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GATE 2022 MT – Question 37

Engineering Mathematics · Numerical methods · 2 marks · Multiple choice

Which equation fails to converge to a root under Newton–Raphson iteration starting at $x=0.5$?

  1. $x(1-x)=0$
  2. $e^x-3x^2=0$
  3. $x-\ln(3x)=0$
  4. $\tan x-x=0$

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Show answer and explanation

Correct answer: (A) $x(1-x)=0$

Explanation

For $f(x)=x(1-x)$, $f^\prime(x)=1-2x$. At the initial value 0.5, the derivative is zero while $f=0.25$. Newton’s update $x-f/f^\prime$ is undefined immediately. Answer: **A**.