Limit of [1 + sin(x)]^(1/x) when x approaches 0

Main Question or Discussion Point

Can somebody solve this problem: the limit of [1 + sin(x)]^(1/x) when x approaches 0 ?

Take the logarithm of that expression, which will let you use L'Hopital to solve it.

arildno
$$(1+\sin(x))^{\frac{1}{x}}=((1+\sin(x))^{\frac{1}{\sin(x)}})^{\frac{\sin(x)}{x}}$$