# Math Help - Unable to solve this limit problem

1. ## [Solved]Unable to solve this limit problem

$\lim \frac{(cos x)^\frac{1}{x} - 1}{x}$
$x\rightarrow0$

Hmm how should i start about doing it?

is it possible to use L'H rule ?

Thanks.

2. Originally Posted by xcluded
$\lim \frac{(cos x)^\frac{1}{x} - 1}{x}$
$x\rightarrow0$

Hmm how should i start about doing it?

is it possible to use L'H rule ?

Thanks.
Of course you can use L'H since you've an indeterminate $\frac{0}{0}$. Just note that in order to derivate the numerator it may be a good idea to write

$\displaystyle{\left(\cos x\right)^\frac{1}{x}=e^{\frac{1}{x}\ln \cos x}}$

Tonio