GATE 2017 ME (ME1) – Question 12

Engineering Mathematics · Calculus: Definite and improper integrals, double and triple integrals · 1 mark · Multiple choice

Evaluate $\displaystyle\lim_{x\to0}\frac{x^3-\sin x}{x}$.

0
3
1
−1

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Correct answer: (D) −1

Explanation

Split the expression into $x^2-\sin x/x$. For angles in radians, $\sin x/x\to1$ as $x\to0$, while $x^2\to0$. Consequently the limit is $0-1=-1$, option D.

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