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Math Help - integral

  1. #1
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    integral

    f(x) = \int_{2}^{x} \ln(t) dt

    find (f^{-1})'(0)
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  2. #2
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    Use the fact that,
    [f^{-1}(c)]'=\frac{1}{f'(f^{-1}(c))}
    In this case,
    c=0.

    [f^{-1}(0)]'=\frac{1}{f'(f^{-1}(0))}
    Now,
    f^{-1}(0)=2 because \int_2^2 \ln t dt =0.
    And,
    f'(x)=\ln x.
    Thus,
    [f^{-1}(0)]'=\frac{1}{\ln 2}
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