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    Determine the pointwise limit of (f_n), then decide whether the convergences is uniform or not (see attachment).

    1. f_n(x)= x/n, x is all real number
    2. f_n(x) = (sin(n*x))/n*x, where 0<=x<=1
    3. f_n(x)=(x^n)*(1-x^n), where 0<=x<=1
    4. f_n(x)={nx, for 0<=x<=1/n and 0, for 1/n<x<=1.

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    https://brainmass.com/math/real-analysis/pointwise-limits-380118

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    Pointwise limits of our functional sequences are depicted in the solution.

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