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Math Help - trig limit problem

  1. #1
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    trig limit problem

    trig limit problem-picture-12.png
    for the problem above, is the idea that u can multiply as many times by 1 as you need to to get the form sinx/x or x/sinx?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: trig limit problem

    Basically, yes. Until you learn L'Hôpital's rule, this is the way you must handle these types of problems, by algebraic manipulation.
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    Re: trig limit problem

    The idea is that yes you multiply by 1, but remember that t is approaching zero which means that the limit has to be equal to 1 for these terms and in case it is.

    If these new limits were not equal to 1 then you couldn't do the substitution.
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  4. #4
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    Re: trig limit problem

    Yes that is exactly the idea. Though I would simply do this...

    \displaystyle \begin{align*} \lim_{x \to 0}\frac{\sin{3x}}{\sin{6x}} &= \lim_{x \to 0}\frac{\sin{3x}}{2\sin{3x}\cos{3x}} \\ &= \lim_{x \to 0}\frac{1}{2\cos{3x}} \\ &= \frac{1}{2 \cos {0}} \\ &= \frac{1}{2 \cdot 1} \\ &= \frac{1}{2} \end{align*}
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