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Limit involving natural log

  1. Dec 20, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the limit of (tanx)^cosx as x-->infinity
    Rearrange the equation so that you can use L'Hopital's rule for the form of (infinity/infinity)

    3. The attempt at a solution
    I did ln(tanx)^cosx = cosxlntanx
    I know the limit of tanx as x-->infinity is pi/2
    the limit of cosx as x-->infinity is infinity

    Now, I don't know where to go from here
    Last edited: Dec 20, 2007
  2. jcsd
  3. Dec 20, 2007 #2


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    Homework Helper

    "the limit of cosx as x-->infinity is 1 (or is it infinity?)"
    That limit doesn't exist.
  4. Dec 20, 2007 #3
    Oh okay. So now I have infinity x infinity. I can use L'Hopital's rule but I don't know how to set up the function.
  5. Dec 20, 2007 #4


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    Staff Emeritus
    Science Advisor

    No, you cannot use L'Hopital's rule for that. "Infinity* infinity" is not one of cases for which you can use L'Hopital's rule- nor do you need to. You have already been told the answer.
  6. Dec 20, 2007 #5
    I just noticed in the directions it says to rearrange the problem so that you can use L'Hopital's rule.
  7. Dec 20, 2007 #6
    Well then, what are the special cases in which L'Hopital's Rule can be applied? That is what are indeterminate forms?

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