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    Calculus: Pointwise limits

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    Let
    fk (x) =
    sin (kx)/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/basic-calculus/calculus-pointwise-limits-526109

    Solution Summary

    Determining pointwise limit of a given sequence of functions and then showing that the sequence converges uniformly on R.

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