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Math Help - Limits question

  1. #1
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    Limits question

    Limit[(x^a - a^x)/(x^x - a^a), x -> a]

    Anyone knows how to solve this? I applied La'Hospitals rule but didnt really proceed far.
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  2. #2
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    Quote Originally Posted by champrock View Post
    Limit[(x^a - a^x)/(x^x - a^a), x -> a]

    Anyone knows how to solve this? I applied La'Hospitals rule but didnt really proceed far.
    It should have worked as long as a > 0, applying L'Hopital's rule once gives

    \lim_{x \to a} \frac{ax^{a-1} - a^x \ln a}{x^x (\ln x+1)} = \frac{1 - \ln a}{1 + \ln a}
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  3. #3
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    Did you do it correctly?
    \lim _{x \to a} \frac{{x^a  - a^x }}<br />
{{x^x  - a^a }}\mathop  = \limits^H \lim _{x \to a} \frac{{ax^{a - 1}  - a^x \ln (a)}}{{x^x \left( {\ln (x) + 1} \right)}}
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  4. #4
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    OK, really silly mistake! i did uptil that point correctly but didnt put in the values of X after that! was somehow expecting something simpler. hehe.

    thanks coming for u guys!
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