GATE 2019 AE – Question 25
Engineering Mathematics · Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration · 1 mark · Numerical answer
Evaluate $\lim_{\theta\to0}(\theta-\sin\theta)/\theta^3$ (two decimal places).
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Show answer and explanation
Correct answer: 0.16 to 0.17
Explanation
Expand $\sin\theta=\theta-\theta^3/6+O(\theta^5)$. The numerator is $\theta^3/6+O(\theta^5)$, so the limit is 1/6 = 0.1667, which rounds to 0.17.
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