Answer to Question #236521 in Quantitative Methods for Harshitha

Question

write coding to find the real root for the equation x^e^x-2=0 and correct to 3 decimal places using newton raphson method

Answer 1

from math import exp, log

def f(x):
    return x**exp(x) -2

def fp(x):
    return exp(x) * x**(exp(x)-1) * (1+x*log(x))

def newton_raphson(x0, f, fp, eps, max_iter=100, show=False):
    iter = 1
    x = x0 - f(x0)/fp(x0)
    if show:
        print(' # |  root')
        print(f'{0:2} | {x0:.4f}')
        print(f'{iter:2} | {x:.4f}')

    while abs(x-x0) > eps:
        iter += 1
        if iter > max_iter:
            print(f'Noconvertion in {max_iter} iterations')
            break
        x0 = x
        x = x0 - f(x0)/fp(x0)
        if show:
            print(f'{iter:2} | {x:.4f}')
    return x

newton_raphson(1, f, fp, 0.001, show=True)

# | root

 0 | 1.0000

 1 | 1.3679

 2 | 1.2666

 3 | 1.2294

 4 | 1.2257

 5 | 1.2257