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    Sequences of Functions and Uniform Convergence

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    Discuss the convergence and the uniform convergence of each of the following sequences of functions on the given set D. Give reasons to your answers:

    a) f_n(x) = (x/n)e^(-x/n), D = [0, infinity)

    b)f_n(x) = (x^n)/(1 + x^2n), D = [2, infinity)

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    a) ,
    First, I claim that is convergent and . We ...

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