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Math Help - Pointwise Convergence

  1. #1
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    Pointwise Convergence

    Could I say that (2x^2/n^2)+(1/n^4) converges pointwise? I would say yes because it depends on x. Any suggestions?
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  2. #2
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    Oct 2008
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    This is my suggestion, I hope it will help you
    Let

    Then the f_n(x) converges pointwise if lim (f_n(x))--> f(x) as n--> infinity
    Thus, in this case lim (f_n(x)) = 0 as n-->infinity

    Hence, f_n ---> f pointwise where f(x) = 0

    That is the way I find convergence pointwise of a function, and if you are given the interval of the function, for example I = [0,1]. Then if x inside that interval then f_n ---> f pointwise.
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