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Homework Help: A limit question

  1. Mar 18, 2008 #1

    daniel_i_l

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    Gold Member

    1. The problem statement, all variables and given/known data
    I was doing a problem and got to the following limit:
    [tex]lim_{x \rightarrow 0^{+}} x^{\frac{1}{x} - 1}[/tex] I calculated it and got 0 but when I calculated it here:
    http://wims.unice.fr/wims/en_tool~analysis~function.en.html
    It said that it wans't defined. Am I right?
    Thanks.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 18, 2008 #2
    try the following:
    [tex]lim_{x \rightarrow 0^{+}} x^{\frac{1}{x} - 1}=\lim_{x\rightarrow 0^{+}}e^{ln(x)^{\frac{1}{x}-1}}=\lim_{x\rightarrow\ 0^{+}} e^{\frac{1-x}{x}ln(x)}=e^{\lim_{x\rightarrow\ 0^{+}}\frac{1-x}{x} \lim_{x\rightarrow\ 0^{+}}ln(x)}=e^{\infty*(-\infty)}=e^{-\infty}=0[/tex]
     
  4. Mar 18, 2008 #3

    daniel_i_l

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    Gold Member

    Thanks, that's what I did but the wims calculator confused me.
     
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