Tiểu luận môn phương pháp tính Phương Trình Phi Tuyến

Bài Tập Lớn Phng Pháp Tính
Nhóm 3
          


Cơ sở lí thuyết

α
−A

≤

α
∆


A
A
α
α
−
=∂
Đề bài
  !
"#$

α
%&'()*(&)
α
∆
%+)*,

3
10
−
"$
α
%)(&+-)
α
∂
%.)*'/
Bài làm

#$012&3'3(3*
45(06
$
α
∂
%.)*'/

⇒

α
∆
%
α
∂
6
a
%.)*'6)(&+-6
2
10

−
%.)7'(&-'6
2
10
−
0122(
Phương Pháp Tính Page 1
Bài Tập Lớn Phng Pháp Tính
Nhóm 3
45*06
          


Cơ sở lí thuyết
 !
8 9:",$%.5;<,
x
=>1;
[ ]
ba;
2
0)()(
<
bfaf
6?@&2
0
x
12A;0!B
[ ]
00

;ba
6C<
)(
0
xf
6D
0)(
0
=xf
9
0
x
<12;2E9FG1B6DH1B,8FI!
)(
0
xf
6D
0)()(
00
<afxf
)@
0101
, xbaa ==
6D
0)()(
00
<bfxf
)@
0101
, bbxa ==

6DH
[ ] [ ]
0011
;; baba ⊂
2JF2
22
0
111
ab
d
abd
−
==−=
6C KE9L
n
1M)H=
E>
2,1,0
{
,
2
,
2
0)()(
=∀
≤
+
=≤≤≤
−
=−=<

n
n
nn
nnnn
n
n
nnnn
b
ba
xabxa
ab
abdbfaf
"#$ 
).(xgx =
Phương Pháp Tính Page 2
Bài Tập Lớn Phng Pháp Tính
Nhóm 3
N5;! 9OHP12A;#IJ!2;
)(xg
6
P;J#M
[ ]
bax ;
0
∈
QR6FSFT1@ 
∞
=1
}{
nn

x
ULV
1@ 
, 3,2,1)(
1
=∀=
−
nxgx
nn
%&'(%
W>X
)(xf
5B2;I 1YK2B2;
)(xf
′
2
)(xf
′′
=LZFI=>1;
[ ]
ba;
V;<,
x
6D
)(xh
122;==L[;P
[ ]
bax ;∈
)9 9
0)(

=
xf

[ ]
ba;
\
[ 9
)()()( xfxhxxgx
−==
]\^;
)(xh

( )
0
=
′
xg
6C5
)()()()(1)( xfxhxfxhxg
′
−
′
−=
′
42G_=
( )
0
=
′
xg

[
( )
0=xf
H
( )
( )
xf
xh
′
=
1
6`2;
)(xh
>
Ia;T_=212
)(
1
)(
xf
xh
′
=
2]LV1@ 
, 3,2,1
)(
)(
1
1
1
=∀

′
−=
−
−
−
n
xf
xf
xx
n
n
nn
Bài Tập
&C9;0=>1;S! 9
Phương Pháp Tính Page 3
Bài Tập Lớn Phng Pháp Tính
Nhóm 3
"$ 
;014
4
=+− xx
"#$
;023
2
=−+− xxe
x
"$
;0132cos
2
=−+− xxxx

"F$
;01sin4 =−+ xx
"U$
;01
2
=−−
− x
ex
":$
;0824
234
=−+− xxx
"$
;0
2
=+− xxe
x
"$
;0ln3
2
=+ xx
Phương Pháp Tính Page 4
*XFK   L^;;M]b1M1 V'
)(
5
x
!
9
0cos =− xx


[ ]
1;0
6XFKLVZE)
c!52[cLV! 
 L
)*+
&
$
014
4
=+− xx
45=>1;12
[ ]
1;0
2
[ ]
2;1
6
#$
023
2
=−+−
xxe
x
x
2
−
1−
0
1

2
)(xf
86,11−
63,9
−
1
72,2
39,7
4=>1;12
[ ]
1;0
6
$
0132cos
2
=−+− xxxx
4=>1
;12
[ ]
1;0
2
[ ]
2;1
6
x
2
−
1
−
0

1
2
)(xf
25
6
1
2−
9
x
2−
1
−
0
1
2
3
)(xf
17,14
−
54,6
−
1
−
54,0
83,3
−
97,12
−
F$
01sin4 =−+ xx

4=>1
;12
[ ]
0;1−
2
[ ]
3;2
6
U$
01
2
=−−
−
x
ex

4=>1;12.2
[ ]
1;5,0
6
:$
0824
234
=−+−
xxx

4=>1;12
[ ]
1;2
−−

2
[ ]
4;3
6
$
0
2
=+−
xxe
x
x
2
−
1−
0
1
2
)(xf
86,11−
63,9
−
1
72,2
39,7
4=>1;12
[ ]
0;1−
6
$
0ln3

2
=+
xx

x
2−
1
−
0
1
2
3
4
)(xf
64,0
−
36,1
−
1
36,3
64,2
43,1
−
03,6
−
x
2
−
1−
0

5,0
1
2
)(xf
6,51−
39,5
−
0
13,0
35,1−
02,1−
x
2−
1
−
0
1
2
3
4
)(xf
48
1−
8
9
−
16−
17
−
24

x
1,0
2,0
3,0
4,0
5,0
6,0
)(xf
2
−
49,1
−
93,0
−
44,0
−
06,0
57,0
4=>1;12
[ ]
5,0;4,0
6
*

[ ]
1;00cos
=−
xx
?@


5,0
2
1
2
1;0
00
0
00
==
+
=
==
ba
x
ba
C5

0)().(
46,0)1(
1)(
17,0)5,0cos(5,0)(
00
0
0
<⇒
=
−=
−=−=
bfxf
f

af
xf
?@

0)().(
13,0)75,0(
75,0
2
15,0
1
5,0
11
1
1
1
<⇒
=
=
+
=
=
=
xfaf
f
x
b
a
?@

02,0)(

625,0
2
5,075,0
75,0
5,0
2
2
2
2
−=
=
+
=
=
=
xf
x
b
a
4
0)().(
22
<bfxf
?@

0)().(
06,0)6875,0(
6875,0
2
75,0625,0

75,0
625,0
33
3
3
3
<⇒
=
=
+
=
=
=
xfaf
f
x
b
a
?@

0)().(
02,0)65625,0(
65625,0
2
6875,0625,0
6875,0
625,0
44
4
4

4
<⇒
=
=
+
=
=
=
xfaf
f
x
b
a
?@

3
3
5
5
10.33,1)640625,0(
640625,0
2
65625,0625,0
65625,0
625,0
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a_=
"$ 
)(xg
5B2;I 1YKYB
[ ]
ba,
6
"#$ CY;oB
[ ]
1
;
+kk
xx

)
1, ,1,0
−=
nk
)
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k
≡
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kkk
yxfxg == )()(
)
nk , ,1,0
=∀
Bài Tập
#>!2;
)(xf
6XFKVJkU
cM]!2;B
∗
x
6[<,6
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x
0
25,0
5,0
1
y

1
1892,1
4142,1
2
4[
x
xfx 2)(,37,0 ==
∗
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x
1,8
3,8
6,8
7,8
y
944,16
565,7,1
505,18
821,18
4[
xxxfx ln)(,4,8 ==
∗
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x
1,0
2,0
3,0
4,0
y
6205,0

−
2840,0
−
0066,0
2484,0
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132cos)(,25,0
2
−+−==
∗
xxxxxfx
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x
0
25,0
5,0
1
y
1
1892,1
4142,1
2
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x
xfx 2)(,37,0 ==
∗
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)5,01)(25,01)(01(

)25,0)(25,0)(0(
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231303
210
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3
321202
310
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3
312101
320
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3
302010
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3
−−−
−−−
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−−−
−−−
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−−−
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−−−
=
−−−
−−−
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xxxxxx
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xxx
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k
k
k
nn
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0
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2).(4142,1).(1892,1).(1).(
)()()()()(
)3(
3
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3
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3
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3
3
)3(
32
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31
)1(
30
)0(
33
xPxPxPxP
yxPyxPyxPyxPxL
+++=
+++=
4[
)37,0(2)(~)(
33
LxLxf
x
=⇒
∗

;2
292295827,1
2.
375,0
)5,037,0)(25,037,0(37,0
4142,1.
0625,0
)137,0)(25,037,0(37,0
1892,1.
046875,0
)137,0)(5,037,0(37,0
1.
125,0
)137,0)(5,037,0)(25,037,0(
)37,0(
3
=
−−
+
−
−−
+
−−
+
−
−−−
=L
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
537,0

3
10.79,5292295827,12)37,0(2
−
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L
x
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x
1,8
3,8
6,8
7,8
y
944,16
565,7,1
505,18
821,18
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xxxfx ln)(,4,8 ==
∗
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)6,8)(3,8)(1,8(
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)(
)7,86,8)(3,86,8)(1,86,8(
)7,8)(3,8)(1,8(
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)7,83,8)(6,83,8)(1,83,8(
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3
321202
310
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3
312101
320
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3
302010
321
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3
−−−
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=
n
k
k
k
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)()()()()(
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3
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3
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3
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3
3
)3(
32
)2(
31
)1(
30
)0(
33
xPxPxPxP
yxPyxPyxPyxPxL
+++=
+++=
4[
xxLxLxf ln)4,8()(~)(
33
=⇒
∗
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877,17
821,18.
024,0
)6,84,8)(3,84,8)(1,84,8(
505,18.
015,0
)7,84,8)(3,84,8)(1,84,8(
565,17.

024,0
)7,84,8)(6,84,8)(1,84,8(
944,16.
06,0
)7,84,8)(6,84,8)(3,84,8(
)4,8(
3
=
−−−
+
−
−−−
+
−−−
+
−
−−−
=L
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5
3
10.64,4877,17)4,8ln(4,8)4,8(ln
−
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x
1,0
2,0
3,0

4,0
y
6205,0
−
2840,0
−
0066,0
2484,0
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132cos)(,25,0
2
−+−==
∗
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)3,0)(2,0)(1,0(
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))()((
)(
)4,03,0)(2,03,0)(1,03,0(
)4,0)(2,0)(1,0(
))()((
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)(
)4,02,0)(3,02,0)(1,02,0(
)4,0)(3,0)(1,0(
))()((
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))()((
))()((
)(
231303
210
)3(
3
321202
310
)2(
3
312101
320
)1(
3
302010
321
)0(
3
−−−
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=
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−−−

−−−
=
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)()()()()(
)3(
3
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3
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3
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3
3
)3(
32
)2(

31
)1(
30
)0(
33
xPxPxPxP
yxPyxPyxPyxPxL
++−+−=
+++=