The value of limx→0 (1+sin⁡x)2cot⁡x, is

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

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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