GmbH Solve the nonlinear equation xex 082436 0 using Newto

Solve the nonlinear equation xex - 0.82436 = 0 using Newton-Raphson Iteration Method\". Obtain the approximate solution after 5 nonlinear iterations. Set initial guess as x0 = 2.

Solution

let f(x) = xe^x - 0.82436
then f\'(x) = (x+1)e^x

let x = 2

Then by Newton-Raphson Method:
x = x - f(x)/f\'(x) = 0.537882842
x = x - f(x)/f\'(x) = 0.566986991
x = x - f(x)/f\'(x) = 0.567143286
x = x - f(x)/f\'(x) = 0.567143290
x = x - f(x)/f\'(x) = 0.567143290

Since x agrees with x up to 9 decimal places, x = 0.567143290