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

Question

Quizplus · Accepted Answer

Newton's method is an iterative numerical technique used to find approximate roots of a real-valued function. For the equation $x \ln x - 1 = 0$, we start with an initial guess and apply the iteration formula $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$. After performing the iterations, the root converges to approximately $1.76322$.

Use Newton's Method to Find the Roots of the Equation xln⁡x−1=0x \ln x - 1 = 0xlnx−1=0

Use Newton's Method to Find the Roots of the Equation $x \ln x - 1 = 0$