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Math Help - Unable to solve this limit problem

  1. #1
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    [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.
    Last edited by xcluded; October 27th 2009 at 09:21 AM. Reason: Solved
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  2. #2
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    Quote Originally Posted by xcluded View Post
     \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
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