5 5 B Z M P S
T
1. f
? ?¨?′? ?£
üiyxyxf cossin),( = )1,0(∈θ
P¤
6
sin
3
sin
66
cos
3
cos
34
3 πθπθππθπθπ
?= b
£
!
00
(, )(0,0),( , )(,)
36
xy xy
π π
=??=f
? yxyxf cossin),( = ?¨±s
?′? ?
'
H¥ Taylor
T V?i0k = )1,0(∈θ
P¤
3
(,) (0,0)
436
ff
π π
=?= (, ) (, )
xy
f xyxf xyyθ θθθ? ??+ ? ??
cos cos sin sin
33 6636
π πθ πθ π πθ πθ
=? b
2. f
? ? ¥ Taylor
Z 7
T b
986223),(
2233
+????+= yxxyyxyxyxf )2,1(
3
33 2
( , ) 3[( 1) 1] [( 2) 2] 2[( 1) 1] [( 2) 2]fxy x y x y=?++?+??+ ?+
2
2[( 1) 1][( 2) 2]xy??+ ?+ 6[( 1) 1] 8[( 2) 2] 9xy? ?+? ?++
22
14 13( 1) 6( 2) 5( 1) 12( 1)( 2) 4( 2)xyx xy y=? ? ? ? ? + ? ? ? ? + ?
3223
)2()2)(1(2)2()1(2)1(3 ?+???????+ yyxyxx b
? '59 V
! ?
^ 1, 2ux vy=? =?
(, ) ( 1, 2)fxy fu v=++
33 2 2
3(1)(2)2(1)(2)2(1)(2)6(1)8(2)uv uv uv uv=+++?+ +?++?+?++9
Z 7a¨ }Dí ? b 1, 2ux vy=? =?
3. pf
? ?¥ Taylor Z 7
T
Z 7??¨
?
?1? b
)1ln(sin),( yxyxf += )0,0(
3
323
33
(,)( ()( ())
62
xyy
f xy x ox y oy=?+ ?++
( )
222
1
()
2
xy xy o x y=? + +
3
b
4. pf
? ?¥ ¨ TaylorZ 7
Ti?[ b
yx
yxf
+
= e),( )0,0( n
3
n
n
Ryx
n
yxyxyxf ++++++++= )(
!
1
)(
!2
1
)(1),(
2
" ,
1
?
)(1
)(
)!1(
1
yxn
n
eyx
n
R
++
+
+
=
θ
b
5.
! 0,
cos
),( >= x
x
y
yxf b
1 p ?¥ Taylor Z 7
T
Z 7?=¨?
? i
9
??[
),( yxf )0,1(
2
R
2 p ?¥ k¨ TaylorZ 7
T i£
ü ?¥
?
5×=?[
?@?
),( yxf )0,1( )0,1(
k
R ∞→k
H b 0→
k
R
3
1
2
22
2
1
)1()1(1),( Ryxxyxf +??+??=
3
2
1
(1) (1(1),
3!
)R xyfx
xy
yθ θ
????
=?+ +?
??
??
??
32 2
43 2
cos sin cos sin
(1) (1) (1)
26
3
x xy xy y
η ηη
ξξ ξ
=? ?? ?+ ?+
η
ξ
? )1(1 ?+= xθξ yθη = 10 <<θ b
2
∑∑
=
??
=
+???+=
n
j
k
jjnjnj
n
k
n
Ryx
j
jnC
n
yxf
01
])1)(
2
cos()!()1(
!
1
[1),( π
∑
+
=
?+
+?
?+
+
?+?+?
+
=
1
0
1
2
1
1
)1)(
2
cos(
1
)!1()1(
)!1(
1
k
j
jjk
jk
jkj
kk
yx
j
jkC
k
R πη
ξ
b
?
H1=x 1=ξ ?i ),( +∞?∞∈y 0→
k
R )( ∞→k A?? ?
?
3
1
|1|0 <?< x
H
3
4
3
2
<<ξ
2
11
<
?
ξ
x
?
^?i ),( +∞?∞∈y μ
∑
+
=
?+
+?
??+
?+
+
+
≤
1
0
1
2
|||1|
||
1
)!1(
)!1(!
)!1(
)!1(
1
||
k
j
jjk
jk
k
yxjk
jkj
k
k
R
ξ
j
jk
k
j
y
x
j
?+
+
=
∑
?
=
1
1
0
1
!
11
ξξ
j
j
k
x
y
j
x
∑
∞
=
+
?
?
≤
0
1
1!
111 ξ
ξξ
1
1
11
?
+
?
=
x
yk
e
x
ξ
ξξ
yN9? ?
b 0→
k
R ∞→k
6. ?¨ Taylor
Tí
?9
?
Z 7?=¨?
? b
03.2
96.8
3 I
n
2
(, ) (9 )
y
f xy x
+
=+ (0 ?¥ Taylor
T : ,0)
222
2
81
( , ) 81 18 81ln 9 (9 18ln 9) ln 9 ( , )
2
f xy x y x xy y R xy=+ + +++ + +
?
^
03.2
96.8 = (0.04,0.03)f ? 81 18( 0.04)≈+? +81ln9 0.03?
2
22
+(-0.04) +(9+18ln9) (-0.04) 0.03+81/2 ln (9) 0.03?? ??
2
≈85.74 b
7
! ),( yxf
2
R
V±