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Math Help - Uniformly Continuous.

  1. #1
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    Uniformly Continuous.

    Prove or disapprove f(x) is uniformly continuous
    f(x)=(sinx)/x for x not equal to zero.
    and f(x)=1 for x=0

    I know f(x) is uniformly continous but I can't prove it. how do i show the derivative (xcosx-sinx)/x^{2} is bounded.

    thanks
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  2. #2
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    Quote Originally Posted by charikaar View Post
    Prove or disapprove f(x) is uniformly continuous
    f(x)=(sinx)/x for x not equal to zero.
    and f(x)=1 for x=0

    I know f(x) is uniformly continous but I can't prove it. how do i show the derivative (xcosx-sinx)/x^{2} is bounded.

    thanks
    Show that the derivative is continous
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  3. #3
    MHF Contributor chisigma's Avatar
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    Take into account that the coefficients of McLaurin expansion of x\cdot \cos x - \sin x of degree < 3 are equal to zero, so that is f^{'}(0)=0 and that both the functions \frac{\cos x}{x} and \frac{\sin x}{x^{2}} tend to 0 if x tends to infinity...

    Kind regards

    \chi \sigma
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