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Limits in a 0/0 case

  1. Sep 23, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm in the early stages of Calculus I.. just doing the basics you learn in the Calc prep course.
    This one problem is really getting me confused.


    2. Relevant equations

    Lim -> 0 in the function 1/x(1/(x+2)^2 -1/4)

    3. The attempt at a solution

    I've tried foiling and cancelling, it hasn't worked.
    I've tried a^2 - b^2 formula to cancel, that hasn't worked either
    Tried using a conjugate without a root and that doesn't work
    Would this be a case where 'The Squeeze' method would be necessary? Or is there a better way.. Thanks in advance
     
  2. jcsd
  3. Sep 23, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You better show us your attempt at doing some algebra and cancelling the x. Because it works for me.
     
  4. Sep 23, 2009 #3
    After about 10 attempts later and numerous sign errors and not simplifying stuff enough i finally got an answer of -1/4.. Thanks anyway guys!
     
  5. Sep 23, 2009 #4
    Can try L'Hopital rule?
     
  6. Sep 23, 2009 #5
    Lim -> 0 in the function 1/x(1/(x+2)^2 -1/4)

    Do you mean this?

    [tex] \lim_{x\to 0}\frac{1}{x} (\frac{1}{(x+2)^{2}} - \frac{1}{4}) [/tex]
     
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