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Homework Help: Limit of logarithm of square roots function

  1. Jul 23, 2010 #1
    1. The problem statement, all variables and given/known data
    I need to prove that the following limit holds when

    [tex]\sqrt{s}>>m[/tex]

    [tex]\log\left(\frac{\sqrt{s}+\sqrt{s-4m^2}}{\sqrt{s}-\sqrt{s-4m^2}}\right) \rightarrow \log\left(\frac{s}{m^2}\right)[/tex]

    3. The attempt at a solution
    I've tried several manipulations using logarithms properties but had no success.

    Thanks
     
    Last edited: Jul 23, 2010
  2. jcsd
  3. Jul 23, 2010 #2

    Mute

    User Avatar
    Homework Helper

    You don't need to bother with the logarithm, just focus on the stuff inside. I'll give you a starting hint; you should provide the rest of your workings after that if you can't get it and want further help. To start, I would pull the factor of [itex]\sqrt{s}[/itex] out from the top and bottom of the fraction inside the logarithm. Find the limiting form of the fraction in your desired limit.
     
  4. Jul 23, 2010 #3
    Hello Mute, thanks for the help. I've managed to do it, after Taylor expansion of [tex]\sqrt{1-x}[/tex], where in my limit:

    [tex]x=\frac{4m^2}{s}\rightarrow 0[/tex].

    As I'm under some time pressure to finish this, very bigg, home exam I'm already not thinking so clearly..

    Thanks again
     
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