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Homework Help: Ok, Limit problem

  1. May 16, 2008 #1
    Ok, the problem is find the limit of x/sqrt(1-cosx) as x approaches 0 from the negative side.

    First I tried simply applying l'hopital's rule to see what would happen, and it didn't work.

    Next I tried rationalizing it by multiplying the numerator and denominator by sqrt(1+cosx), then using a trig identity (1-(cosx)^2=(sinx)^2 to get sqrt((sinx)^2) or simply sinx. Then I applied l'hopital's rule and ended up with a big mess that still ended up with 0/0.

    Did I miss something or do something incorrectly?
  2. jcsd
  3. May 16, 2008 #2


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    1 - cos(x) = 2sin^2(x/2)

    x/sqrt(1-cos(x)) = x/sqrt(2)sin(x/2)

    Using L'Hopitals on this does not lead to 0/0.
  4. May 16, 2008 #3
    So I was missing something, thanks.
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