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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


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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E$em%lo


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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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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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


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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*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


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



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


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


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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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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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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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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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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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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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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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

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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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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

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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

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*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

Documents

Tarea No.3 MA3