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Let fn(x) = sin" x and let 8 > 0. a) Prove: fn converges uniformly on [0, 5 – 8], but not uniformly on [0, ). b) In which sense does fn converge on [0, 7/2)? Prove your claim. 2.67 %3D

Let fn(x) = sin" x and let 8 > 0. a) Prove: fn converges uniformly on [0, 5 – 8], but not uniformly on [0, ). b) In which sense does fn converge on [0, 7/2)? Prove your claim. 2.67 %3D

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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2.67 Let fn(x) = sin" x and let d > 0. a) Prove: fn converges uniformly on [0, 5 - 8), but not uniformly on [0, ). b) In which sense does fn converge on 0, 7/2)? Prove your claim.
Transcribed Image Text:2.67 Let fn(x) = sin" x and let d > 0. a) Prove: fn converges uniformly on [0, 5 - 8), but not uniformly on [0, ). b) In which sense does fn converge on 0, 7/2)? Prove your claim.
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