First slide

Introduction to limits

Question

The value of $lim_{x \to 0} (1 + \sin x)^{2 \cot x},$ is

Moderate

A

$e$
B

$e^{2}$
C

$\sqrt{e}$
D

none of these

Solution

We have,
$lim_{x \to 0} (1 + \sin x)^{2 \cot x} = e^{lim_{x \to 0} \sin x \times 2 \cot x} = e^{lim_{x \to 0} 2 \cos x} = e^{2}$

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