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Weird Limit Problem

  1. Sep 16, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the limit as x approaches 0 of x^2/(1-cosx).

    2. Relevant equations


    3. The attempt at a solution

    I know from L'Hopital's rule that the limit is 2, but I'm not supposed to use L'Hopital's rule to calculate it. What else can I do here?
  2. jcsd
  3. Sep 16, 2007 #2


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    How about the identity cos(x) = 1 - 2sin^2(x/2)?
  4. Sep 16, 2007 #3


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    You could also consider the power series expansion of cos(x) around zero.
  5. Sep 17, 2007 #4


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    Multiply both numerator and denominator by 1+ cos(x). Then use the fact that
    [tex]lim_{x\rightarrow 0}\frac{x}{sin(x)}= 1[/tex].
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