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Math Help - [SOLVED] Limit

  1. #1
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    [SOLVED] Limit



    How do I get this answer?
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  2. #2
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    \cos x = 1-\frac{x^2}{2} + O(x^4). Alternatively, use l'Hopitals rule.
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  3. #3
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    Quote Originally Posted by Susaluda View Post


    How do I get this answer?
    A lazy way is to use l'Hopital's Rule twice.

    A not so lazy way is to substitute the power series for cos(2x) and cos(3x), simplify and then take the limit.

    Another not so lazy way is to use the well known limit \lim_{t \to 0} \frac{\cos (t) - 1}{t^2} = 1.
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  4. #4
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    it's actually \frac{1-\cos t}{t^2}\to\frac12.
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  5. #5
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    Quote Originally Posted by Krizalid View Post
    it's actually \frac{1-\cos t}{t^2}\to\frac12.
    Thanks. Careless typos on my part.
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