For each n ≥ 1, let fn : R → R, fn(x) =nx/(n + x^2) Show that the sequence of functions {fn}n≥1 converges pointwise, but it does not converge uniformly

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.4: Improper Integrals
Problem 37E
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For each n 1, let

fn : R R, fn(x) =nx/(n + x^2)

Show that the sequence of functions {fn}n1 converges pointwise, but it does not converge uniformly

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