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Math Help - Evaluate the limit

  1. #1
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    Evaluate the limit

    Evaluate the limit of
    \lim_{x \to \pi} \frac {sin^2{x}} {1+cos{3x}}

    I assume I use L'Hopital's rule here?
    This gives me:
     \frac {sin{2x}} {-3sin{3x}}
    which comes to 0/0.
    wanting some reassurance here that I'm on the right track!
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  2. #2
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    Quote Originally Posted by Dr Zoidburg View Post
    Evaluate the limit of
    \lim_{x \to \pi} \frac {sin^2{x}} {1+cos{3x}}

    I assume I use L'Hopital's rule here? <<<<<<< OK
    This gives me:
     \frac {sin{2x}} {-3sin{3x}}
    which comes to 0/0.
    wanting some reassurance here that I'm on the right track!
    I would use:

    \lim_{x \to \pi} \frac {sin^2{x}} {1+cos{3x}} = \lim_{x\to \pi}\dfrac{2 \sin(x) \cdot \cos(x)}{-3\sin(3x)}

    As long as the quotient becomes \frac00 you can apply l'Hopitals's rule.

    In the end you should get \frac29
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  3. #3
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    In other words, apply L'Hopital's rule again!
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  4. #4
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    cool. Got it now.
    Thanks all for your help. I'm doing this paper by correspondence so this is the only place (other than the textbooks) I can turn for advice/help when I get stuck or just when I want confirmation I'm on the right track.
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