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Math Help - Limits (with sin)

  1. #1
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    Limits (with sin)

    lim of sin 4x / sin 6x as x approaches 0. I'm pretty sure the answer is 2/3, but I need a method of doing it. Any help is appreciated.
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  2. #2
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    Quote Originally Posted by Archduke01 View Post
    lim of sin 4x / sin 6x as x approaches 0. I'm pretty sure the answer is 2/3, but I need a method of doing it. Any help is appreciated.
    Well, put it this way:

     \frac{\sin(4x)}{\sin(6x)} = \frac{\sin(4x)}{4x} \times \frac{6x}{\sin(6x)} \times \frac{4x}{6x}

    The xs cancel, and 4/6 simplifies to 2/3

     \frac{\sin(4x)}{\sin(6x)} = \frac{\sin(4x)}{4x} \times \frac{6x}{\sin(6x)} \times \frac{2}{3}

    Now, do you know that  \displaystyle  \lim_{x \to 0} \frac{\sin(nx)}{nx} = 1 . If so, then the limit we have is trivial now .
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