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GATE 2025 AE – Question 41

Engineering Mathematics · Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration · 2 marks · Numerical answer

$\lim_{x \to 0}\frac{1 - \cos(2x)}{x^2} = $ _____ (answer in integer).

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Correct answer: 2

Explanation

$1 - \cos 2x = 2\sin^2 x$, so the limit is $2\left(\frac{\sin x}{x}\right)^2 \to 2$.