1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    That's right.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook