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    Pointwise limit question

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    Let
    fk (x) = (e^(-x^(2) /k) / k , k = 1, 2, 3, . . . .
    a) Determine the pointwise limit f of the sequence {fk} infinity k=1 on R.
    b) Show that the sequence {fk} infinity k=1 converges to f uniformly to f on R.

    © BrainMass Inc. brainmass.com October 10, 2019, 6:02 am ad1c9bdddf
    https://brainmass.com/math/real-analysis/pointwise-limit-question-526113

    Solution Summary

    Determine the pointwise limit of a given sequence of exponential functions. Show that the sequence converges uniformly on R.

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