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Limit question

  1. Feb 28, 2010 #1
    1. The problem statement, all variables and given/known data
    I've done thsi limit, i think I'm half right. I'm sure I have done something wrong, but I'm not sure what.

    [tex] lim_{x-> \infty} ( \frac {x+lnx}{x-lnx})^(x/lnx) [/tex]


    3. The attempt at a solution
    [tex] lim_{x-> \infty} ( \frac {x+lnx}{x-lnx})^{x/lnx} = lim_{x-> \infty} ( \frac {x(1 +\frac {lnx}{x})}{x(1- \frac {lnx}{x})})^{x/lnx}= [/tex]
    [tex]
    t= \frac {x}{lnx}; lim_{t-> \infty} (\frac {1 + \frac {1}{t}} {1 - \frac{1}{t}})^t= [/tex]
    [tex] \frac {e}{e^{-1}}=e^2 [/tex]
     
    Last edited: Feb 28, 2010
  2. jcsd
  3. Feb 28, 2010 #2

    vela

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    That's right.
     
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