The GATE Grind

GATE 2024 BM – Question 12

Engineering Mathematics · Numerical Methods · 1 mark · Multiple choice

Which Newton–Raphson iteration solves x=2cos x?

  1. $x_{n+1}=x_n-\frac{x_n-2\cos x_n}{1+2\sin x_n}$
  2. $x_{n+1}=x_n+\frac{x_n-2\cos x_n}{1+2\sin x_n}$
  3. $x_{n+1}=x_n+\frac{1+2\sin x_n}{x_n-2\cos x_n}$
  4. $x_{n+1}=x_n-\frac{1+2\sin x_n}{x_n-2\cos x_n}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $x_{n+1}=x_n-\frac{x_n-2\cos x_n}{1+2\sin x_n}$

Explanation

Set f(x)=x−2cos x, with derivative 1+2sin x. Newton’s method subtracts f divided by its derivative from the current iterate. Therefore A has both the correct numerator/denominator and sign.

More Numerical Methods questions

All Numerical Methods questions →