problemas 19-25.xlsx

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

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

0 11; -1

𝑓( )= ^3+3 −1 𝑥 𝑥 𝑥

-12 -10 -8 -6 -4 -2 0

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

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

f(x)=2x^3-3x+4

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

f(x)=2x^3-3x+4

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

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

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

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

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

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

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

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

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

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

𝒙^𝟒−𝒙^𝟑−𝟐𝒙^𝟐−𝟔𝒙−𝟒=𝟎

Segunda raiz Error

############

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

´-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

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

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

-15 -10 -5 0 5 10 15-5000

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%

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

´-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

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

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

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

-15 -10 -5 0 5 10 15

-5000-4000-3000-2000-1000

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 ###

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

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

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

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