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2. Show that if a > 0, then the sequence (²x²e¬n) converges uniformly on the interval [a, ∞), but that it does not converge uniformly on the interval [0, 0). -nx

2. Show that if a > 0, then the sequence (²x²e¬n) converges uniformly on the interval [a, ∞), but that it does not converge uniformly on the interval [0, 0). -nx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using | fn(x) - f(x) |
2. Show that if a > 0, then the sequence (n²x²e¬na) converges uniformly on the interval [a, ∞), but that it does not converge uniformly on the interval [0, 0). -nx
Transcribed Image Text:2. Show that if a > 0, then the sequence (n²x²e¬na) converges uniformly on the interval [a, ∞), but that it does not converge uniformly on the interval [0, 0). -nx
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I am trying to compute this problem WITHOUT using the sup property. By stating that for any n > N(\epsilon) | fn(x) - f(x) | < \epsilon

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