Question

Equation x² − 1 = 0 is required to be solved using Newton Raphson’s method with an initial guess x0 = −1. Then after one step of Newton’s method, the estimate x1 of the solution will be given by

• A. 0.71828
• B. 0.36784
• C. 0.20587
• D. 0.0000

Hint:

Substitute values into the Newton-Raphson formula and simplify step by step to avoid errors.

Answer 1

The Correct Option is C

The Newton-Raphson formula is: x_n+1 = x_n − f (x_n)/f′(x_n). For f (x) = e^x − 1, the derivative is: f′(x) = e^x. Substituting x_0 = −1, the function and derivative values are: f(x_0) = e−1 − 1 and f′(x_0) = e−1. Consequently, x_1 is calculated as: −1 − (e−1 − 1)/e−1 = 0.20587.