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L'hospital's Rule Problem

  1. Jan 25, 2012 #1
    Using L'hospitals rule, find the limit
    2rgdgmh.png




    I seem to stuck using L'hospital's rule ,I replaced cotx=1/tanx but the derivatives of even 4th order are not simplying things.
     
  2. jcsd
  3. Jan 25, 2012 #2

    Dick

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    Before you even start with l'Hopital's rule you need to check you can write the limit in an indeterminant form 0/0 or infinity/infinity. Did you check that? And do you really mean lim x->inf??
     
    Last edited: Jan 25, 2012
  4. Jan 25, 2012 #3
    Yes,
    put cotx=(tanx)^-1, we have then
    tan^2x-x^2
    --------------
    x^2tan^2x
    Then we can use the rule.

    But I tried wolfram alpha just now and found out that this limit does not exist.
    http://www.wolframalpha.com/input/?i=limit+x%5E%28-2%29-%28cotx%29%5E2%2C++x-%3Einf

    But instead x->0 exists.
    http://www.wolframalpha.com/input/?i=limit+x%5E%28-2%29-%28cotx%29%5E2%2C++x-%3E0
    This is the same answer given in textbook. Probably a printing error.
    Sorry If I wasted your time.
     
  5. Jan 25, 2012 #4

    Dick

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    Yes, that's the way to set it up, and I'm sure they mean lim x->0. Given that you should get the right result after four derivatives.
     
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