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Let fn : [0, 0) –→ R be given by fn(x) = e-na. (a) Find the pointwise limit f of the fn. (b) Show that fn does not f uniformly, as follows: Pick some e > 0. Then for every n, show how to find an x such that |fn(x) – f(x)| > E.

Let fn : [0, 0) –→ R be given by fn(x) = e-na. (a) Find the pointwise limit f of the fn. (b) Show that fn does not f uniformly, as follows: Pick some e > 0. Then for every n, show how to find an x such that |fn(x) – f(x)| > E.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let fn : [0, 00) → R be given by fn(x) = e=na. (a) Find the pointwise limit f of the fn. (b) Show that fn does not –→ f uniformly, as follows: Pick some e > 0. Then for every n, show how to find an x such that | fn(x) – f(x)| > e.
Transcribed Image Text:Let fn : [0, 00) → R be given by fn(x) = e=na. (a) Find the pointwise limit f of the fn. (b) Show that fn does not –→ f uniformly, as follows: Pick some e > 0. Then for every n, show how to find an x such that | fn(x) – f(x)| > e.
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