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Calculus: Pointwise limits

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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.

Solution provided by:
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
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