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Math Help - Expo-limit

  1. #1
    Super Member dhiab's Avatar
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    Expo-limit

    Calculate this limit:
    \mathop {\lim }\limits_{x \to 0} \left( {x^x } \right)
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by dhiab View Post
    Calculate this limit:
    \mathop {\lim }\limits_{x \to 0} \left( {x^x } \right)
    Are you allowed to use l'Hopital's Rule? NB: This limit will only be valid if it's a right hand limit: \mathop {\lim }\limits_{x \to 0^{\color{red}+}} \left( {x^x } \right).
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  3. #3
    MHF Contributor
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    Talking

    Let y = x^x. Then ln(y) = x*ln(x) = ln(x)/(1/x). You can apply l'Hospital's Rule to this, and get the limit, as x tends to zero from the right, of ln(y). Then raise this value as a power on e, to get the limit of y.
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