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Math Help - point convergence and uniform convergence definition question

  1. #16
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    Re: point convergence and uniform convergence definition question

    f'(x)=n(1+n^2x^2)-nx(2n^2x)/dominator squared
    f'(x)=0
    n(1+n^2x^2)-nx(2n^2x)=0
    n+n^3x^2-2x^2n^3=0
    n-n^3x^2=0
    1-n^2x^2=0
    x=+- sqrt(1/n)
    f(1/n)=1/2 got it

    so i see that we take the extreme points of the expression and do a limit on them
    correct?(could you please help me with the question bellow about the cauchy serieses,you have been very helpfull)
    Last edited by transgalactic; April 12th 2012 at 12:49 PM.
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  2. #17
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    Re: point convergence and uniform convergence definition question

    Quote Originally Posted by transgalactic View Post
    1-n^2x^2=0
    x=+- sqrt(1/n)
    Should be x = \pm1/n.

    Quote Originally Posted by transgalactic View Post
    so i see that we take the extreme points of the expression and do a limit on them
    correct?
    That's one way.
    Thanks from transgalactic
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  3. #18
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    Re: point convergence and uniform convergence definition question

    what are the other ways

    i see only the extereme point method
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  4. #19
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    Re: point convergence and uniform convergence definition question

    Quote Originally Posted by transgalactic View Post
    what are the other ways

    i see only the extereme point method
    To prove that f_n(x)=(\sin x+\cos x)/n converges uniformly to 0 we note that for all x, |(\sin x+\cos x) / n-0|\le2/ n\to0 as n\to\infty. In this case, there is no need to find exact extrema of f_n(x).
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