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Math Help - lim

  1. #1
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    lim

    without l hopetal

    find

    lim(x- sin x ) / x^3

    x-----> 0
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  2. #2
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    Quote Originally Posted by perash View Post
    without l hopetal

    find

    lim(x- sin x ) / x^3

    x-----> 0
    \sin x = x - \frac{x^3}{3!}+E(x) where E(x)/x^5\to 0 as x\to 0 by Taylor's theorem.

    Thus,
    \lim_{x\to 0}\frac{\frac{x^3}{3!}+E(x)}{x^3} = \frac{1}{3!}.
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