7/18/2019 Newton Raphson

http://slidepdf.com/reader/full/newton-raphson-56d6d46270a1b 1/8

investigar sobre el metodo de Newton Raphson y resolver este ejemplo

Ejemplo

Usar el método de Newton Raphson y una calculadora ,para aproximar la solución de la ecuación

e^(-x)=LnX

con X0=1 y hasta que ep < 1%

Iteración Xn f(xn) f´(xn) f(xn)/f´(xn) Xn+1=Xn- f(xn)/f´(xn)0 1 0.36787944 -1.36787944 -0.26894142 1.2689414211 1.26894142 0.17768749 -1.0691875 -0.16618927 1.4351306882 1.43513069 0.0811928 -0.9348849 -0.08684791 1.5219785943 1.52197859 0.03587103 -0.87531904 -0.04098052 1.5629591134 1.56295911 0.01556756 -0.84932718 -0.01832928 1.5812883955 1.58128839 0.00669881 -0.8381056 -0.0079928 1.5892811926 1.58928119 0.0028715 -0.83328752 -0.00344599 1.5927271867 1.59272719 0.00122883 -0.83122414 -0.00147834 1.5942055288 1.59420553 0.00052549 -0.83034149 -0.00063286 1.5948383849 1.59483838 0.00022464 -0.82996411 -0.00027067 1.595109052

10 1.59510905 9.6022E-05 -0.82980279 -0.00011572 1.59522476911 1.59522477 4.1042E-05 -0.82973383 -4.9464E-05 1.59527423312 1.59527423 1.7541E-05 -0.82970436 -2.1142E-05 1.595295375

7/18/2019 Newton Raphson

http://slidepdf.com/reader/full/newton-raphson-56d6d46270a1b 2/8

Ec. Método de Newton Función Erxj+1 = xj −f(xj)/f'(xj) e^(-x)=LnX 0.21194156

0.115800790.0570625

Ep f(x)= e^(-x)-LnX=0 0.02621983f'(x)= #NAME? 0.0115913621.1941558 0.00502919

11.580079 xj+1=xj-((e^(-x))-LnX)/(-e^(-x)-1/x) 0.002163585.70625016 0.000927322.62198279 0.00039682

1.1591359 0.000169690.50291902 Ep=(Xn+1-Xn/Xn+1)100% 7.254E-050.21635809 3.1006E-050.092732180.039681550.016968620.007253970.00310063 <-------4 decimales iguales que los 3 resultados anteriores en Xn+1=Xn- f(xn)/f´(xn)

7/18/2019 Newton Raphson

http://slidepdf.com/reader/full/newton-raphson-56d6d46270a1b 3/8

Ea0.268941420.166189270.08684791

0.040980520.018329280.0079928

0.003445990.001478340.000632860.000270670.000115724.9464E-05

7/18/2019 Newton Raphson

http://slidepdf.com/reader/full/newton-raphson-56d6d46270a1b 4/8

7/18/2019 Newton Raphson

http://slidepdf.com/reader/full/newton-raphson-56d6d46270a1b 5/8

33 -8.77403109 -11.1123467 1.95201754 -5.69274943 -5.41959729834 -5.4195973 -11.2656297 2.9936886 -3.76312677 -7.50250291735 -7.50250292 -20.7146844 8.40566827 -2.46437092 -18.2503134936 -18.2503135 -9.79360752 1.80427675 -5.42799631 -4.36561121637 -4.36561122 -8.35999558 8.60172619 -0.97189743 -7.38809814738 -7.38809815 -13.8532747 5.18848031 -2.67000622 -11.18326849

39 -11.1832685 -13.0621634 44.3652686 -0.29442318 -12.7677402540 -12.7677403 -7.09647917 1.21817392 -5.82550573 -1.27097344441 -1.27097344 -11.0065115 11.0224531 -0.99855371 -10.0079577842 -10.0079578 -10.1106805 1.63356037 -6.18935224 -3.92132828843 -3.92132829 -12.081303 2.2062357 -5.47598018 -6.60532280444 -6.6053228 -9.97286579 1.28983042 -7.73192011 -2.24094567945 -2.24094568 -12.1838117 3.29217851 -3.70083568 -8.482976023

Segunda raíz Xa Xb f(a) f(b) Xr

0 0.7 0.8 -6.56111335 2.99133514 0.751 0.75 0.8 -4.43468756 2.99133514 0.7752 0.775 0.8 -2.14929735 2.99133514 0.78753 0.7875 0.8 -0.19096519 2.99133514 0.793754 0.7875 0.79375 -0.19096519 1.18514018 0.7906255 0.7875 0.790625 -0.19096519 0.45353701 0.78906256 0.7875 0.7890625 -0.19096519 0.12140055 0.788281257 0.78828125 0.7890625 -0.03714162 0.12140055 0.788671875

8 0.78828125 0.78867188 -0.03714162 0.04152617 0.7884765639 0.78828125 0.78847656 -0.03714162 0.00204316 0.78837890610 0.78837891 0.78847656 -0.0175863 0.00204316 0.78842773411 0.78842773 0.78847656 -0.00778086 0.00204316 0.78845214812 0.78845215 0.78847656 -0.00287117 0.00204316 0.78846435513 0.78846436 0.78847656 -0.00041459 0.00204316 0.78847045914 0.78846436 0.78847046 -0.00041459 0.00081414 0.78846740715 0.78846436 0.78846741 -0.00041459 0.00019974 0.78846588116 0.78846588 0.78846741 -0.00010743 0.00019974 0.78846664417 0.78846588 0.78846664 -0.00010743 4.6152E-05 0.78846626318 0.78846626 0.78846664 -3.0641E-05 4.6152E-05 0.788466454

Segunda raíz 0.78846645

s= 10.0000078 TRUE

1.570846

7/18/2019 Newton Raphson

http://slidepdf.com/reader/full/newton-raphson-56d6d46270a1b 6/8

izontal,

se ha Newton-Raphson f(x)=tgBx-(gx^2)/(2Vo^2*cos

g(x)=

g= 9.81

ado de E-7 % Ec. Método de Newtonxj+1 = xj −f(xj)/f'(xj)

Epf(x)= tgBx-(gx^2)/(2Vo^2*cos^2B)-10

106.696121 f'(x)= (secBx)^2-((2gx*(2Vo^2*(cosB)^2)-(gx^2)*-105.999854-247.208739 xj+1=xj-((e^(-x))-LnX)/(-e^(-x)-1/x)

83.582576-30.443952

-62.065327728.2265078 Ep=(Xn+1-Xn/Xn+1)100%81.2294056

-720.14202765.7891725

-436.329989-13.444240170.9757461

29.568657-39.31620613.1553177

-615.61588388.4148497

-34.7480008-14.105272248.6204487

-77.558381420.8643344

-41.833507820.3146958-147.006479.6469294 Valor de la primera raíz -8.48297602 s=

62.797906895.5003381

-15511.147999.9974454

-172387.713

7/18/2019 Newton Raphson

http://slidepdf.com/reader/full/newton-raphson-56d6d46270a1b 7/8

-305.856064-61.89452127.762809958.8911011

-318.04715540.9102163

33.936146212.4099624-904.56388987.3003716

-155.21856540.633813

-194.756043

f(Xr) Ep

-4.43468756-2.14929735 3.22580645-0.19096519 1.587301591.18514018 0.787401570.45353701 -0.395256920.12140055 -0.1980198

-0.03714162 -0.099108030.04152617 0.04952947

0.00204316 -0.02477087-0.0175863 -0.01238697-0.00778086 0.0061931-0.00287117 0.00309645-0.00041459 0.00154820.00081414 0.00077410.00019974 -0.00038705

-0.00010743 -0.000193534.6152E-05 9.6762E-05

-3.0641E-05 -4.8381E-057.7555E-06 2.4191E-05

7/18/2019 Newton Raphson

http://slidepdf.com/reader/full/newton-raphson-56d6d46270a1b 8/8

^2B)-10

(4Vo*2cosB(-senB))/(2Vo^2*(cosB)^2)^2

-0.6519987