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Limit question

  • Thread starter talolard
  • Start date
  • #1
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Homework Statement


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]


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:

Answers and Replies

  • #2
vela
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That's right.
 

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