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Thread: Evaluating limit of cube root function algebraically

  1. #1
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    Evaluating limit of cube root function algebraically

    Hello

    I am having trouble evaluating the following problem

    Lim cuberoot(sin8x/x)
    x->0

    It needs to be evaluated algebraically. I think it needs to be rationalized but I dont really know where to start

    Any help is greatly appreciated. Sorry if this is the wrong forum
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  2. #2
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    Re: Evaluating limit of cube root function algebraically

    $\displaystyle \lim_{x \to 0} \sqrt[3]{ \dfrac{ \sin(8x) }{x} } = \sqrt[3]{ \displaystyle \lim_{x \to 0} \dfrac{ \sin(8x) }{x}} = \sqrt[3]{ \displaystyle 8\lim_{x \to 0} \dfrac{ \sin(8x) }{ 8x } } = \sqrt[3]{8\cdot 1} = 2$
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  3. #3
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    Re: Evaluating limit of cube root function algebraically

    SlipEternal has used
    1) the fact that the cube root function is continuous.

    2) the fact that the limit of sin(u)/u, as u goes to 0, is 1.
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