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Homework Help: Basic limits

  1. Jun 17, 2017 #1
    1. The problem statement, all variables and given/known data

    Find limit for x tending to infinity of: (e^(x^-2)-1)/(2arctan(x^2) - pi)
    2. Relevant equations
    arctanx +arccotx=pi/2

    3. The attempt at a solution
    P.S I haven't written limit before each step, and hope you can get how I arrived at the first step.I just took 2 common from the denominator and used simple inverse trig.

    However,the answer is -1/2
    Where am I going wrong?
  2. jcsd
  3. Jun 17, 2017 #2


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    ##\frac{1}{\cot^{-1}(x^2)} = \tan^{-1}(x^2)## is not true.

    I didn't check whether you made other mistakes though.
  4. Jun 17, 2017 #3


    Staff: Mentor

    Do you know L'Hopital's Rule?
  5. Jun 18, 2017 #4
  6. Jun 18, 2017 #5
    Yes,I do
  7. Jun 18, 2017 #6
    Ok,I got where I am going wrong,but how to go right?
    It looks like we won't be able to use inverse trig
  8. Jun 18, 2017 #7


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    Use l'Hopital's rule on the first step you wrote down and you should be fine.
  9. Jun 18, 2017 #8


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    Staff Emeritus
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    Gold Member

    Can you find the derivative of ##\ \tan^{-1}(x^2) - \frac \pi 2 \,,\ ## and derivative of ##\ e^{1/x^2}-1\,?##
  10. Jun 19, 2017 #9
    Yeah,I can..and I did,thanks
  11. Jun 19, 2017 #10


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    Did you get the right answer?
  12. Jun 19, 2017 #11
    Yep,-1/2 (I used another inverse property in b/w though,I had gone wrong in writing the last step,that way I didn't need l'hospital)
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