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Find limits of sine and cosine functions

  1. Jun 17, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the limit:

    lim (1-cos2x)/(xsinx)
    x->0


    2. Relevant equations
    Identities


    3. The attempt at a solution

    I've done this over and over and over again! The answer is supposed to be 0 but I keep getting 2 ):

    lim (1-cos2x)/(xsinx)
    x->0

    lim (1-1+2sin2x)/(xsinx)
    x->0

    lim (2sin2x)/(xsinx)
    x->0

    lim (2sinx)/x
    x->0

    = 2*1 = 2

    Any help is appreciated!! Thank you!
     
  2. jcsd
  3. Jun 17, 2011 #2

    micromass

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    Last edited by a moderator: Apr 26, 2017
  4. Jun 17, 2011 #3

    Dick

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    I don't see anything wrong with what you did. I'd say the limit is 2 as well.
     
  5. Jun 17, 2011 #4
    Thanks guys (: I guess textbook error then! Yay!

    Thank you <3
     
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