# 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.

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##### Solution Summary

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

###### Education

- BSc, University of Bucharest
- MSc, Ovidius
- MSc, Stony Brook
- PhD (IP), Stony Brook

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