problemas 19-25.xlsx
TRANSCRIPT
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Punto Fijo
Problema numero 19
Ecu. OriginalEcu. Iterativa
x f(x)-10 -1031
-9 -757-8 -537 Paso -7 -365 1-6 -235 2-5 -141 3-4 -77 4-3 -37-2 -15 El método no converge porque se sale del rango -1 -50 -11 32 133 354 755 1396 2337 3638 5359 755
10 1029
𝑓(𝑥)=𝑥^3+3𝑥−1𝐺( )=𝑥 𝑥^3+4𝑥−1
𝑥^3+3𝑥−1=0
-12 -10 -8 -6 -4 -2 0
-1200
-1000
-800
-600
-400
-200
0 11; -1
𝑓( )= ^3+3 −1 𝑥 𝑥 𝑥
x G(x) Error0.5 1.125 112.50%
1.125 4.92382813 492.38%4.92382813 138.069012 13806.90%138.069012 2632568.05 263256805.50%
El método no converge porque se sale del rango
-12 -10 -8 -6 -4 -2 0
-1200
-1000
-800
-600
-400
-200
0 11; -1
𝑓( )= ^3+3 −1 𝑥 𝑥 𝑥
-12 -10 -8 -6 -4 -2 0
-1200
-1000
-800
-600
-400
-200
0 11; -1
𝑓( )= ^3+3 −1 𝑥 𝑥 𝑥
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Bisección
Problema numero 19
Ecu. Original
x f(x) Intervalo -10 -1031 0<x<1
-9 -757-8 -537 0<x<0.5-7 -365-6 -235 0.25<x<0.5-5 -141-4 -77 0.25<x<0.375-3 -37-2 -15 0.3125<x<0.375-1 -50 -1 0.3125<x<0.343751 32 13 0.3125<x<0.333 354 75 0.32125<x<0.335 1396 233 0.32125<x0.3256257 3638 535 0.32125<x0.32343759 755
10 1029
La Raiz esta en : 0.32234375
𝑓(𝑥)=𝑥^3+3𝑥−1𝑥^3+3𝑥−1=0
x f(x) x media f(x) media Error 0 -1 0.5 0.625 62.500%1 30 -1 0.25 -0.234375 -23.438%
0.5 0.6250.25 -0.234375 0.375 0.17773438 17.773%
0.5 0.6250.25 -0.234375 0.3125 -0.03198242 -3.198%
0.375 0.177734380.3125 -0.03198242 0.34375 0.0718689 7.187%
0.375 0.177734380.3125 -0.03198242 0.33 0.025937 2.594%
0.34375 0.07186890.3125 -0.03198242 0.32125 -0.0030965 -0.310%
0.33 0.0259370.32125 -0.0030965 0.325625 0.01140155 1.140%
0.33 0.0259370.32125 -0.0030965 0.3234375 0.00414788 0.415%
0.325625 0.011401550.32125 -0.0030965 0.32234375 0.00052454 0.052%
0.3234375 0.00414788
La Raiz esta en : 0.32234375
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Newton-Raphson
Problema numero 19
Ecu. Original
Derivada
x f(x) Xn f(Xn)-10 -1031 0.5 0.625
-9 -757 0.3718 0.16677835-8 -537 0.3241 0.00650443-7 -365 0.3220 -0.00063248-6 -235 0.3222 6.60607E-05-5 -141 0.3222 -6.8529E-06-4 -77-3 -37
La raiz esta en: 0.3222-2 -15-1 -50 -11 32 133 354 755 1396 2337 3638 5359 755
10 1029
𝑓(𝑥)=𝑥^3+3𝑥−1𝑥^3+3𝑥−1=0𝑓´(𝑥)=3𝑥+3
f´(xn) Xn+14.875 0.3718
3.50033505 0.32413.01951329 0.32202.99810255 0.32223.00019818 0.32222.99997944 0.3222
La raiz esta en: 0.3222
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Punto Fijo
Problema numero 20
Ecu. Original
Ecu. Iterativa
x f(x)-10 -1966
-9 -1427-8 -996-7 -661-6 -410-5 -231 Paso -4 -112 1-3 -41 2-2 -6 3-1 5 40 4 51 32 14
El metodo no converge porque supera el rango 3 494 1205 2396 4187 6698 10049 1435
10 1974
𝑓(𝑥)=〖 2𝑥〗^3−3𝑥+4𝐺( )=𝑥 〖 2𝑥〗 ^3−2𝑥+4
2𝑥^3−3𝑥+4=0-15 -10 -5 0 5 10 15
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
f(x)=2x^3-3x+4
f(x)
x G(x) Error-1.5 0.25 25.00%0.25 0.015625 1.56%
0.015625 -0.9374962 -93.75%-0.93749619 -5.5739493 -557.39%-5.57394929 -196.47233 -19647.23%
El metodo no converge porque supera el rango
-15 -10 -5 0 5 10 15
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
f(x)=2x^3-3x+4
f(x)
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Bisección
Problema numero 20
Ecu. Original
x f(x)-10 -1966
-9 -1427-8 -996-7 -661-6 -410-5 -231-4 -112-3 -41-2 -6-1 50 41 32 143 494 1205 2396 4187 6698 10049 1435
10 1974
𝑓(𝑥)=〖 2𝑥〗^3−3𝑥+42𝑥^3−3𝑥+4=0
Intervalo x f(x) x media f(x) media Error
´-2<x<-1-2 -6 -1.5 1.7500 175.000%-1 5
´-2<x<-1.5 -2 -6 -1.75 -1.4688 -146.875%-1.5 1.7500
´-1.75<x<-1.5 -1.75 -1.4688 -1.625 0.2930 29.297%-1.5 1.7500
´-1.75<x<-1.625 -1.75 -1.4688 -1.6875 -0.5483 -54.834%-1.625 0.2930
´-1.6875<x<-1.625 -1.6875 -0.5483 -1.65625 -0.1180 -11.798%-1.625 0.2930
´-1.65625<x<-1.625 -1.65625 -0.1180 -1.640625 0.0899 8.990%-1.625 0.2930
´-1.65625<x<-1.640625 -1.65625 -0.1180 -1.6484375 -0.0134 -1.344%-1.640625 0.0899
´-1.6484375<x<-1.640625 -1.6484375 -0.0134 -1.645 0.0384 3.838%-1.640625 0.0899
´-1.6484375<x<1.645 -1.6484375 -0.0134 -1.647 0.0094 0.940%-1.645 0.0322
´-1.6484375<x<-1.647 -1.6484375 -0.0134 -1.648 -0.0039 -0.388%-1.647 0.0057
´-1.648<x<-1.647 -1.648 -0.0076 -1.648 -0.0010 -0.097%-1.647 0.0057
La raiz se encuentra en: -1.648
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Newton-Raphson
Problema numero 20
Ecu. Original
Derivada
x f(x) Xn f(Xn)-10 -1966 -1.5 1.75
-9 -1427 -1.6667 -0.25925926-8 -996 -1.6477 -0.00358503-7 -661 -1.6474 -7.1941E-07-6 -410 -1.6474 -2.8422E-14-5 -231-4 -112
La raiz se encuentra en: -1.6474-3 -41-2 -6-1 50 41 32 143 494 1205 2396 4187 6698 10049 1435
10 1974
𝑓(𝑥)=〖 2𝑥〗^3−3𝑥+4〖 2𝑥〗^3−3𝑥+4=0
𝑓´(𝑥)=〖 6𝑥〗 ^2−3
f´(xn) Xn+110.5 -1.6667
13.6666667 -1.647713.2894221 -1.647413.2840886 -1.647413.2840875 -1.6474
La raiz se encuentra en: -1.6474
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Punto Fijo
Problema numero 21
Ecu. Original
Ecu. Iterativa
x f(x)-12 -120.6-11 11.1999999999999-10 101.2
-9 155.4-8 179.8-7 180.4-6 163.2-5 134.2-4 99.4-3 64.8-2 36.4-1 20.20 22.21 48.42 104.83 197.44 332.25 515.26 752.47 1049.88 1413.49 1849.2
10 2363.211 2961.412 3649.8
𝑓(𝑥)= ^3+12.1 ^2+13.1 +22.2𝑥 𝑥 𝑥𝐺(𝑥)= ^3+12.1 ^2+1𝑥 𝑥 4.1 +22.2𝑥𝑥^3+12.1 ^𝑥 2+13.1𝑥+22.2=0
Paso x G(x) Error1 -11.5 -60.6 -6060.00%2 -60.6 -178941.72 -17894172.0%3 -178941.72 -5.729E+15 -572935133415326000%4 -5.7294E+15 -1.881E+47 ###5 -1.8807E+47 -6.65E+141 ###
El metodo no converge ya que esta fuera del rango
-15 -10 -5 0 5 10 15-500
0
500
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1500
2000
2500
3000
3500
4000
f(x)
-15 -10 -5 0 5 10 15-500
0
500
1000
1500
2000
2500
3000
3500
4000
f(x)
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Bisección
Problema numero 21
Ecu. Original
x f(x)-12 -120.6-11 11.1999999999999-10 101.2
-9 155.4-8 179.8-7 180.4-6 163.2-5 134.2-4 99.4-3 64.8-2 36.4-1 20.20 22.21 48.42 104.83 197.44 332.25 515.26 752.47 1049.88 1413.49 1849.2
10 2363.211 2961.412 3649.8
𝑓(𝑥)= ^3+12.1 ^2+13.1 +22.2𝑥 𝑥 𝑥𝑥^3+12.1 ^𝑥 2+13.1𝑥+22.2=0
Intervalo x f(x) x media f(x) media Error
´-12<x<-11 -12 -120.6 -11.5 -49.1 -4910.000%-11 11.2
´-11.5<x<-11 -11.5 -49.1 -11.25 -17.596875 -1759.688%-11 11.2
´-11.25<x<-11 -11.25 -17.596875 -11.125 -2.86601563 -286.602%-11 11.2
´-11.125<x<-11 -11.125 -2.866015625 -11.0625 4.24936523 424.937%-11 11.2
´-11.125<x<-11.0625 -11.125 -2.866015625 -11.09375 0.71235962 71.236%-11.0625 4.2493652344
´-11.125<x<-11.09375 -11.125 -2.866015625 -11.109375 -1.07164536 -107.165%-11.09375 0.7123596191
´-11.109375<x<-11.09375 -11.109375 -1.0716453552 -11.1015625 -0.17834864 -17.835%-11.09375 0.7123596191
´-11.1015625<x<-11.09375 -11.1015625 -0.1783486366 -11.098 0.26732887 26.733%-11.09375 0.7123596191
´-11.101563<x<-11.098 -11.102 -0.1784057248 -11.10 0.0249 2.493%-11.098 0.228135208
´-11.101563<x<-11.10 -11.156 -6.4917688815 -11.13 -3.229 -322.902%-11.100 0
´-11.13<x<-11.10 -11.130 -3.442407 -11.12 -1.716 -171.642%-11.100 0
´-11.12<x<-11.1 -11.120 -2.290688 -11.11 -1.143 -114.322%-11.100 0
´-11.110<x<11.1-11.110 -1.143221 -11.105 -0.571 -57.108%-11.100 0
´-11.105<x<11.100 -11.105 -0.571080125 -11.103 -0.285 -28.541%-11.100 0
´-11.103<x<-11.100 -11.103 -0.342520827 -11.102 -0.171 -17.121%-11.100 0
´-11.102<x<-11.100 -11.102 -0.228304808 -11.101 -0.114 -11.413%-11.100 0
´-11.101<x<-11.100 -11.101 -0.114131201 -11.101 -0.057 -5.706%-11.100 0
´-11.101<x<-11.100 -11.101 -0.114131201 -11.100500 -0.057 -5.706%-11.100 0
´-11.1005<x<-11.100 -11.1005 -0.05706030 -11.100250 -0.029 -2.853%-11.1000 0.000000E+00
´-11.100<x<-11.100 -11.100 -0.022822848 -11.100100 -0.011 -1.141%-11.100 0
´-11.10<x<-11.100 -11.100 -0.011411212 -11.100050 -0.006 -0.571%-11.100 0
´-11.100<x<-11.100 -11.100 -0.005705553 -11.100025 -0.003 -0.285%-11.100 0
La raiz esta en: 11.1
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Newton-Raphson
Problema numero 21
Ecu. Original
Derivada
x f(x)-12 -120.6-11 11.1999999999999-10 101.2
-9 155.4-8 179.8-7 180.4-6 163.2-5 134.2-4 99.4-3 64.8-2 36.4-1 20.20 22.21 48.42 104.83 197.44 332.25 515.26 752.47 1049.88 1413.49 1849.2
10 2363.211 2961.412 3649.8
𝑓(𝑥)= ^3+12.1 ^2+13.1 +22.2𝑥 𝑥 𝑥𝑥^3+12.1 ^𝑥 2+13.1𝑥+22.2=0〖𝑓´(𝑥)=3𝑥〗^2+24.2𝑥+13.1
Xn f(Xn) f´(xn) Xn+1-12 -120.6 154.7 -11.2204
-11.2204 -14.0510841 119.259597 -11.1026-11.1026 -0.29766506 114.220571 -11.1000-11.1000 -0.00014402 114.110054 -11.1000-11.1000 -3.3868E-11 114.11 -11.1000-11.1000 0 114.11 -11.1000
La raiz esta en: -11.100
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Punto Fijo
Problema numero 22
Ecu. Original
Ecu. Iterativa
x f(x)-12 -406.36-11 -190.21-10 -26.86
-9 89.69-8 165.44-7 206.39-6 218.54-5 207.89-4 180.44-3 142.19-2 99.14-1 57.290 22.641 1.192 -1.063 21.894 76.045 167.396 301.947 485.698 724.649 1024.79
10 1392.1411 1832.6912 2352.44
𝑓(𝑥)= ^3𝑥 +6.6 ^2𝑥 −29.05 +22.𝑥 64𝐺(𝑥)= ^3+𝑥 6.6 ^2𝑥 −28.05 +22.𝑥 64
𝑥^3+6.6 ^𝑥 2−29.05𝑥+22.64=0
Primera raiz Segunda raiz Paso x G(x) Error Paso x G(x)
1 -10 -36.86 -3686.00% 1 1.5 -1.212 -36.86 -40056.476 ### 2 -1.21 64.4719993 -40056.4765 -6.426E+13 ### 3 64.471999 293634.8194 -6.4261E+13 -2.654E+41 ### 4 293634.819 2.5318E+165 -2.6536E+41 -1.87E+124 ### 5 2.5318E+16 1.6229E+49
Tercera raiz Paso x G(x) Error
1 2.5 9.39 939.00%El método no converge ya que sobre pasa el rango
2 9.39 1169.12238 116912.2%3 1169.12238 1606999996 ###4 1606999996 4.15E+27 ###5 4.15E+27 7.1473E+82 ###
-15 -10 -5 0 5 10 15
-1000
-500
0
500
1000
1500
2000
2500
3000
𝑓( )= ^3+6.6 ^2−29.05 +22.64𝑥 𝑥 𝑥 𝑥f(x)
Segunda raiz Error
-121.00%6447.2%
29363482%######
El método no converge ya que sobre pasa el rango
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Bisección
Problema numero 22
Ecu. Original
x f(x)-12 -406.36-11 -190.21-10 -26.86
-9 89.69-8 165.44-7 206.39-6 218.54-5 207.89-4 180.44-3 142.19-2 99.14-1 57.290 22.641 1.192 -1.063 21.894 76.045 167.396 301.947 485.698 724.649 1024.79
10 1392.1411 1832.6912 2352.44
𝑓(𝑥)= ^3𝑥 +6.6 ^2𝑥 −29.05 +22.𝑥 64𝑥^3+6.6 ^𝑥 2−29.05𝑥+22.64=0
Primera raiz Intervalo x f(x) x media f(x) media Error
´-10<x<-9 -10 -26.86 -9.5 36.89 3689.000%-9 89.69
´-10<x<-9.5 -10 -26.86 -9.75 6.430625 643.063%-9.5 36.89
´-10<x<-9.75 -10 -26.86 -9.875 -9.85492187 -985.492%-9.75 6.430625
´--9.875<x<-9.75 -9.875 -9.85492187 -9.813 -1.62293945 -162.294%-9.75 6.430625
´-9.813<x<-9.75 -9.813 -1.6880854 -9.782 2.39383803 239.384%-9.75 6.430625
´-9.813<x<-9.782 -9.813 -1.6880854 -9.798 0.32613252 32.613%-9.782 2.32939863
´-9.813<x<-9.798 -9.813 -1.6880854 -9.806 -0.71209487 -71.209%-9.798 0.26132881
´-9.806<x<-9.798 -9.806 -0.77708102 -9.802 -0.25751121 -25.751%-9.798 0.26132881
´-9.802<x<-9.798 -9.802 -0.25751121 -9.800 0.002 0.200%-9.798 0.26132881
La primera raiz esta en: -9.800
Segunda RaizIntervalo x f(x) x media f(x) media Error
1<x<2 1 1.19 1.5 -2.71 -271.000%2 -1.06
1<x<1.5 1 1.19 1.25 -1.406875 -140.687%1.5 -2.71
1<x<1.25 1 1.19 1.125 -0.26429687 -26.430%1.25 -1.406875
1<x<1.125 1 1.19 1.063 0.42461914 42.462%1.125 -0.26429687
1.063<x<1.125 1.063 0.41880245 1.094 0.06775618 6.776%1.125 -0.26429687
1.094<x<1.125 1.094 0.06775618 1.110 -0.10065567 -10.066%1.125 -0.26429687
1.094<x<1.11 1.094 0.06775618 1.102 -0.01976039 -1.976%1.11 -0.106009
1.094<x<1.102 1.094 0.06775618 1.098 0.02383959 2.384%1.102 -0.01976039
1.098<x<1.102 1.098 0.02383959 1.100 0.002 0.200%1.102 -0.01976039
La segunda raiz esta en: -1.100
Tercera RaizIntervalo x f(x) x media f(x) media Error
2<x<3 2 -1.06 2.5 6.89 689.000%3 21.89
2<x<2.5 2 -1.06 2.25 2.080625 208.063%2.5 6.89
2<x<2.25 2 -1.06 2.125 0.30757812 30.758%2.25 2.080625
2<x<2.125 2 -1.06 2.063 -0.42616211 -42.616%2.125 0.30757812
2.063<x<2.125 2.063 -0.42069055 2.094 -0.06893582 -6.894%2.125 0.30757812
2.094<x<2.125 2.094 -0.06893582 2.109 0.11621508 11.622%2.125 0.30757812
2.094<x<2.11 2.094 -0.06893582 2.102 0.02585161 2.585%2.11 0.122291
2.094<x<2.102 2.094 -0.06893582 2.098 -0.02174841 -2.175%2.102 0.02585161
2.098<x<2.102 2.098 -0.02174841 2.100 0.002 0.200%2.102 0.02585161
La tercera raiz esta en: -2.100
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Newton-Raphson
Problema numero 22
Ecu. Original
Derivada
x f(x)-12 -406.36-11 -190.21-10 -26.86
-9 89.69-8 165.44-7 206.39-6 218.54-5 207.89-4 180.44-3 142.19-2 99.14-1 57.290 22.641 1.192 -1.063 21.894 76.045 167.396 301.947 485.698 724.649 1024.79
10 1392.1411 1832.6912 2352.44
𝑓(𝑥)= ^3+𝑥 6.6 ^2+𝑥 29.05 +22.𝑥 64𝑥^3+6.6 ^𝑥 2+29.05𝑥+22.64=0〖𝑓´(𝑥)=3𝑥〗^2+13.2𝑥+29.05
Primera raiz Segunda raizXn f(Xn) f´(xn) Xn+1 Xn f(Xn) f´(xn)
-10 -607.86 197.05 -6.9152 1 59.29 45.25-6.9152 -193.319355 81.2293101 -4.5353 -0.3103 14.2319953 25.2431676-4.5353 -66.6410828 30.8905702 -2.3780 -0.8741 1.62282451 19.8042538-2.3780 -22.5652531 14.6249989 -0.8350 -0.9560 0.02615937 19.172493-0.8350 2.40221063 20.1194546 -0.9544 -0.9574 6.94504E-06 19.1623147-0.9544 0.05667401 19.1843763 -0.9574 -0.9574 4.90274E-13 19.162312-0.9574 3.25852E-05 19.1623246 -0.9574 -0.9574 0 19.162312-0.9574 1.07789E-11 19.162312 -0.9574 -0.9574 0 19.162312
En este caso el metodo no converge puesto encuentra una misma raiz para todos los casos
Segunda raiz Tercera raizXn+1 Xn f(Xn) f´(xn) Xn+1
-0.3103 2 115.14 67.45 0.2930-0.8741 0.2930 31.7420054 33.174515 -0.6639-0.9560 -0.6639 5.97095731 21.609167 -0.9402-0.9574 -0.9402 0.33075803 19.2914607 -0.9573-0.9574 -0.9573 0.00110598 19.1627423 -0.9574-0.9574 -0.9574 1.2418E-08 19.162312 -0.9574-0.9574 -0.9574 0 19.162312 -0.9574-0.9574 -0.9574 0 19.162312 -0.9574
En este caso el metodo no converge puesto encuentra una misma raiz para todos los casos
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Punto Fijo
Problema numero 23
Ecu. Original
Ecu. Iterativa
x f(x)-12 22244-11 15792-10 10856
-9 7178-8 4524-7 2684-6 1472-5 726-4 308-3 104-2 24-1 20 -41 -122 -163 144 1325 4166 9687 19148 34049 5612
10 873611 1299812 18644
𝑓(𝑥)= ^4− ^3−2 ^2−6 −4𝑥 𝑥 𝑥 𝑥𝐺(𝑥)= ^4− ^3−2 ^2−𝑥 𝑥 𝑥 5 −4𝑥
𝑥^4−𝑥^3−2 ^𝑥 2−6𝑥−4=0
Primera raiz Segunda raiz Paso x G(x) Error Paso x G(x)
1 -1 1 100.00% 1 14 352062 1 -11 -1100.0% 2 35206 1.5362235E+183 -11 15781 1578100% 3 1.5362E+18 5.5695179E+724 15781 6.2017E+16 ### 4 5.5695E+72 9.622112E+2905 6.2017E+16 1.4793E+67 ### 5 9.622E+290 #NUM!
El metodo no converge se sale del rango
-15 -10 -5 0 5 10 15-5000
0
5000
10000
15000
20000
25000
f(x)
𝒙^𝟒−𝒙^𝟑−𝟐𝒙^𝟐−𝟔𝒙−𝟒=𝟎
Segunda raiz Error
############
#NUM!
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Bisección
Problema numero 23
Ecu. Original
x f(x)-12 22244-11 15792-10 10856
-9 7178-8 4524-7 2684-6 1472-5 726-4 308-3 104-2 24-1 20 -41 -122 -163 144 1325 4166 9687 19148 34049 5612
10 873611 1299812 18644
𝑓(𝑥)= ^4− ^3−2 ^2−6 −4𝑥 𝑥 𝑥 𝑥𝑥^4−𝑥^3−2 ^𝑥 2−6𝑥−4=0
Primera raiz Intervalo x f(x) x media f(x) media Error
´-1<x<0 -1 2 -0.5 -1.3125 -131.250%0 -4
´-1<x<0.5 -1 2 -0.75 0.11328125 11.328%-0.5 -1.3125
´-0.75<x<0.5 -0.75 0.11328125 -0.625 -0.634521484375 -63.452%-0.5 -1.3125
´-0.75<x<0.6255 -0.75 0.11328125 -0.688 -0.2719573974609 -27.196%-0.625 -0.63452148
´-0.75<x<0.6875 -0.75 0.11328125 -0.7188 -0.0825185775757 -8.252%-0.6875 -0.2719574
´-0.75<x<0.7188 -0.75 0.11328125 -0.734 0.01454168558121 1.454%-0.7188 -0.08251858
´-0.734<x<0.7188 -0.734 0.01219293 -0.7264 -0.0352020368196 -3.520%-0.7188 -0.08221057
´-0.734<x<0.7264 -0.734 0.01219293 -0.7302 -0.0115535008726 -1.155%-0.7264 -0.03520204
´-0.734<x<0.7302 -0.734 0.01219293 -0.7321 0.00030739755657 0.031%-0.7302 -0.0115535
La raiz esta en:-0.732
Segunda raiz Intervalo x f(x) x media f(x) media Error
2<x<3 2 -16 2.5 -8.0625 -806.250%3 14
2.5<x<3 2.5 -8.0625 2.75 0.76953125 76.953%3 14
2.5<x<2.75 2.5 -8.0625 2.625 -4.13842773 -413.843%2.75 0.76953125
2.625<x<2.75 2.625 -4.13842773 2.688 -1.81443787 -181.444%2.75 0.76953125
2.688<x<2.75 2.688 -1.79481675 2.7190 -0.54551061 -54.551%2.75 0.76953125
2.719<x<2.75 2.719 -0.54551061 2.734 0.10368285 10.368%2.7500 0.76953125
2.719<x<2.735 2.719 -0.54551061 2.727 -0.21250902 -21.251%2.735 0.12490068
2.727<x<2.735 2.727 -0.21250902 2.731 -0.04435708 -4.436%2.735 0.12490068
2.731<x<2.735 2.731 -0.04435708 2.733 0.04013333 4.013%2.735 0.12490068
2.731<x<2.733 2.731 -0.04435708 2.732 -0.00214647 -0.215%2.733 0.04013333
La raiz esta en:2.732
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Newton-Raphson
Problema numero 23
Ecu. Original
Derivada
x f(x)-12 22244-11 15792-10 10856
-9 7178-8 4524-7 2684-6 1472-5 726-4 308-3 104-2 24-1 20 -41 -122 -163 144 1325 4166 9687 19148 34049 5612
10 873611 1299812 18644
𝑓(𝑥)= ^4− ^3−2 ^2−6 −4𝑥 𝑥 𝑥 𝑥𝑥^4−𝑥^3−2 ^𝑥 2−6𝑥−4=0
〖𝑓´(𝑥)=4𝑥^3−3𝑥〗^2−4𝑥-6
Primera raiz Segunda raizXn f(Xn) f´(xn) Xn+1 Xn f(Xn)
-1 2 -9 -0.7778 2 -16-0.7778 0.29324798 -6.58573388 -0.7333 4.6667 297.08642-0.7333 0.00749843 -6.25691057 -0.7321 3.7281 87.1869727-0.7321 4.91326E-06 -6.24871667 -0.7321 3.1253 22.5917963-0.7321 2.10942E-12 -6.24871131 -0.7321 2.8213 4.0514621-0.7321 0 -6.24871131 -0.7321 2.7380 0.2526417-0.7321 0 -6.24871131 -0.7321 2.7321 0.00121718-0.7321 0 -6.24871131 -0.7321 2.7321 2.87067E-08
La raiz esta en:-0.732 La raiz esta en: 2.732
Segunda raizf´(xn) Xn+1
6 4.6667316.518519 3.7281144.649198 3.125374.3029242 2.8213
48.659974 2.738042.6614267 2.732142.2507043 2.732142.2487114 2.7321
La raiz esta en: 2.732
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Punto Fijo
Problema numero 24
Ecu. Original
Ecu. Iterativa
x f(x)-12 19103.04-11 13390.72-10 9067.52
-9 5887.44-8 3628.48-7 2092.64-6 1105.92-5 518.32-4 203.84-3 60.48-2 10.24-1 -0.880 -2.881 -1.762 20.483 105.844 320.325 753.926 1520.647 2758.488 4629.449 7319.52
10 11038.7211 16021.0412 22524.48
𝑓(𝑥)= ^4𝑥 + ^3𝑥 +0.56 ^2−𝑥 1.44 −𝑥 2.88𝐺(𝑥)= ^4𝑥 + ^3𝑥 +0.56 ^2𝑥 −0.44 −𝑥 2.88
𝑥^4+𝑥^3+0.56 ^𝑥 2−1.44𝑥−2.88=0
Primera raiz Segunda raiz Paso x G(x) Error Paso x
1 -1 -1.88 -188.00% 1 12 -1.88 17.4678554 1746.8% 2 -0.763 17.4678554 87070.3706 8707037% 3 -0.582602244 87070.3706 5.7475E+19 ### 4 -1.452879985 5.7475E+19 1.0912E+79 ### 5 6.5652369
El metodo no converge se sale del rango
-15 -10 -5 0 5 10 15-5000
0
5000
10000
15000
20000
25000
𝑓( )= ^4+ ^3+0.56 ^2−1.44 −2.88𝑥 𝑥 𝑥 𝑥 𝑥f(x)
Segunda raiz G(x) Error
-0.76 -76.00%-0.5826022 -58.3%
-1.45288 -145%6.5652369 657%
1451.80343 145180%
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Bisección
Problema numero 24
Ecu. Original
x f(x)-12 19103.04-11 13390.72-10 9067.52
-9 5887.44-8 3628.48-7 2092.64-6 1105.92-5 518.32-4 203.84-3 60.48-2 10.24-1 -0.880 -2.881 -1.762 20.483 105.844 320.325 753.926 1520.647 2758.488 4629.449 7319.52
10 11038.7211 16021.0412 22524.48
𝑓(𝑥)= ^4𝑥 + ^3𝑥 +0.56 ^2−𝑥 1.44 −𝑥 2.88𝑥^4+𝑥^3+0.56 ^𝑥 2−1.44𝑥−2.88=0
Primera raiz Intervalo x f(x) x media f(x) media Error
´-2<x<-1 -2 10.24 -1.5 2.2275 222.750%-1 -0.88
´-1.5<x<-1 -1.5 2.2275 -1.25 0.28328125 28.328%-1 -0.88
´-1.25<x<-1 -1.25 0.28328125 -1.125 -0.37327148 -37.327%-1 -0.88
´-1.25<x<-1.1225 -1.25 0.28328125 -1.186 -0.07287109 -7.287%-1.1225 -0.38473777
´-1.25<x<-1.186 -1.25 0.28328125 -1.218 0.09860467 9.860%-1.186 -0.07417679
´-1.218<x<-1.186 -1.218 0.09860467 -1.202 0.01077443 1.077%-1.186 -0.07417679
´-1.202<x<-1.186 -1.202 0.01077443 -1.194 -0.03205522 -3.206%-1.186 -0.07417679
´-1.202<x<-1.194 -1.202 0.01077443 -1.198 -0.01072963 -1.073%-1.194 -0.03205522
´-1.202<x<-1.98 -1.202 0.01077443 -1.200 0 0.000%-1.198 -0.01072963
La raiz esta en: -1.200
Segunda raiz Intervalo x f(x) x media f(x) media Error
2<x<1 2 20.48 1.5 4.6575 465.750%1 -1.76
1.5<x<1 1.5 4.6575 1.25 0.58953125 58.953%1 -1.76
1.25<x<1 1.25 0.58953125 1.125 -0.76561523 -76.562%1 -1.76
1.25<x<1.1225 1.25 0.58953125 1.186 -0.15071504 -15.072%1.1225 -0.78882373
1.25<x<1.186 1.25 0.58953125 1.218 0.20462913 20.463%1.186 -0.15341108
1.218<x<1.186 1.218 0.20462913 1.202 0.02232325 2.232%1.186 -0.15341108
1.202<x<1.186 1.202 0.02232325 1.194 -0.06635645 -6.636%1.186 -0.15341108
1.202<x<1.194 1.202 0.02232325 1.198 -0.02222085 -2.222%1.194 -0.06635645
1.202<x<1.98 1.202 0.02232325 1.200 0 0.000%1.198 -0.02222085
La raiz esta en: 1.200
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Newton-Raphson
Problema numero 24
Ecu. Original
Derivada
x f(x)-12 19103.04-11 13390.72-10 9067.52
-9 5887.44-8 3628.48-7 2092.64-6 1105.92-5 518.32-4 203.84-3 60.48-2 10.24-1 -0.880 -2.881 -1.762 20.483 105.844 320.325 753.926 1520.647 2758.488 4629.449 7319.52
10 11038.7211 16021.0412 22524.48
𝑓(𝑥)= ^4𝑥 + ^3𝑥 +0.56 ^2−𝑥 1.44 −𝑥 2.88𝑥^4+𝑥^3+0.56 ^𝑥 2−1.44𝑥−2.88=0
〖𝑓´(𝑥)=4𝑥^3+3𝑥〗^2+1.12𝑥-1.44
Primera raiz Segunda raizXn f(Xn) f´(xn) Xn+1 Xn f(Xn) f´(xn)
-2 10.24 -23.68 -1.5676 2 20.48 44.8-1.5676 2.93960009 -11.2316064 -1.3058 1.5429 5.57028705 22.1197434-1.3058 0.636371 -6.69388016 -1.2108 1.2910 1.12426033 13.6136542-1.2108 0.05857739 -5.49800035 -1.2001 1.2084 0.09501255 11.3535555-1.2001 0.00064507 -5.37734388 -1.2000 1.2001 0.00090333 11.1380765-1.2000 8.05995E-08 -5.37600017 -1.2000 1.2000 8.41996E-08 11.1360002-1.2000 0 -5.376 -1.2000 1.2000 0 11.136-1.2000 0 -5.376 -1.2000 1.2000 0 11.136
La raiz esta en: -1.200 La raiz esta en: 1.200
Segunda raizXn+1
1.54291.29101.20841.20011.20001.20001.20001.2000
La raiz esta en: 1.200
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Punto Fijo
Problema numero 25
Ecu. Original
Ecu. Iterativa
x f(x)-12 -4698-11 -3831-10 -3070
-9 -2409-8 -1842-7 -1363-6 -966-5 -645-4 -394-3 -207-2 -78-1 -10 301 212 -223 -934 -1865 -2956 -4147 -5378 -6589 -771
10 -87011 -94912 -1002
𝑓(𝑥)= ^3𝑥 −20 ^2𝑥 +10𝑥+30𝐺(𝑥)= ^3𝑥 −20 ^2𝑥 +11𝑥+30
𝑥^3−20 ^𝑥 2+10𝑥+30=0
Primera raiz Segunda raiz Paso x G(x) Error Paso x
1 -1 -2 -200.00% 1 22 -2 -80 -8000.0% 2 -203 -80 -640850 ### 3 -161904 -640850 -2.632E+17 ### 4 -4.2489E+125 -2.632E+17 -1.823E+52 ### 5 -7.6706E+37
El metodo no converge se sale del rango
-15 -10 -5 0 5 10 15
-5000-4000-3000-2000-1000
01000
𝑓( )= ^3−20 ^2+10 +30𝑥 𝑥 𝑥 𝑥f(x)
Segunda raiz G(x) Error
-20 -2000.00%-16190 ###
-4.249E+12 ###-7.671E+37 ###-4.51E+113 ###
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Bisección
Problema numero 25
Ecu. Original
x f(x)-12 -4698-11 -3831-10 -3070
-9 -2409-8 -1842-7 -1363-6 -966-5 -645-4 -394-3 -207-2 -78-1 -10 301 212 -223 -934 -1865 -2956 -4147 -5378 -6589 -771
10 -87011 -94912 -1002
𝑓(𝑥)= ^3𝑥 −20 ^2𝑥 +10𝑥+30𝑥^3−20 ^𝑥 2+10𝑥+30=0
Primera raiz Segunda raiz x f(x) x media f(x) media Error Intervalo
-1 -1 -0.5 19.875 1987.500% 1<x<20 30
-1 -1 -0.75 10.828125 1082.813% 1.5<x<2-0.5 19.875
-1 -1 -0.875 5.26757813 526.758% 1.5<x<1.75-0.75 10.828125
-1 -1 -0.938 2.22290039 222.290% 1.5<x<1.625-0.875 5.26757813
-1 -1 -0.969 0.63381958 63.382% 1.563<x<1.625-0.9375 2.22290039
-1 -1 -0.984 -0.18402203 -18.402% 1.563<x<1.594-0.969 0.62092679-0.985 -0.21017163 -0.977 0.20684517 20.685% 1.563<x<1.579-0.969 0.62092679-0.985 -0.21017163 -0.981 -0.00129614 -0.130% 1.571<x<1.579-0.977 0.20684517
La raiz esta en: -0.981
Segunda raiz x f(x) x media f(x) media Error
1 21 1.5 3.375 337.500%2 -22
1.5 3.375 1.75 -8.390625 -839.063%2 -22
1.5 3.375 1.625 -2.27148438 -227.148%1.75 -8.390625
1.5 3.375 1.563 0.61157227 61.157%1.625 -2.2714843751.563 0.588980547 1.594 -0.82662742 -82.663%1.625 -2.2714843751.563 0.588980547 1.579 -0.11515614 -11.516%1.594 -0.8266274161.563 0.588980547 1.571 0.22647241 22.647%1.579 -0.1379924611.571 0.226472411 1.575 0.04448438 4.448%1.579 -0.137992461
1.575<x<1.1579 1.575 0.04448438 1.577 -0.04669297 -4.669%1.579 -0.13799246
1.575<x<1.577 1.575 0.04448438 1.576 -0.00108902 -0.109%1.577 -0.04669297
La raiz esta en: 1.576
NOMBRE Adrián Antonio Avalos Rivera MATERIA Análisis numéricos GRUPO CMETODO Newton-Raphson
Problema numero 25
Ecu. Original
Derivada
x f(x)-12 -4698-11 -3831-10 -3070
-9 -2409-8 -1842-7 -1363-6 -966-5 -645-4 -394-3 -207-2 -78-1 -10 301 212 -223 -934 -1865 -2956 -4147 -5378 -6589 -771
10 -87011 -94912 -1002
𝑓(𝑥)= ^3𝑥 −20 ^2𝑥 +10𝑥+30𝑥^3−20 ^𝑥 2+10𝑥+30=0
〖𝑓 ´(𝑥)=3𝑥〗^2−40+10
Primera raiz Segunda raiz Xn f(Xn) f´(xn) Xn+1 Xn f(Xn)
-1 -1 53 -0.9811 1 21-0.9811 -0.00818125 52.1331435 -0.9810 1.7778 -9.81344307-0.9810 -5.6502E-07 52.1259425 -0.9810 1.5877 -0.5367454-0.9810 0 52.125942 -0.9810 1.5760 -0.00208101-0.9810 0 52.125942 -0.9810 1.5760 -3.1821E-08-0.9810 0 52.125942 -0.9810 1.5760 0-0.9810 0 52.125942 -0.9810 1.5760 0-0.9810 0 52.125942 -0.9810 1.5760 0
La raiz esta en: -0.981 La raiz esta en: 1.5760
Segunda raiz f´(xn) Xn+1
-27 1.7778-51.6296296 1.5877-45.9457455 1.5760-45.5893366 1.5760-45.5879424 1.5760-45.5879424 1.5760-45.5879424 1.5760-45.5879424 1.5760
La raiz esta en: 1.5760