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Limit of sin(3x)/sin(5x) as x→0

  1. Nov 28, 2011 #1
    1. The problem statement, all variables and given/known data
    Find [tex]\lim_{x\rightarrow 0} {\frac{\sin(3x)}{\sin(5x)}}[/tex]

    3. The attempt at a solution
    I know that the limit equals 0.6 (by typing it into my calculator), but I have no idea how to prove this, or even where to start. I know that sin is continuous, so I theoretically should be able to just plug it in, but obviously this doesn't work because it isn't divisible by 0.
  2. jcsd
  3. Nov 28, 2011 #2


    Staff: Mentor

    Try multiplying by 3x/(3x) and 5x/(5x), and placing the numerators and denominators strategically. The basic idea is that [itex]\lim_{u \to 0} \frac{sin u}{u} = 1[/itex]
  4. Nov 28, 2011 #3


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  5. Nov 28, 2011 #4
    Thank you! I can't believe I didn't think of that answer - that helped me figure out the later questions as well.
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