limn→∞ 1+sin⁡ann equals

$lim_{n \to \infty} {(1 + \sin \frac{a}{n})}^{n}$ equals

A
$e^{a}$
B
$e$
C
$e^{2 a}$
D
0

Solution:

We have,

$lim_{n \to \infty} {(1 + \sin \frac{a}{n})}^{n}$

$= e^{lim_{n \to \infty} n \sin \frac{a}{n}} = e^{lim_{n \to \infty} \sin (\frac{a / n}{(a / n)}) \times a} = e^{1 \times a} = e^{a}$

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