Results 1 to 2 of 2

Math Help - uniform convergence

  1. #1
    Newbie
    Joined
    Jun 2009
    Posts
    5

    uniform convergence

    Show that the sequence of functions [f_n], defined on R for each n in N as the top half of the hyperbolae
    y^2 - x^2 = 1/(n^2)
    converges uniformly on R to f(x) = abs(x). What do you note about the differentiability of the function at x=0?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2009
    From
    Chennai
    Posts
    148

    reply

    See as far the convergence is concerned i havent worked out it yet. But as for the differentiablity of f(x)=|x| is concerned you should not that the function is not differentiable at the point x=0 for the left hand derivative at x=0 is -1 whereas the R.H.D at x=0 is 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Uniform convergence vs pointwise convergence
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 15th 2012, 11:03 PM
  2. Replies: 1
    Last Post: October 31st 2010, 07:09 PM
  3. Pointwise convergence to uniform convergence
    Posted in the Calculus Forum
    Replies: 13
    Last Post: November 29th 2009, 08:25 AM
  4. Pointwise Convergence vs. Uniform Convergence
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 31st 2007, 05:47 PM
  5. Uniform Continuous and Uniform Convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 28th 2007, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum