Allied & ICAR Exam Bank • ALLIED_1012 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Newton-Raphson method

Question Statement:

Using the Newton-Raphson method to solve $f(x) = x^3 - x - 1 = 0$ with an initial guess $x_0 = 1$, the value of the next approximation $x_1$ is:

Answer Key:

1.5

Step-by-Step Solution & Explanation

$f(x) = x^3 - x - 1 \implies f'(x) = 3x^2 - 1$. For $x_0 = 1$: $f(1) = 1 - 1 - 1 = -1$, and $f'(1) = 3(1) - 1 = 2$. $x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 1 - \frac{-1}{2} = 1 + 0.5 = 1.5$.
← Previous (ALLIED_1011) Next (ALLIED_1013) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test