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Mtodo de NewtonFormula
n Newton Error abs Error Relativo
Po= 0 1.000000000000000
1 3.500000000000000 2.50000E+00 7.14286E-01
2 2.607142857142860 -8.92857E-01 -3.42466E-01
3 2.454256360078280 -1.52886E-01 -6.22944E-02
4 2.449494371606970 -4.76199E-03 -1.94407E-03
5 2.449489742787550 -4.62882E-06 -1.88971E-06
6 2.449489742783180 -4.37383E-12 -1.78561E-12
7 2.449489742783180 0.00000E+00 0.00000E+00
8 2.449489742783180 0.00000E+00 0.00000E+00
9 2.449489742783180 0.00000E+00 0.00000E+00
10 2.449489742783180 0.00000E+00 0.00000E+00
11 2.449489742783180 0.00000E+00 0.00000E+00
12 2.449489742783180 0.00000E+00 0.00000E+00
13 2.449489742783180 0.00000E+00 0.00000E+00
14 2.449489742783180 0.00000E+00 0.00000E+00
15 2.449489742783180 0.00000E+00 0.00000E+0016 2.449489742783180 0.00000E+00 0.00000E+00
17 2.449489742783180 0.00000E+00 0.00000E+00
18 2.449489742783180 0.00000E+00 0.00000E+00
19 2.449489742783180 0.00000E+00 0.00000E+00
20 2.449489742783180 0.00000E+00 0.00000E+00
21 2.449489742783180 0.00000E+00 0.00000E+00
22 2.449489742783180 0.00000E+00 0.00000E+00
23 2.449489742783180 0.00000E+00 0.00000E+00
24 2.449489742783180 0.00000E+00 0.00000E+00
25 2.449489742783180 0.00000E+00 0.00000E+0026 2.449489742783180 0.00000E+00 0.00000E+00
27 2.449489742783180 0.00000E+00 0.00000E+00
28 2.449489742783180 0.00000E+00 0.00000E+00
29 2.449489742783180 0.00000E+00 0.00000E+00
30 2.449489742783180 0.00000E+00 0.00000E+00
31 2.449489742783180 0.00000E+00 0.00000E+00
32 2.449489742783180 0.00000E+00 0.00000E+00
33 2.449489742783180 0.00000E+00 0.00000E+00
!2"6( =!# =( 2
)('
)(
1
11
=
n
nnn
pf
pfpp
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34 2.449489742783180 0.00000E+00 0.00000E+00
35 2.449489742783180 0.00000E+00 0.00000E+00
36 2.449489742783180 0.00000E+00 0.00000E+00
37 2.449489742783180 0.00000E+00 0.00000E+00
38 2.449489742783180 0.00000E+00 0.00000E+00
39 2.449489742783180 0.00000E+00 0.00000E+00
40 2.449489742783180 0.00000E+00 0.00000E+0041 2.449489742783180 0.00000E+00 0.00000E+00
42 2.449489742783180 0.00000E+00 0.00000E+00
43 2.449489742783180 0.00000E+00 0.00000E+00
44 2.449489742783180 0.00000E+00 0.00000E+00
45 2.449489742783180 0.00000E+00 0.00000E+00
46 2.449489742783180 0.00000E+00 0.00000E+00
47 2.449489742783180 0.00000E+00 0.00000E+00
48 2.449489742783180 0.00000E+00 0.00000E+00
49 2.449489742783180 0.00000E+00 0.00000E+00
50 2.449489742783180 0.00000E+00 0.00000E+0051 2.449489742783180 0.00000E+00 0.00000E+00
52 2.449489742783180 0.00000E+00 0.00000E+00
53 2.449489742783180 0.00000E+00 0.00000E+00
54 2.449489742783180 0.00000E+00 0.00000E+00
55 2.449489742783180 0.00000E+00 0.00000E+00
56 2.449489742783180 0.00000E+00 0.00000E+00
57 2.449489742783180 0.00000E+00 0.00000E+00
58 2.449489742783180 0.00000E+00 0.00000E+00
59 2.449489742783180 0.00000E+00 0.00000E+00
60 2.449489742783180 0.00000E+00 0.00000E+00
61 2.449489742783180 0.00000E+00 0.00000E+00
62 2.449489742783180 0.00000E+00 0.00000E+00
63 2.449489742783180 0.00000E+00 0.00000E+00
64 2.449489742783180 0.00000E+00 0.00000E+00
65 2.449489742783180 0.00000E+00 0.00000E+00
66 2.449489742783180 0.00000E+00 0.00000E+00
67 2.449489742783180 0.00000E+00 0.00000E+00
68 2.449489742783180 0.00000E+00 0.00000E+00
69 2.449489742783180 0.00000E+00 0.00000E+00
70 2.449489742783180 0.00000E+00 0.00000E+00
71 2.449489742783180 0.00000E+00 0.00000E+00
72 2.449489742783180 0.00000E+00 0.00000E+00
73 2.449489742783180 0.00000E+00 0.00000E+00
74 2.449489742783180 0.00000E+00 0.00000E+00
75 2.449489742783180 0.00000E+00 0.00000E+00
76 2.449489742783180 0.00000E+00 0.00000E+00
77 2.449489742783180 0.00000E+00 0.00000E+00
78 2.449489742783180 0.00000E+00 0.00000E+00
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79 2.449489742783180 0.00000E+00 0.00000E+00
80 2.449489742783180 0.00000E+00 0.00000E+00
81 2.449489742783180 0.00000E+00 0.00000E+00
82 2.449489742783180 0.00000E+00 0.00000E+00
83 2.449489742783180 0.00000E+00 0.00000E+00
84 2.449489742783180 0.00000E+00 0.00000E+00
85 2.449489742783180 0.00000E+00 0.00000E+0086 2.449489742783180 0.00000E+00 0.00000E+00
87 2.449489742783180 0.00000E+00 0.00000E+00
88 2.449489742783180 0.00000E+00 0.00000E+00
89 2.449489742783180 0.00000E+00 0.00000E+00
90 2.449489742783180 0.00000E+00 0.00000E+00
91 2.449489742783180 0.00000E+00 0.00000E+00
92 2.449489742783180 0.00000E+00 0.00000E+00
93 2.449489742783180 0.00000E+00 0.00000E+00
94 2.449489742783180 0.00000E+00 0.00000E+00
95 2.449489742783180 0.00000E+00 0.00000E+0096 2.449489742783180 0.00000E+00 0.00000E+00
97 2.449489742783180 0.00000E+00 0.00000E+00
98 2.449489742783180 0.00000E+00 0.00000E+00
99 2.449489742783180 0.00000E+00 0.00000E+00
100 2.449489742783180 0.00000E+00 0.00000E+00
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Mtodo de la secante
Formula
E$em%lo
n Secante Error abs
Po= 0.5 0 3.000000000000000
P1= Pi&4 1 2.000000000000000 -1.000000E+00
2 2.400000000000000 4.000000E-01
3 2.454545454545450 5.454545E-02
4 2.449438202247190 -5.107252E-03
Secante
!2"6( =
)()(
))((
21
2111
=
nn
nnnnn
pfpf
pppfpp
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Formula
E$em%lo
Error Relativo Po= 0.5
P1= Pi&4
-5.000000E-01 0 * 1
1.666667E-01 1 * 2
2.222222E-02 1 * 3
-2.085071E-03
La parte (a) es as cercana al !alor correcto
'e(a)te
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Mtodo de la "alsa pos#c#$n
n %alsa pos#c#$n &n0 3.000000000000000
1 3.0000000000 2.000000000000000
2 3.0000000000 2.400000000000000
3 3.0000000000 2.444444444444440
4 3.0000000000 2.448979591836730
'art #tl
P)
!2"6( =
)()(
))((
21
211
1
=
nn
nnn
nnpfpf
pppfpp
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*rror a+s *rror ,elat#!o %(&n) %(&n)-%(&n1)
-3.9900E+00
-1.000000E+00 -5.000000E-01 -2.4161E+00 9.6404E+00
4.000000E-01 1.666667E-01 -3.1374E+00 7.5804E+00
4.444444E-02 1.818182E-02 -3.2111E+00 1.0075E+01
4.535147E-03 1.851852E-03 -3.2186E+00 1.0335E+01
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Mtodo de Newton o)ver,e)(ia (uartiFormula &ara ceros de /lt#p
E$em%lo
n Newton Error abs Error Relativo
Po= 0 2.500000000000000
1 2.714285714285710 2.14286E-01 7.89474E-02
2 2.690951516722840 -2.33342E-02 -8.67136E-03
3 2.690647499256890 -3.04017E-04 -1.12990E-04
4 2.690647448028620 -5.12283E-08 -1.90394E-08
5 2.690647448028620 0.00000E+00 0.00000E+006 2.690647448028620 0.00000E+00 0.00000E+00
7 2.690647448028620 0.00000E+00 0.00000E+00
8 2.690647448028620 0.00000E+00 0.00000E+00
9 2.690647448028620 0.00000E+00 0.00000E+00
10 2.690647448028620 0.00000E+00 0.00000E+00
11 2.690647448028620 0.00000E+00 0.00000E+00
12 2.690647448028620 0.00000E+00 0.00000E+00
13 2.690647448028620 0.00000E+00 0.00000E+00
14 2.690647448028620 0.00000E+00 0.00000E+00
15 2.690647448028620 0.00000E+00 0.00000E+0016 2.690647448028620 0.00000E+00 0.00000E+00
17 2.690647448028620 0.00000E+00 0.00000E+00
18 2.690647448028620 0.00000E+00 0.00000E+00
19 2.690647448028620 0.00000E+00 0.00000E+00
20 2.690647448028620 0.00000E+00 0.00000E+00
21 2.690647448028620 0.00000E+00 0.00000E+00
!3" !2"5 /14( = 2
!# =( 3!2"4
)('
)(
1
11
=
n
nnn
pf
pfpp
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a %ara (eros e multi%li(ia 1. Mtodol#c#dad aor a 1 p/ede con!erer pero no c Formula
E$em%lo
n
Po= 0
1
2
3
4
56
7
8
9
10
11
12
13
14
1516
17
18
19
20
21
= nn pp
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e Newton
Newton Error abs Error Relativo
0.700000000000000
0.739436497848058 3.94365E-02 5.33332E-02
0.739085160465107 -3.51337E-04 -4.75368E-04
0.739085133215161 -2.72499E-08 -3.68698E-08
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+000.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+000.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
0.739085133215161 0.00000E+00 0.00000E+00
"(os /0( = ( &2
!# =1 ( +(
)('
)(
1
11
n
n
pf
pf
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Mtodo de NewtonFormula
E$em%lo
n Newton Error abs Error Relativo
Po= 0
1 -7.43863E-02 -5.21785E-02
2 -2.04756E-02 -1.45719E-02
3 -5.42218E-03 -3.87378E-03
4 -1.44257E-03 -1.03168E-03
5 -3.84758E-04 -2.75242E-046 -1.02699E-04 -7.34729E-05
7 -2.74182E-05 -1.96158E-05
8 -7.32040E-06 -5.23727E-06
9 -1.95450E-06 -1.39832E-06
10 -5.21844E-07 -3.73346E-07
11 -1.39330E-07 -9.96818E-08
=l) "1+(os "1 /1.32( ( (# =1& "1 "1( ( +(
)('
)(
1
11
=
n
nnn
pf
pfpp
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Mtodo de NewtonFormula
E$em%lo
n Newton
Po= 0 1.000000000000000
1 0.914155281832543
2 0.910017665783406
3 0.910007572548888
4 0.910007572488709
5 0.910007572488709
6 0.910007572488709
7 0.910007572488709
8 0.910007572488709
9 0.910007572488709
10 0.910007572488709
11 0.910007572488709
12 0.910007572488709
" !2( =^ 3!# "( =^ 6
)('
)(
1
11
=
n
nnn
pf
pfpp
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Error abs Error Relativo n Newton
0
-8.58447E-02 -9.39061E-02 1
-4.13762E-03 -4.54674E-03 2
-1.00932E-05 -1.10914E-05 3
-6.01790E-11 -6.61302E-11 4
0.00000E+00 0.00000E+00 5
0.00000E+00 0.00000E+00 6
0.00000E+00 0.00000E+00 7
0.00000E+00 0.00000E+00 8
0.00000E+00 0.00000E+00 9
0.00000E+00 0.00000E+00 10
0.00000E+00 0.00000E+00 11
0.00000E+00 0.00000E+00 12
/01 /35
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Error abs Error Relativo
1.52136E-01 4.05464E-02
-1.87283E-02 -5.01640E-03
-3.28221E-04 -8.79223E-05
-9.93990E-08 -2.66266E-08
0.00000E+00 0.00000E+000.00000E+00 0.00000E+00
0.00000E+00 0.00000E+00
0.00000E+00 0.00000E+00
0.00000E+00 0.00000E+00
0.00000E+00 0.00000E+00
0.00000E+00 0.00000E+00
0.00000E+00 0.00000E+00
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Mtodo de la secanteFormula
n Secante Error abs
Po= -3 0 3.000000000000000
P1= -2 1 2.000000000000000 1.000000E+00
2 2.750000000000000 -7.500000E-01
3 3.066666666666670 -3.166667E-01
4 2.862024387687360 2.046423E-01
5 2.877185936462370 -1.516155E-02
6 2.879413897566940 -2.227961E-037 2.879385194736810 2.870283E-05
8 2.879385241570820 -0.000000046834011
9 2.879385241571820 -0.000000000000997
10 2.879385241571820 0.000000000000000
Secante
!3+ !2"1 /"3"2( = 3
)()(
))((
21
2111
=
nn
nnnnn
pfpf
pppfpp
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MtodoFormula
Error Relativo n
Po= 0 0
-5.000000E-01 P1= Pi&2 1
2.727273E-01 2
1.032609E-01 3
-7.150263E-02 4
5.269576E-03 5
7.737551E-04 6-9.968388E-06 7
0.000000016265281 8
0.000000000000346 9
0.000000000000000 10
'e(a)te
1= nn pp
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e la secante
Secante Error abs Error Relativo
0.000000000000000
1.570796326794900 1.570796E+00 1.000000E+00
0.916720476173219 -6.540759E-01 -7.134954E-01
0.961551326382852 4.483085E-02 4.662346E-02
0.964346085103906 2.794759E-03 2.898087E-03
0.964333884548886 -1.220056E-05 -1.265180E-05
0.964333887695219 3.146333E-09 3.262701E-090.964333887695223 3.552714E-15 3.684112E-15
0.964333887695223 0.000000000000000 0.000000000000000
0 &0 &0
0 &0 &0
Secante
'e(a)te
"08"0 /0( = 2( &2
)()(
))((
21
211
nn
nnn
pfpf
pppf
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Mtodo de la "alsa pos#c#$nFormula
n %alsa pos#c#$n &nPo= -2 0
P1= -3 1
0 * 1 2 -3.0000000000
1 * 2 3 -3.0000000000
1 * 3 4 -3.0000000000
4 * 1 5 -3.0000000000
5 * 1 6 -3.0000000000
6 * 1 7 -3.0000000000
7 * 1 8
9
!3+ !2"1 /"3"2( = 3
)()(
))((
21
211
1
=
nn
nnn
nnpfpf
pppfpp
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*rror a+s *rror ,elat#!o %(&n) %(&n)-%(&n1)
3.0000E+00
-1.000000E+003.333333E-01 -1.0000E+00 -3.0000E+00
2.500000E-01 -9.090909E-02 8.9063E-01 -8.9063E-01
-1.177686E-01 4.106628E-02 8.7484E-02 7.7915E-02
-1.063750E-02 3.695623E-03 7.4324E-03 6.5022E-04
-8.970698E-04 3.115579E-04 6.2341E-04 4.6334E-06
-7.519640E-05 2.611550E-05 5.2233E-05 3.2562E-08
-6.300106E-06 2.188004E-06 4.3760E-06 2.2857E-10
-5.278131E-07 1.833076E-07 3.6662E-07 1.6043E-12
-4.421921E-08 1.535717E-08 3.0714E-08 1.1260E-14
&n
P)
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Mtodo de la "alsa pos#c#Formula
n %alsa pos#c#$Po= 0.5 0
P1= Pi&4 1
0 * 1 2 1.5707963268
1 * 2 3 1.5707963268
1 * 3 4 1.5707963268
4 * 1 5 1.5707963268
5 * 1 6 1.5707963268
6 * 1 7 1.5707963268
7 * 1 8
9
"08"0 /0( = 2( &2
()(
)((
21
11
1
=
nn
nnn
nnpfpf
pppfpp
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n
&n *rror a+s *rror ,elat#!o %(&n)
0.000000000000000 -8.0000E-01
1.570796326794900 1.570796E+00 1.000000E+00 5.7080E-01
0.916720476173219 -6.540759E-01 -7.134954E-01 -4.2002E-02
0.961551326382852 4.483085E-02 4.662346E-02 -2.4647E-03
0.964170772570201 2.619446E-03 2.716787E-03 -1.4452E-04
0.964324324214020 1.535516E-04 1.592324E-04 -8.4733E-06
0.964333326980445 9.002766E-06 9.335741E-06 -4.9680E-07
0.964333854820035 5.278396E-07 5.473619E-07 -2.9128E-08
0.964333885767722 3.094769E-08 3.209229E-08 -1.7078E-09
0.964333887582212 1.814489E-09 1.881599E-09 -1.0013E-10
&n
P)
)
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%(&n)-%(&n1)
-4.5664E-01
-2.3974E-02
1.0352E-04
3.5620E-07
1.2246E-09
4.2095E-12
1.4471E-14
4.9744E-17
1.7100E-19
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Mtodo de la secanteFormula
n Secante Error abs
0 1.000000000000000
1 2.000000000000000 1.000000E+00
2 0.774600326439436 -1.225400E+00
3 0.617356509651259 -1.572438E-01
4 0.281621814892654 -3.357347E-01
5 0.119175588559544 -1.624462E-01
6 0.027908311035698 -9.126728E-027 0.003096144054368 -2.481217E-02
8 0.000085084782508 -0.003011059271860
9 0.000000263016187 -0.000084821766320
10 0.000000000022378 -0.000000262993810
11 0.000000000000000 -0.000000000022378
12 0.000000000000000 0.000000000000000
Secante
= /12( 3^
)()(
))((
21
211
1
=
nn
nnn
nnpfpf
pppfpp
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Mtodo de la "alsa pos#c#$n
Formula
n %alsa pos#c#$nPo= 0.5 0
P1= Pi&4 1
0 * 1 2 2.0000000000
1 * 2 3 2.0000000000
1 * 3 4 2.0000000000
4 * 1 5 2.00000000005 * 1 6 2.0000000000
6 * 1 7 2.0000000000
7 * 1 8
9
Mtodo de NewtonFormula
n Newton Error absPo= 0 1.000000000000000
1 0.500000000000000 -5.00000E-01
2 0.166666666666667 -3.33333E-01
3 0.023809523809524 -1.42857E-01
4 0.000553709856035 -2.32558E-02
5 0.000000306424934 -5.53403E-04
6 0.000000000000094 -3.06425E-07
7 0.000000000000000 -9.38962E-14
= /12( 3^
!# = +3( 3^ ^
)()(
))((
21
211
1
=
nn
nnn
nnpfpf
pppfpp
)('
)(
1
11
=
n
nnn
pf
pfpp
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8 0.000000000000000 -8.81000E-27
9 0.000000000000000 0.00000E+00
10 0.000000000000000 0.00000E+00
11 0.000000000000000 0.00000E+00
12 0.000000000000000 0.00000E+00
13 0.000000000000000 0.00000E+00
14 0.000000000000000 0.00000E+00
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MtodoFormula
Error Relativo n
0
5.000000E-01 1
-1.581977E+00 2
-2.547050E-01 3
-1.192147E+00 4
-1.363083E+00 5
-3.270254E+00 6-8.013893E+00 7
-35.388928350250200 8
-322.496372381404000 9
-11752.484524752700000
-3802046.854950870000000
-44687441574.869600000000000
'e(a)te
1= nn pp
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&n *rror a+s *rror ,elat#!o
1.000000000000000
2.000000000000000 1.000000E+00 5.000000E-01
0.774600326439436 -1.225400E+00-1.581977E+00
0.617356509651259 -1.572438E-01 -2.547050E-01
0.501277751750407 -1.160788E-01 -2.315657E-01
0.412376223639335 -8.890153E-02 -2.155835E-010.342518225243719 -6.985800E-02 -2.039541E-01
0.286583508464352 -5.593472E-02 -1.951777E-01
0.241155755655092 -4.542775E-02 -1.883752E-01
0.203851925665223 -3.730383E-02 -1.829947E-01
0.000000000000000 -2.038519E-01
0
0
0
Formula
Error RelativoPo=
-1.00000E+00
-2.00000E+00
-6.00000E+00
-4.20000E+01
-1.80600E+03
-3.26344E+06
-1.06579E+13
-
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&0
&0
&0
&0
&0
&0
&0
-
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e la secante
Secante Error abs Error Relativo
0.000000000000000
1.000000000000000 1.000000E+00 1.000000E+00
1.822531188035290 8.225312E-01 4.513125E-01
1.177094755137110 -6.454364E-01 -5.483301E-01
1.224384519298240 4.728976E-02 3.862329E-02
1.240229087599910 1.584457E-02 1.277552E-02
1.239710599680350 -5.184879E-04 -4.182330E-041.239714696887490 4.097207E-06 3.304960E-06
1.239714697975220 0.000000001087726 0.000000000877400
1.239714697975220 0.000000000000000 0.000000000000000
Secante
= + /01( 2 3( ^
)()(
))((
21
211
nn
nnn
pfpf
pppf
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Mtodo de la
Formula
n
0
1
0 * 1 2
1 * 2 3
1 * 3 4
4 * 1 55 * 1 6
6 * 1 7
7 * 1 8
9
Mtodo de Newton
n Newton Error abs0 1.000000000000000
1 1.278356474963380 2.78356E-01
2 1.240458501586290 -3.78980E-02
3 1.239714983300630 -7.43518E-04
4 1.239714697975260 -2.85325E-07
5 1.239714697975220 -4.21885E-14
6 1.239714697975220 0.00000E+00
7 1.239714697975220 0.00000E+00
!# =2 "3'e)( ^
= + /01( 2 3( ^
(
(1 =
n
nnf
pfpp
)('
)(
1
11
=
n
nnn
pf
pfpp
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8 1.239714697975220 0.00000E+00
9 1.239714697975220 0.00000E+00
10 1.239714697975220 0.00000E+00
11 1.239714697975220 0.00000E+00
12 1.239714697975220 0.00000E+00
13 1.239714697975220 0.00000E+00
14 1.239714697975220 0.00000E+00
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'e(a)te
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alsa pos#c#$n
%alsa pos#c#$n &n *rror a+s
1.000000E+00
1.0000000000 8.225312E-01
1.0000000000 -6.454364E-01
1.0000000000 7.168360E-02
1.0000000000 -1.032424E-021.0000000000 1.436893E-03
1.0000000000 -2.009519E-04
2.808449E-05
-3.925383E-06
1.280549E-06
0
0
Error Relativo
2.17746E-01
-3.05516E-02
-5.99749E-04
-2.30154E-07
-3.40308E-14
0.00000E+00
0.00000E+00
)()
))(
21
211
nn
nn
pf
pp
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0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
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-
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*rror ,elat#!o
1.000000E+00
4.513125E-01
-5.483301E-01
5.740298E-02
-8.336396E-031.158887E-03
-1.620985E-04
2.265394E-05
-3.166361E-06
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Mtodo de la "alsa pos#c#$nFormula
n %alsa pos#c#$n &nPo= 0.5 0 1.000000000000000
P1= Pi&4 1 0.000000000000000
0 * 1 2 0.0000000000 0.020361990950226
1 * 2 3 0.0000000000 0.040691256435242
1 * 3 4 0.0000000000 0.040659237361887
4 * 1 5 0.0000000000 0.040659288396971
5 * 1 6 0.0000000000 0.0406592883156306 * 1 7 0.0000000000 0.040659288315759
7 * 1 8 0.040659288315759
9 0.040659288315759
0.040659288315759
0.040659288315759
Mtodo de la secanteFormula
n Secante Error abs Error Relativo
Po= 0 1.000000000000000P1= 1 0.000000000000000 1.000000E+00 &0
2 0.020361990950226 -2.036199E-02 1.000000E+00
3 0.040691256435242 -2.032927E-02 4.995979E-01
4 0.040659262577691 3.199386E-05 -7.868775E-04
5 0.040659288315725 -2.573803E-08 6.330173E-07
6 0.040659288315759 -3.372996E-14 8.295758E-13
7 0.040659288315759 0.000000E+00 -0.000000E+00
=23 !4+1 !3+ !2"22 "9( 0 8 9 1
)()(
))((
21
211
1
=
nn
nnn
nnpfpf
pppfpp
)()(
))((
21
211
1
=
nn
nnn
nnpfpf
pppfpp
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8 0 &0 &0
9 0 &0 &0
10 0 &0 &0
11 0 &0 &0
12 0 &0 &0
13 0 &0 &0
14 0 &0 &0
Mtodo de NewtonFormula
n Newton Error abs Error Relativo
Po= 0 0.000000000000000
1 0.040723981900453 -4.07240E-02 1.00000E+00
2 0.040659288487324 6.46934E-05 -1.59111E-03
3 0.040659288315759 1.71565E-10 -4.21957E-09
4 0.040659288315759 0.00000E+00 -0.00000E+005 0.040659288315759 0.00000E+00 -0.00000E+00
6 0.040659288315759 0.00000E+00 -0.00000E+00
7 0.040659288315759 0.00000E+00 -0.00000E+00
8 0.040659288315759 0.00000E+00 -0.00000E+00
=23 !4+1 !3+ !2"22 "9( 0 8 9 1
!# =92 !3+5 !2+1 "221( 0 4 8
)('
)(
1
11
=
n
nnn
pf
pfpp
-
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*rror a+s *rror ,elat#!o
Po= 0.5
1.000000E+00 &0 P1= Pi&4
-2.036199E-02 1.000000E+00 0 * 1
-2.032927E-02 4.995979E-01 1 * 2
3.201907E-05 -7.874981E-04 1 * 3
-5.103508E-08 1.255189E-06 4 * 1
8.134172E-11 -2.000569E-09 5 * 1-1.296463E-13 3.188602E-12 6 * 1
2.151057E-16 -5.290445E-15 7 * 1
0.000000E+00 -0.000000E+00
0.000000E+00 -0.000000E+00
0.000000E+00 -0.000000E+00
Formula
%0%1
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Formula
Po=
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n %alsa pos#c#$n &n0 0.000000000000000
1 1.000000000000000
2 1.0000000000 0.250000000000000
3 1.0000000000 0.773762765121760
4 1.0000000000 0.944885169479175
5 1.0000000000 0.961110796844463
6 1.0000000000 0.9623056624240777 1.0000000000 0.962391746837012
8 0.962397938894912
9 0.962398384238757
0.962400843606160
0.962228074514036
Mtodo de la secante
n Secante Error abs Error Relativo
0 1 1.000000E+00 1.000000E+00
2 -7.500000E-01 -3.000000E+00
3 5.237628E-01 6.769036E-01
4 -2.059181E+00 1.601954E+00
5 1.880013E+00 3.161836E+00
6 -1.999544E-01 -5.066741E-01
7 -1.063959E+00 1.589617E+00
)()(
))((
21
2111
=
nn
nnnnn
pfpf
pppfpp
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8 0.719032533167658 14.463265525623000
9 -0.070468548439889 3.395395409723210
10 -0.019981182072562 0.490512305948001
11 0.000076104653172 -0.001871768266649
12 -0.000000060072366 0.000001477457380
13 -0.000000000000187 0.000000000004605
14 0.000000000000000 0.000000000000000
Mtodo de Newton
n Newton Error abs Error Relativo
0
1 -3.50195E-02 -3.62903E-02
2 -2.56882E-03 -2.66915E-03
3 -1.33059E-05 -1.38257E-05
4 -3.55777E-10 -3.69678E-10
5 0.00000E+00 0.00000E+006 0.00000E+00 0.00000E+00
7 0.00000E+00 0.00000E+00
8 0.00000E+00 0.00000E+00
9 0.00000E+00 0.00000E+00
=23 !4+1 !3+ !2"22 "9( 0 8 9 1
!# =92 !3+5 !2+1 "221( 0 4 8
)('
)(
1
11
=
n
nnn
pf
pfpp
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*rror a+s *rror ,elat#!o
1.000000E+00 1.000000E+00
-7.500000E-01 -3.000000E+00
5.237628E-01 6.769036E-01
1.711224E-01 1.811039E-01
1.622563E-02 1.688216E-02
1.194866E-03 1.241669E-038.608441E-05 8.944841E-05
6.192058E-06 6.433989E-06
4.453438E-07 4.627438E-07
2.459367E-06 2.555450E-06
-1.727691E-04 -1.795511E-04
=23 !4+1 !3+ !2"22 "9( 0 8 9 1
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Mtodo de la secanteFormula
n Secante Error abs
Po= 0.5 0 1.000000000000000
P1= Pi&4 1 1.000000000000000 2.000000E+00
2 0.347370566912635 -1.347371E+00
3 0.071344640456353 2.760259E-01
4 0.140953090168911 2.122977E-01
5 0.097689172518305 -4.326392E-02
6 0.100935933874513 3.246761E-037 0.100998026456134 6.209258E-05
8 0.100997929682921 -9.677321E-08
9 0.100997929685749 2.828418E-12
10 0.100997929685749 0.000000E+00
=%obla(io)
2.000000000000000 8778675.80044807
=100000 +435000 "1"1564000( 0^ / (^
)()(
))((
21
2111
=
nn
nnnnn
pfpf
pppfpp
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Error Relativo
2.000000E+00
3.878770E+00
-3.868909E+00
1.506159E+00
-4.428732E-01
3.216656E-026.147900E-04
-9.581703E-07
2.800471E-11
0.000000E+00
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Mtodo de la secanteFormula
n Secante Error abs Error Relativo
Po 0
P1 1 5.000000E+00 1.000000E+00
2 6.950406E-01 1.220431E-01
3 6.787380E-01 1.064891E-01
4 1.242109E-01 1.911527E-02
5 1.456027E-02 2.235724E-03
6 2.983763E-04 4.581348E-057 6.552370E-07 1.006068E-07
8 2.895639E-11 4.446041E-12
9 0.000000E+00 0.000000E+00
10 0 &0 &0
:os os )umeros
=20 +;20 < + "15555( (
)()(
))((
21
211
1
=
nn
nnn
nnpfpf
pppfpp
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Mtodo de la secanteFormula
n Secante Error abs
Po 0
P1 1 5.000000E+00
2 -2.587805E+00
3 8.483855E-01
4 2.705428E-01
5 -4.548216E-02
6 1.500659E-037 9.759760E-06
8 -2.178421E-09
9 0.000000E+00
10 0 &0
so) a%roimaame)te 6512849 * 13487151
=20 +;20 < + "15555( (
)()(
))((
21
211
1
=
nn
nnn
nnpfpf
pppfpp
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Error Relativo
3.333333E-01
-2.084889E-01
6.397801E-02
1.999411E-02
-3.372636E-03
1.112659E-047.236339E-07
-1.615182E-10
0.000000E+00
&0
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Mtodo de NewtonFormula
n Newton Error abs Error Relativo
Po= 0 0.000000000000000
1 0.250000000000000 2.50000E-01 1.00000E+00
2 0.398639686946376 1.48640E-01 3.72867E-01
3 0.480194115423827 8.15544E-02 1.69836E-01
4 0.522966807453253 4.27727E-02 8.17885E-02
5 0.544876120719795 2.19093E-02 4.02097E-026 0.555964542595883 1.10884E-02 1.99445E-02
7 0.561542572005132 5.57803E-03 9.93340E-03
8 0.564340088372212 2.79752E-03 4.95715E-03
9 0.565740977843925 1.40089E-03 2.47620E-03
10 0.566441956135353 7.00978E-04 1.23751E-03
11 0.566792578761605 3.50623E-04 6.18608E-04
12 0.566967923456317 1.75345E-04 3.09267E-04
13 0.567055604150462 8.76807E-05 1.54625E-04
14 0.567099446584643 4.38424E-05 7.73100E-05
15 0.567121368323456 2.19217E-05 3.86544E-0516 0.567132329322772 1.09610E-05 1.93271E-05
17 0.567137809854511 5.48053E-06 9.66349E-06
18 0.567140550130898 2.74028E-06 4.83174E-06
19 0.567141920265349 1.37013E-06 2.41586E-06
20 0.567142605355333 6.85090E-07 1.20797E-06
21 0.567142947884591 3.42529E-07 6.03956E-07
22 0.567143119092528 1.71208E-07 3.01878E-07
23 0.567143204784635 8.56921E-08 1.51094E-07
24 0.567143247680440 4.28958E-08 7.56349E-08
25 0.567143269368487 2.16880E-08 3.82409E-0826 0.567143269368487 0.00000E+00 0.00000E+00
27 0.567143285992109 1.66236E-08 2.93111E-08
28 0.567143285992109 0.00000E+00 0.00000E+00
29 0.567143285992109 0.00000E+00 0.00000E+00
30 0.567143285992109 0.00000E+00 0.00000E+00
!2" ! !" /01( = 2 + 2
!# = " !" " ! +2( 2 2 2 2 !
)('
)(
1
11
=
n
nnn
pf
pfpp
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Mtodo de NewtonFormula
n Newton Error abs Error Relativo
Po= 0 0.500000000000000
1 0.352638435772713 1.47362E-01 -4.17883E-01
2 0.285436422563078 6.72020E-02 -2.35436E-01
3 0.247646487946270 3.77899E-02 -1.52596E-014 0.224739834149389 2.29067E-02 -1.01925E-01
5 0.210322220957174 1.44176E-02 -6.85501E-02
6 0.201051649286195 9.27057E-03 -4.61104E-02
7 0.195013099886463 6.03855E-03 -3.09648E-02
8 0.191047783922534 3.96532E-03 -2.07556E-02
9 0.188430335622209 2.61745E-03 -1.38908E-02
10 0.186696756659368 1.73358E-03 -9.28553E-03
11 0.185546036926585 1.15072E-03 -6.20180E-03
12 0.184781094658766 7.64942E-04 -4.13972E-03
13 0.184272107578169 5.08987E-04 -2.76215E-0314 0.183933214408090 3.38893E-04 -1.84248E-03
15 0.183707476980887 2.25737E-04 -1.22879E-03
16 0.183557070286230 1.50407E-04 -8.19400E-04
17 0.183456836674012 1.00234E-04 -5.46361E-04
18 0.183390031165168 6.68055E-05 -3.64281E-04
19 0.183345502229404 4.45289E-05 -2.42869E-04
20 0.183315818959750 2.96833E-05 -1.61924E-04
21 0.183296041121577 1.97778E-05 -1.07901E-04
22 0.183282841228857 1.31999E-05 -7.20192E-05
23 0.183274068255444 8.77297E-06 -4.78681E-0524 0.183268221090391 5.84717E-06 -3.19050E-05
25 0.183264254051164 3.96704E-06 -2.16466E-05
26 0.183261624147652 2.62990E-06 -1.43505E-05
27 0.183261624147652 0.00000E+00 -0.00000E+00
28 0.183261624147652 0.00000E+00 -0.00000E+00
29 0.183261624147652 0.00000E+00 -0.00000E+00
30 0.183261624147652 0.00000E+00 -0.00000E+00
! +3( = 6 2( !2 ! " 8 ! " 2 ( 4 2( !3 /"10
!# = ! + !( 6 6 6 2 2( !2" ! 84 4 (
)('
)(
1
11
=
n
nnn
pf
pfpp
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Newton
e>to)
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-
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-
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-
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Mtodo de NewtonFormula
n Newton Error abs Error Relativo
Po= 0
1 3.90995E-01 -1.85393E-01
2 2.98820E-01 -1.65077E-01
3 2.19618E-01 -1.38075E-01
4 1.47875E-01 -1.02499E-01
5 8.03202E-02 -5.89561E-026 2.55512E-02 -1.91134E-02
7 2.45362E-03 -1.83879E-03
8 2.14868E-05 -1.61029E-05
9 1.63745E-09 -1.22716E-09
10 0.00000E+00 -0.00000E+00
11 0.00000E+00 -0.00000E+00
12 0.00000E+00 -0.00000E+00
13 0.00000E+00 -0.00000E+00
14 0.00000E+00 -0.00000E+00
15 0.00000E+00 -0.00000E+0016 0.00000E+00 -0.00000E+00
17 0.00000E+00 -0.00000E+00
18 0.00000E+00 -0.00000E+00
19 0.00000E+00 -0.00000E+00
20 0.00000E+00 -0.00000E+00
21 0.00000E+00 -0.00000E+00
22 0.00000E+00 -0.00000E+00
23 0.00000E+00 -0.00000E+00
24 0.00000E+00 -0.00000E+00
25 0.00000E+00 -0.00000E+0026 0.00000E+00 -0.00000E+00
27 0.00000E+00 -0.00000E+00
28 0.00000E+00 -0.00000E+00
29 0.00000E+00 -0.00000E+00
30 0.00000E+00 -0.00000E+00
=+ !5+ !4" !3" !2+1 /"3"2( 6 9 2 5
!# =3 !4+3 !3" !2"1( 0 6 6 0
)('
)(
1
11
=
n
nnn
pf
pfpp
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Mtodo de NewtonFormula
n Newton Error abs
Po= 0 3.500000000000000
1 3.599997591332020 9.99976E-02
2 3.650710513650460 5.07129E-02
3 3.680454490466880 2.97440E-02
4 3.698898274611950 1.84438E-02
5 3.710664707666210 1.17664E-026 3.718294413687420 7.62971E-03
7 3.723290906701650 4.99649E-03
8 3.726583383789180 3.29248E-03
9 3.728761662865030 2.17828E-03
10 3.730206542696880 1.44488E-03
11 3.731166582673110 9.60040E-04
12 3.731805191436940 6.38609E-04
13 3.732230301824200 4.25110E-04
14 3.732513429537440 2.83128E-04
15 3.732702067458620 1.88638E-0416 3.732827769304510 1.25702E-04
17 3.732911493262870 8.37240E-05
18 3.732967260320420 5.57671E-05
19 3.733004449634910 3.71893E-05
20 3.733029265434270 2.48158E-05
21 3.733045877860470 1.66124E-05
22 3.733055262936060 9.38508E-06
23 3.733055262936060 0.00000E+00
24 3.733055262936060 0.00000E+00
25 3.733055262936060 0.00000E+0026 3.733055262936060 0.00000E+00
27 3.733055262936060 0.00000E+00
28 2.951191908121710 -7.81863E-01
29 2.331828015589110 -6.19364E-01
30 1.843898901954020 -4.87929E-01
! "2 !6+2 !4 " !2 ! /( = 3 7 7 ^ 9 2
!# =? 3 e( 3 -18 e2 -18 e2 2+108 e3+27 e4-162
)('
)(
1
11
=
n
nnn
pf
pfpp
-
7/26/2019 Tarea No.3 MA3
65/68
Error Relativo
2.77771E-02
1.38912E-02
8.08160E-03
4.98629E-03
3.17098E-032.05194E-03
1.34196E-03
8.83511E-04
5.84183E-04
3.87346E-04
2.57303E-04
1.71126E-04
1.13903E-04
7.58544E-05
5.05366E-053.36747E-05
2.24286E-05
1.49391E-05
9.96230E-06
6.64763E-06
4.45010E-06
2.51405E-06
0.00000E+00
0.00000E+00
0.00000E+000.00000E+00
0.00000E+00
-2.64931E-01
-2.65613E-01
-2.64618E-01
35
5?
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66/68
Mtodo de NewtonFormula
n Newton Error abs Error Relativo
Po= 0
1 6.87190E-01 -2.19683E+00
2 4.97316E-02 -1.89037E-01
3 2.95945E-02 -1.26752E-01
4 1.89620E-02 -8.83916E-02
5 1.33884E-02 -6.65648E-026 1.20550E-02 -6.37567E-02
7 2.42552E-02 -1.47159E-01
8 -3.74823E-03 2.22352E-02
9 -9.73786E-04 5.74350E-03
10 -6.07554E-05 3.58214E-04
11 -2.26356E-07 1.33460E-06
12 -3.03430E-12 1.78902E-11
13 0.00000E+00 -0.00000E+00
14 0.00000E+00 -0.00000E+00
! +144 ! "207 ! "03330( = 6 1 2 9 4 /-10
!# =288 ! "831 ! + !( 2 2 6 4 6 6
)('
)(
1
11
=
n
nnn
pf
pfpp
-
7/26/2019 Tarea No.3 MA3
67/68
Mtodo de Newton od#cadoFormula
n Newton od#cado *rror a+s
Po= 0
1 4.02457E-01
2 2.81965E-01
3 1.18118E-014 -2.80134E-02
5 5.36040E-02
6 1.94315E-03
7 3.14014E-04
8 6.30328E-06
9 2.43087E-09
10 0.00000E+00
11 0.00000E+00
12 0.00000E+00
13 0.00000E+0014 0.00000E+00
15 -1.38379E-02
! +144 ! "207 ! "03330( = 6 1 2 9 4
!# =288 ! "831 ! + !( 2 2 6 4 6 6
[ ] ('')()('
)(')(
1
2
1
11
1
=
nnn
nn
nnpfpfpf
pfpfpp
-
7/26/2019 Tarea No.3 MA3
68/68
*rror ,elat#!o
-6.73520E-01
-8.93486E-01
-5.98183E-011.24242E-01
-3.11887E-01
-1.14352E-02
-1.85136E-03
-3.71641E-05
-1.43324E-08
-0.00000E+00
-0.00000E+00
-0.00000E+00
-0.00000E+00-0.00000E+00
7.54339E-02
/-10
)1