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Math Help - Problem with integration

  1. #1
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    Problem with integration

     f(x)= \left( 1-\frac{x}{2}  \right)^{\frac{a}{x}}

    How can i find f ' (0) ?
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  2. #2
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    Quote Originally Posted by atlantis84 View Post
     f(x)= \left( 1-\frac{x}{2} \right)^{\frac{a}{x}}

    How can i find f ' (0) ?
    First find f(0). Take ln's so

    \ln f = \frac{a \ln \left(1 - \frac{x}{2}\right)}{x} (1)

    use L'Hopital's rule. This gives f(0) = e^{-a/2}. Then differentiate (1) and use L'Hoptials rule again on this. This gives

     <br />
\frac{f'(0)}{f(0)} = - \frac{a}{8}<br />

    so f'(0) = - \frac{a}{8} e^{-a/2}.
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  3. #3
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    Thnxxx for helping, i got it till f(0) = e^{-a/2}

    but i have a really hard time calculating

    <br />
\frac{f'(0)}{f(0)} = - \frac{a}{8}<br />


    Could you give me the exact calculations? thnx anyway
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