1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Limit Problem

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

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Gold Member

    Can you decompose tan(x) into sin(x)/cos(x) and work from there?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted