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Math Help - Using L'Hopital's Rule :)

  1. #1
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    Using L'Hopital's Rule :)

    Let f(x) = x^2\sin{1/x} for x\neq 0 , let g(x) = \sin{x} for x\in\mathbb{R} . Show that \lim_{x\to 0 }f(x)/g(x) = 0 but that \lim_{x\to 0}f'(x)/g'(x) does not exist.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by CrazyCat87 View Post
    Let f(x) = x^2\sin{1/x} for x\neq 0 , let g(x) = \sin{x} for x\in\mathbb{R} . Show that \lim_{x\to 0 }f(x)/g(x) = 0 but that \lim_{x\to 0}f'(x)/g'(x) does not exist.
    Just do it? That's all I have to say. There is no mysticism here.
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