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Math Help - A Question on Uniform Convergence

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    Post A Question on Uniform Convergence

    Give an example of a uniformly convergent sequence (f_{n})_{n\in\mathbb N} of continuously differentiable functions such that (f\prime_{n})_{n\in\mathbb N} is not uniformly continuous.


    Just preparing for my exams in a few weeks. Need to know the answer to this one to have as an example. Just in case!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Choose:

    f_n(x)=\dfrac{\sin nx}{n}


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    Many many thanks. Simple when you know how isn't it??
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    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by garunas View Post
    Many many thanks. Simple when you know how isn't it??
    No wonder. It is a typical counter example.


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    Quote Originally Posted by garunas View Post
    Give an example of a uniformly convergent sequence (f_{n})_{n\in\mathbb N} of continuously differentiable functions such that (f\prime_{n})_{n\in\mathbb N} is not uniformly continuous.
    Sorry, what exactly is not uniformly continuous? Should f'_n be not uniformly continuous for every n?
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by emakarov View Post
    Sorry, what exactly is not uniformly continuous? Should f'_n be not uniformly continuous for every n?
    I supposed that is a typo and he meant " ... (f'_n) not uniformly convergent".


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    Yeah sorry I am a bit new to Latex
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