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Math Help - How do I evaluate this limit?

  1. #1
    Junior Member
    Joined
    Sep 2008
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    How do I evaluate this limit?

    Hi can someone please help me with this:

    lim \frac{sin^2(4x)}{x^2}
    x->0

    I know by finding derivative of the function I get:

    \frac{4x^2cos^2(4x) - 2xsin^2(4x)}{x^4}
    (hopefully that's right so far)

    what do I do next? is there a trig I identity that I can use to simplify or something?

    thanks!
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Chaneysville, PA
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    Split it up and use the famous limit \lim_{x\to 0}\frac{sin(x)}{x}=1

    \lim_{x\to 0}\frac{sin(4x)}{x}\cdot\lim_{x\to 0}\frac{sin(4x)}{x}

    Now, using one of them multiply top and bottom by 4:

    \lim_{x\to 0}\frac{4sin(4x)}{4x}

    Let t=4x:

    4\lim_{t\to 0}\frac{sin(t)}{t}=4
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