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5. Let h, : [0, o∞) → R be given by h„(x) and let h : [0, ∞) → R be given by I +n %3D h(x) = = x. (a) Prove that for each c> 0, (h„) converges uniformly to h on the interval [0, c). (b) Prove that (hn) does not converge uniformly to h on [0, ∞).

5. Let h, : [0, o∞) → R be given by h„(x) and let h : [0, ∞) → R be given by I +n %3D h(x) = = x. (a) Prove that for each c> 0, (h„) converges uniformly to h on the interval [0, c). (b) Prove that (hn) does not converge uniformly to h on [0, ∞).

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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5. Let h, : [0, o∞) → R be given by h„(x) and let h : [0, ∞) → R be given by I +n %3D h(x) = = x. (a) Prove that for each c> 0, (h„) converges uniformly to h on the interval [0, c). (b) Prove that (hn) does not converge uniformly to h on [0, ∞).
Transcribed Image Text:5. Let h, : [0, o∞) → R be given by h„(x) and let h : [0, ∞) → R be given by I +n %3D h(x) = = x. (a) Prove that for each c> 0, (h„) converges uniformly to h on the interval [0, c). (b) Prove that (hn) does not converge uniformly to h on [0, ∞).
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