Question

Evaluate

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

Answer 1

We have,

$\begin{array}{c}{lim}_{x\to 0}\frac{e^{\sin x}-1}{\sin x\cdot x}x\sin x\\ {lim}_{x\to 0}\frac{e^{\sin x}-1}{\sin x}\cdot {lim}_{x\to 0}\frac{\sin x}{x}\\ =1\times 1\\ =1\end{array}$

Hence, this is the answer.