Question Bank • QB_EM_NM_001 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

The order of convergence of the Newton–Raphson method for finding a simple real root of $f(x) = 0$ is:

Options:

  • (A) 1 (Linear)
  • (B) 1.618 (Golden ratio)
  • (C) 2 (Quadratic)
  • (D) 3 (Cubic)

Answer Key:

C

Step-by-Step Solution & Explanation

The Newton–Raphson iteration formula is $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$. For a simple root (multiplicity $m = 1$), Taylor expansion gives the error relation $\epsilon_{n+1} \approx \frac{f''(r)}{2f'(r)} \epsilon_n^2$. Hence, the rate (order) of convergence is 2 (quadratic).
← Previous (QB_EM_NM_003) Next (QB_EM_116) →

Practice In Authentic CBT Exam Interface

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

Launch CBT Mock Test