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Homework Help: Limit of a trig function

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data
    lim as x approaches pi


    2. Relevant equations

    above equation

    3. The attempt at a solution
    well, i substituted pi-x for t
    then took the limit as x approaches pi
    got zero, so the equation is now

    lim as t approaches 0


    i know the answer is one, but how can i get it after this step

    edit: i can't use l'hopital's rule
  2. jcsd
  3. Oct 20, 2009 #2


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    Homework Helper

    if you want to substitute for x, you should do both

    x = t+ pi

    so your limit becomes

    you could try expanding sin in a taylor series if you can't use L'Hop
  4. Oct 20, 2009 #3
    thank you
  5. Oct 20, 2009 #4


    Staff: Mentor

    Can you use the fact that [tex]\lim_{x \rightarrow 0}\frac{sin x}{x}~=~1[/tex]?

    If you can, you might also make use of the identity that sin(pi - x) = sin(x).
  6. Oct 20, 2009 #5


    User Avatar
    Homework Helper

    yeah thats cleaner
  7. Oct 20, 2009 #6
    yeah, i saw that

    thank you to the both of you
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