Limit

[rene]

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

[awvvu]

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

[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.