First slide

Introduction to limits

Question

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

Moderate

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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