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Homework Help: Limit x -> 0 cos(x) - 1 / sin(x)

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data
    x in the following is actually Theta

    Limit as x -> 0 (cos(x) - 1) / sin(x)



    2. Relevant equations

    none

    3. The attempt at a solution

    Multiply both sides by cos x +1

    [ (cos x - 1) / sin x ] * [ (cos x + 1 )/ (cos x + 1)]

    = [ cos2 x -1 ] / sin(x) (cos(x) +1)

    = -sin2 x / sin x (cos x + 1)

    - sin x / sin x cancels to -1 leaving sin x / (cos x + 1)

    Sub in x -> 0

    = (-1) (sin(0) / cos(0) + 1)

    = (-1) (0/2) = 0


    The only step I am not sure about the is cancelation of sin x /sin x. Is this allowed? How does the solution look?
     
  2. jcsd
  3. Oct 15, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The solution looks fine. Sure you can cancel the sin(x)/sin(x).
     
  4. Oct 15, 2008 #3
    Thank you for the fast response. Your help is much appreciated.
     
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