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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d456ce1-cbfb-470f-8ef9-05bd7d57f044%2F191c4fc3-a46b-41f0-bf6c-f9bda81a97fc%2F2ppd0f2_processed.jpeg&w=3840&q=75)
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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