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  1. #1
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    help

    Is f(x)=x*sin(x) uniformly continuous? justify.

    please help.
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  2. #2
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    Here's my adhoc attempt, please trump in anybody...

    f_1(x) = x is uniformly continuous

    f_2(x) = sin(x) is uniformly continuous

    therefore f(x) =  x\times sin(x) is also uniformly continuous
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  3. #3
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    You're wrong.

    Product of two uniformly continuous functions is not uniformly continuous.

    Cheap example: f(x)=x is uniformly continuous and g(x)=f(x)\cdot f(x)=x^2 is not uniformly continuous.

    ---

    h(x)=\sin x is also uniformly continuous. (Actually Lipschitz.)
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  4. #4
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    Quote Originally Posted by Krizalid View Post
    h(x)=\sin x is also uniformly continuous. (Actually Lipschitz.)
    Don't you mean h(x)=x \sin x
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  5. #5
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    No, I was giving another example about another uniformly continuous function.
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  6. #6
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    Good point Krizalid, also if you graph the function you can see it is not uniformly continuous.
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