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Math Help - L'Hospital

  1. #1
    Super Member
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    Jun 2008
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    829

    L'Hospital

    calculate:

    \lim_{x \to 0} (cotx)^\frac{1}{lnx}



    Answer:
    -1
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  2. #2
    Super Member wingless's Avatar
    Joined
    Dec 2007
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    Istanbul
    Posts
    585
    In these kind of limits, do this:

    \lim_{x\to a} {f(x)}^{g(x)}

    \lim_{x\to a} e^{g(x) \ln [f(x)]}

    Now find the limit g(x) \ln [f(x)] using L'hopital.

    If you don't see how it's done,

    g(x) \ln [f(x)] = \frac{\ln [f(x)]}{\frac{1}{g(x)}}

    or

    g(x) \ln [f(x)] = \frac{g(x)}{\frac{1}{\ln [f(x)]}}

    Now it's ready for using L'hopital. The other question of you is done the same way too.
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