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Limit Problem

  1. Sep 13, 2014 #1
    So I've been trying to solve this limit problem for some time. Here is the problem:-
    [tex]
    \lim_{x\rightarrow 0} {\frac{6sin(x) - 2sin(3x)}{tan^3(3x)}}
    [/tex]


    I cannot use l'hopital's rule to solve it. I've tried taking 2 as a factor, then trying to use a trig identity, but I couldn't figure a thing. Dividing by x doesn't work either.

    I have a feeling this problem is easy, yet I can't grasp the solution. So I figured I would get some help here.
     
  2. jcsd
  3. Sep 13, 2014 #2

    Ray Vickson

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    Do you mean that you are not allowed to use l'Hospital's rule, or do you mean you don't know how to use it in this problem?
     
  4. Sep 13, 2014 #3
    Yeah the textbook does not allow it.
     
  5. Sep 13, 2014 #4

    Ray Vickson

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    What ARE you allowed to use? If we don't know that we cannot make any sensible suggestions.
     
  6. Sep 13, 2014 #5
    Ok, let me explain. The textbook has no mention of l'hopital's rule, thus we cannot use it. The way we are supposed to solve limits is by the "theorem" : the lim as x approaches 0 of sin(a*x) / sin(b*x) = a / b. To solve trigonometric limits, we use trigonometric identities usually to reach a state where we can use this theorem to "get rid" of what makes the denominator zero and then get the answer by substituting.
     
  7. Sep 13, 2014 #6

    Char. Limit

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    Can you decompose tan(x) into sin(x)/cos(x) and work from there?
     
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