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Math Help - Need some help in showing that the function f '(x) is not continuous at 0.

  1. #1
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    Need some help in showing that the function f '(x) is not continuous at 0.

    Here is the problem: Consider the function f(x) defined by
    f(x)= x2sin(1/x) if x does not = 0
    0 if x = 0

    Show that the function f ' (x) is not continuous at 0.

    Any help would be appreciated.
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    Re: Need some help in showing that the function f '(x) is not continuous at 0.

    Quote Originally Posted by marsalanuddin View Post
    Here is the problem: Consider the function f(x) defined by
    f(x)= x2sin(1/x) if x does not = 0
    0 if x = 0

    Show that the function f ' (x) is not continuous at 0.

    Any help would be appreciated.
    Use the limit definition of the derivative and the squeeze theorem to prove that f(x) is differentiable. Then just use the product and chain rule to find the derivative. Once you have f'(x) show that \lim_{x \to 0}f'(x) \ne f'(0)

    Hint the limit of the derivative does not exist
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