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Trig limits question

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data
    evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3


    2. Relevant equations



    3. The attempt at a solution
    the answer in the textbook is 8/27
    i figured they got that by raising 2 to the 3rd and 3 to the 3rd
    but i'm not entirely sure what happens to the sin's

    id really appreciate a worked out answer (that doesn't use l'hopital's rule)
     
  2. jcsd
  3. Nov 27, 2011 #2

    LCKurtz

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    We don't do worked out answers. But here's a hint: Presumably you know something about the limit of sin(x)/x as x → 0. Make use of that by multiplying and dividing by certain powers of x.
     
  4. Nov 27, 2011 #3
    well
    lim
    x->0 sinx/x = 1
    the problem is that i don't know how to apply it to this question
     
  5. Nov 27, 2011 #4

    LCKurtz

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    What would be the limit of [itex]\frac {\sin(2x)}{2x}[/itex] as x → 0?
     
  6. Nov 27, 2011 #5
    that limit would be 1 as well
    but i'm still not sure how it'd help
     
  7. Nov 27, 2011 #6

    LCKurtz

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    Now read the hint I gave in post #2 again. Hopefully you will see it; I'm signing off for tonight.
     
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