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Math Help - Limit Problem

  1. #1
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    Limit Problem

    Hi, I'm having trouble starting this problem. Someone suggested using L'Hospital's rule but I can't figure out how to apply that here. Anyway, here's the problem, any help would be appreciated. Thanks in advance.

    Lim x-->0+

    X ^ ( -1 / ln(x) )
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  2. #2
    Super Member Random Variable's Avatar
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    take the natural log

     \lim_{x \to 0^{+}} \ln \Big(x^{\frac {\text{-}1}{ln(x)}}\Big) = \lim_{x \to 0^{+}} \frac {\text{-}1}{\ln(x)} \ln(x)  = \text{-}1

    therefore,  \lim_{x \to 0^{+}} x^{\frac {\text{-}1}{ln(x)}} = e^{-1} = \frac {1}{e}
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  3. #3
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    Take log of the expression.

    EDIT: Tooooo slooow.
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