Results 1 to 7 of 7

Thread: A Question on Uniform Convergence

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    21

    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!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,163
    Thanks
    46
    Choose:

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


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    21
    Many many thanks. Simple when you know how isn't it??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,163
    Thanks
    46
    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.


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,573
    Thanks
    789
    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?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,163
    Thanks
    46
    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".


    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2010
    Posts
    21
    Yeah sorry I am a bit new to Latex
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question about uniform convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Dec 14th 2010, 11:41 PM
  2. Functional Series and Uniform Convergence Question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Nov 28th 2010, 08:09 PM
  3. Replies: 1
    Last Post: Oct 31st 2010, 08:09 PM
  4. Pointwise Convergence vs. Uniform Convergence
    Posted in the Calculus Forum
    Replies: 8
    Last Post: Oct 31st 2007, 06:47 PM
  5. Uniform Continuous and Uniform Convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 28th 2007, 03:51 PM

Search Tags


/mathhelpforum @mathhelpforum