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Math Help - limits

  1. #1
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    limits

    lim ((1+x)^(1/x)-e)/x can yu do it by l,hospital rule
    x\to0
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  2. #2
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    Quote Originally Posted by prasum View Post
    lim ((1+x)^(1/x)-e)/x can yu do it by l,hospital rule
    x\to0
    You can but it get really nasty! Are you required to us L'Hopital's rule?
    It's much easier if you recognize that letting 1/x= p gives
    lim(p-> infinity) (1+ 1/p)^p = e. This turns out to be, essentially, a derivative.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    You can but it get really nasty! Are you required to us L'Hopital's rule?
    It's much easier if you recognize that letting 1/x= p gives
    lim(p-> infinity) (1+ 1/p)^p = e. This turns out to be, essentially, a derivative.

    i have done by substituting (1+x)^1/x=e^((1/x)(ln(1+x))) so appling expansion of e we get limit as -e/2 can yu please suggest graphical approach
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