GATE 2020 AG – Question 25
Evaluate $\lim_{x\to0}(e^x-e^{-x}-2x)/(x-\sin x)$.
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Correct answer: 2 to 2
Explanation
The numerator expansion is x³/3+O(x⁵), since the linear terms cancel. The denominator is x³/6+O(x⁵). Their ratio therefore tends to (1/3)/(1/6)=2.