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Lim of trig functions

  1. Mar 9, 2013 #1
    1. The problem statement, all variables and given/known data

    lim 2x/(sin3x)
    x-> 0


    2. Relevant equations

    lim sinx/x = 1
    x->0

    3. The attempt at a solution

    is it correct to say the following:

    lim 2/3 (sinx/x)
    x-> 0

    lim 2/3 (1)
    x-> 0

    Answer: lim 2x/sin3x = 2/3
    x-> 0

    Because it's on the book:
    cos 2x(2)/3 = 2/3
    x->0

    So I want to know if I solve it the way I did before, would it be correct?
     
    Last edited: Mar 9, 2013
  2. jcsd
  3. Mar 10, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    lim 2/3 sin(x)/x is zero at x=0, but 2x/sin(3x) is not the same as (2/3)sin(x)/x.

    Rewrite 2x/sin(3x) as 2/3 (3x)/sin(3x).

    ehild
     
  4. Mar 10, 2013 #3
    Thanks!! Got it!! =)
     
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