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Math Help - uniform convergence problem

  1. #1
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    uniform convergence problem

    Let S_n(x)= \displaystyle \frac{1}{n}e^{-n^2x^2}. Show that there is a function, S(x), such that S_n(x)-->S(x) uniformly on R and that S'_n(x)-->S'(x) for every x but that the convergence of the derivatives is not uniform in any interval which contains the orgin.
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  2. #2
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    Quote Originally Posted by wopashui View Post
    Let S_n(x)= \displaystyle \frac{1}{n}e^{-n^2x^2}. Show that there is a function, S(x), such that S_n(x)-->S(x) uniformly on R and that S'_n(x)-->S'(x) for every x but that the convergence of the derivatives is not uniform in any interval which contains the orgin.
    What have you done so far? The first step is obviously to find the limit function S(x) = {\displaystyle\lim_{n\to\infty}}\,\frac1ne^{-n^2x^2}. So, what is that limit?
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