# Pointwise limit question

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.

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.

$2.19