GATE 2017 CE (CE1) – Question 31

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 1 mark · Numerical answer

Evaluate $\displaystyle\lim_{x\to0}\frac{\tan x}{x^2-x}$.

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Correct answer: -1.1 to -0.9

Explanation

Factor the denominator as $x(x-1)$. The expression becomes $(\tan x/x)/(x-1)$. As $x\to0$, $\tan x/x\to1$ and $x-1\to-1$. Therefore the limit is −1. Both numerator and denominator vanish linearly, so direct substitution without taking the limit is not valid.

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