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Homework Help: Limit of a function

  1. May 8, 2006 #1
    could anyone tell me if this have a limit:
    lim ((exp(x)-1-x)^2)/(x^2 - ln(x^2+1)))
    x->0

    My conclusion is that this doesn't have a limit. Tried everything, this is an problem that i run into.
     
    Last edited: May 8, 2006
  2. jcsd
  3. May 8, 2006 #2
    Have you tried applying L'Hospital's?
     
  4. May 9, 2006 #3

    VietDao29

    User Avatar
    Homework Helper

    Have you tried using Maclaurin Series to solve this problem? :)
    Hint:
    The expansion of exp(x) arround x = 0 is:
    [tex]e ^ x = 1 + x + \frac{x ^ 2}{2} + ...[/tex]
    The expansion of ln(x + 1) arround x = 0 is:
    [tex]\ln (x + 1) = x - \frac{x ^ 2}{2} + ...[/tex]
    So what's the expansion of ln(x2 + 1) arround x = 0?
    Can you go from here? :)
     
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