0
,10

9v

 D
ü
??
%é
 D
ü¥á
?
F £a??
3
,
2
rA π=
!
.05.0,10 D
ü D
ü =?= rr
rrdAA=≈?∴ π2 05.0102 ××π=
).(
2
D
üπ=
.)(
0
xxf

=
00
xxxx
dyy
==
≈?
?a±s¥?¨
~ ?yvD ?Dy
a9
f
¥í
′;)(.1
0
?í¥í
′? p xxxf =
)()(
00
xfxxfy+=?,)(
0
xxf


.)()()(
000
xxfxfxxf

+≈?+
)(l
Hx?
è
.0360cos
o
¥í
′9

3,cos)( xxf =
! )(,sin)( 1xxxf?=


,
360
,
3
0
π
=?
π
= xxQ
~ ?yvD ?Dy
.
2
3
)
3
(,
2
1
)
3
(?=
π

=
π
∴ ff
)
3603
cos(0360cos
o
π
+
π
=


3603
sin
3
cos
π
π
π

3602
3
2
1 π
=
.4924.0≈;0)(.2 ?í¥í
′? p =xxf
.)0()0()( xffxf?

+≈∴
,)()()(
000
xxfxfxxf

+≈?+Q
.,0
0
xxx =?=
7
~ ?yvD ?Dy
è¨í

T
)(l
Hx
.)1ln()5(;1)4();(tan)3(
);(sin)2(;
1
11)1(
xx
xexxx
xxxx
n
x
x
n
≈+
+≈≈
≈+≈+
1
1
£
ü,1)()1(
n
xxf +=
!
,)1(
1
)(
1
1
+=

n
x
n
xf
.
1
)0(,1)0(
n
ff =

=
xffxf )0()0()(

+≈∴
.1
n
x
+=
~ ?yvD ?Dy
è
.9
/
ò
¥í
′
3
.)2(;5.998)1(
03.0
3
e
33
5.110005.998)1(?=
3
)
1000
5.1
1(1000?=
3
0015.0110?=
)0015.0
3
1
1(10 ×?≈,995.9=
03.01)2(
03.0

e
.97.0=
~ ?yvD ?Dy
aμ9
???
N ¥úa?
¥Hq?
¥ZE
?ò?y
í¥?Y?¤¥
aa{μμ
7? {μμ¥
9
¤¥2T9μ
μá
ìü
?S W¤?
μ,
?l
.,
,
¥ 'μ?S
*
1
¥í
′ ?T
?
¥ú′1
aaAa
A
.¥Mμ?S¥1′7 'μD a
a
aA
a
ù5,
L=yT?, 'μDMμíE p¤?
~ ?yvD ?Dy
÷E|μ ??
B?S?
=
.
,
,
,
,,
¥MμK
?S?
7¥ 'μK?S?

*

'???
¥μ??V
?¤
¥í
′
^ ?T
?
¥ú′
^
A
a
A
aA
aA
A
A
A
A
δ
δ
δ≤?
δ
Yèü 'μKDMμKe?1 '
μ D Mμ,
~ ?yvD ?Dy
è
.
,,005.041.2
μi9 'μDM
p
¥

ü?Z?Hé1 ±
3 5
1
!?Z?Hé1,,yx
.
2
xy =
,41.2
H? =x ).(8081.5)41.2(
22
my ==
41.241.2
2
==
=

xx
xy
.82.4=
,005.0=
x
δHé¥ 'μ1Q
005.082.4 ×=∴
y
δ
¥ 'μ1
).(0241.0
2
m=
y
y
δ
¥Mμ1∴
8081.5
0241.0
= %.4.0≈
~ ?yvD ?Dy
?al2
±sD
13 %¥
 ?ù5,
f
¥M
qù5
f
¥9
ù5 ±s¥à
Q
?
¥à
Q
p?
D±s¥ZE,?S ±sE,
ù?±sED?
?
# ?¨¥ SD,?
S ±sD,
?
D±s¥ ó",, V± V
?
?
~ ?yvD ?Dy
?
D±s¥ uY,
.,,
,))((
),()(.1
000
00
^í kl
L=
¥?l×
^
¥L?f
^7±s
)¥?
^B??
?f
R
xxxxxfdy
xfxxf


=

))((limlim
00
00
xxxfdy
xxxx

=
→→
Q
.0=
.
))(,()()(
)(,))(,(
)()(,.2
0
000
000
0
¥:US9
LZ??
)¥ M?
^ wL
7±s) ML¥|
q?

^ wLV+il
 ? A
x
xfxxfyxx
xfdyxfx
xfyxf
=?

=
=

?
~ ?yvD ?Dy

9
¥'
T
.)0()0()( xffxf?

+≈
00
xxxx
dyy
==
≈?,)(
0
xxf

=
),()()()(
000
xxxfxfxf

+≈
,l
H? x?
,0
H? =x