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

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

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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