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

1. Apr 5, 2008

rene

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

2. Apr 5, 2008

awvvu

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

3. Apr 6, 2008

arildno

The simplest is to rewrite this as:
$$(1+\sin(x))^{\frac{1}{x}}=((1+\sin(x))^{\frac{1}{\sin(x)}})^{\frac{\sin(x)}{x}}$$
The correct limit is quite easy to deduce from this.