Use Newton's method to find the roots of the equation correct to five decimal places. x ln x - 1 = 0
A)0.88161
B)1.76322
C)2.26322
D)1.26322

Question

Quizplus · Accepted Answer

Newton's method is an iterative numerical technique. Starting with an initial guess, we apply the formula x_(n+1) = x_n - f(x_n)/f'(x_n). For the equation x ln x - 1 = 0, the derivative is ln x + 1. Starting with an initial guess close to the expected root, such as x_0 = 1.5, and iterating, we find the root converges to approximately 1.76322.

Use Newton's Method to Find the Roots of the Equation