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Math Help - L'Hopital's Rule

  1. #1
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    L'Hopital's Rule

    I am to use L'Hopital's Rule on the following problem:

    limit as x --> infinity of (1 + (1/x))^x

    f(x) = (1 + (1/x))^x
    ln[f(x)] = ln [(1 + (1/x))^x] = x ln (1 + (1/x)) = x ln ((x+1)/x)

    I can't seem to convert it into a form where I have simply infinity over infinity or zero over zero, because of the 'x' in front of the ln.

    :S
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  2. #2
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    Quote Originally Posted by niyati View Post
    I am to use L'Hopital's Rule on the following problem:

    limit as x --> infinity of (1 + (1/x))^x

    f(x) = (1 + (1/x))^x
    ln[f(x)] = ln [(1 + (1/x))^x] = x ln (1 + (1/x)) = x ln ((x+1)/x)

    I can't seem to convert it into a form where I have simply infinity over infinity or zero over zero, because of the 'x' in front of the ln.

    :S
    Hi,

    maybe this will do:

    f(x) = \left(1+\left(\frac1x\right)\right)^x = \left(\frac{x+1}{x}\right)^x = \frac{(x+1)^x}{x^x}
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