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Math Help - confusion with limit theory, involving l'Hopital's rule

  1. #1
    Junior Member
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    confusion with limit theory, involving l'Hopital's rule

    This is actually a problem from a subject thats mainly involved with Laplace transforms.

    it starts off with expanding f(s) = ln(1+1/s) around infinity (by taylor series)

    so firstly, evaluating ln(1+1/s) at s = infinity, which tends towards log (1 + 0 ) = 0

    then the next term of the taylor series involves f ' (s) evaluated at infinity

    f'(s) = -1 / (s^2 + s )
    f ' (inf) = -1 / (inf) = 0 .... right?

    f '' (s) = (2s + 1) / (s^2 + s)^2

    now for evaluating this one at infinity directly would yield inf / inf = 1 ?

    but i know (of) l'Hopital's rule
    which i tried

    so lim s -> \infty of (2s + 1) / (s^2 + s)^2

    = lim s -> inf of 2 / 4s(s^2 + s) = 0

    here i derived both top and bottom of the fraction (seperately) with respect to s

    long story short, if you use l'hopitals rule for the following terms as well, you get 0 for every term in the taylor series, which im assuming isnt right.

    am i using l'hopitals correctly? any other help?


    also any tips on using the Math-notation available here? :P
    Last edited by walleye; September 27th 2009 at 05:58 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by walleye View Post
    This is actually a problem from a subject thats mainly involved with Laplace transforms.

    it starts off with expanding f(s) = ln(1+1/s) around infinity (by taylor series)

    so firstly, evaluating ln(1+1/s) at s = infinity, which tends towards log (1 + 0 ) = 0

    then the next term of the taylor series involves f ' (s) evaluated at infinity

    f'(s) = -1 / (s^2 + s )
    f ' (inf) = -1 / (inf) = 0 .... right?

    f '' (s) = (2s + 1) / (s^2 + s)^2

    now for evaluating this one at infinity directly would yield inf / inf = 1 ?

    but i know (of) l'Hopital's rule
    which i tried

    so lim s -> inf of (2s + 1) / (s^2 + s)^2

    = lim s -> inf of 2 / 4s(s^2 + s) = 0

    here i derived both top and bottom of the fraction (seperately) with respect to s

    long story short, if you use l'hopitals rule for the following terms as well, you get 0 for every term in the taylor series, which im assuming isnt right.

    am i using l'hopitals correctly? any other help?


    also any tips on using the Math-notation available here? :P
    Put u=1/s, then expand \ln(1+u) about zero, and then make the substitution s=1/u into that series.

    CB
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