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Limit of sin2x/sin3x

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine the limit of

    [itex] \lim_{x \to 0} \frac {sin2x}{sin3x}[/itex]

    2. Relevant equations

    Hint: Find [itex]\lim_{x\to 0} (\frac{2 sin 2x}{2x}) (\frac{3x}{3 sin 3x})[/itex]
    3. The attempt at a solution

    I've been blankly staring at it not knowing where to start. I think the only thing that the hint manages to do is to confuse me.

    Any help on helping me to start it? I don't understand the hint.

    Thanks in advance.
     
  2. jcsd
  3. Oct 9, 2011 #2

    ehild

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    Do you not what is [tex] \lim _{x \to 0} \frac{sin(x)}{x}[/tex]?

    ehild
     
  4. Oct 9, 2011 #3

    vela

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    In your book or notes, you should find how to evaluate
    [tex]\lim_{x \to 0} \frac{\sin x}{x}[/tex]
     
  5. Oct 9, 2011 #4
    Yes they are equal to one, but they aren't asking for [tex] \lim_{x \to 0} \frac {sinx}{x}[/tex]

    They are asking for [tex]\lim_ {x \to 0} \frac{sin2x}{sin3x}[/tex]
     
  6. Oct 9, 2011 #5

    vela

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    And you see absolutely no connection to that limit and the hint?
     
  7. Oct 9, 2011 #6
    Ohhhhhh !

    Its funny how someone can say so little yet help so much hehe. Thanks, I got it now.
     
  8. Oct 9, 2011 #7
    Answer is 2/3.
     
  9. Oct 9, 2011 #8

    vela

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    I think we've all had those moments where we fail to see what in hindsight seems so obvious. :wink:
     
  10. Oct 9, 2011 #9
    Thank you for your help by the way:)
     
  11. Oct 9, 2011 #10

    HallsofIvy

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    For a more "formal" look, let u= 2x so that you have
    [tex]\lim_{x\to 0}\frac{sin(2x)}{2x}= \lim_{u\to 0}\frac{sin(u)}{u}[/tex]
     
  12. Oct 9, 2011 #11
    Hey halls, thanks for the suggestion. Will keep in mind in the future. ^.^
     
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