Question

$\underset{x\to 0}{lim}\frac{e^{\sin x}-1}{x}$ is equal to

• A. $0$
• B. $e$
• C. $1$
• D. Does not exist

Answer 1

Answer: (C)

$1$

The value of $\underset{x\to 0}{lim}\frac{e^{\sin x}-1}{x}$ is
$=\underset{x\to 0}{lim}[\frac{(e^{\sin x}-1)}{\sin x}\times \frac{\sin x}{x}]$
$=\underset{\sin x\to 0}{lim}\frac{e^{\sin x}-1}{\sin x}\times \underset{x\to 0}{lim}\frac{\sin x}{x}$
$=1\times 1=1$