Question

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

Answer 1

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

Using L'Hospital's rule we get,

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