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Math Help - Limit of [1 - cos (x)]/x as x --> 0

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    Limit of [1 - cos (x)]/x as x --> 0

    WHAT IS LIMIT OF , [1 - cos (x)]/x such that "x approaches zero"

    i think the answer is "limit doesnt exist"..

    The book says its 0.
    Last edited by mr fantastic; June 30th 2011 at 01:24 PM. Reason: Re-titled.
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  2. #2
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    Re: Need help with solving a limit....

    Are you allowed to use L'Hopital's rule?
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  3. #3
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    Re: Need help with solving a limit....

    Quote Originally Posted by khamaar View Post
    WHAT IS LIMIT OF , [1 - cos (x)]/x such that "x approaches zero"

    i think the answer is "limit doesnt exist"..

    The book says its 0.
    \displaystyle \begin{align*} \lim_{x \to 0}\frac{1 - \cos{x}}{x} &= \lim_{x \to 0}\frac{(1 - \cos{x})(1 + \cos{x})}{x(1 + \cos{x})} \\ &= \lim_{x \to 0}\frac{1 - \cos^2{x}}{x(1 + \cos{x})} \\ &= \lim_{x \to 0}\frac{\sin^2{x}}{x(1 + \cos{x})} \\ &= \lim_{x \to 0}\frac{\sin{x}}{x}\cdot\lim_{x \to 0}\frac{\sin{x}}{1 + \cos{x}} \\ &= 1\cdot 0 \\ &= 0   \end{align*}
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  4. #4
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    Re: Need help with solving a limit....

    thank you very much, case closed.

    Thanks again...Hugs!!
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