4. i) Let X = B[a, b] and let d be the sup metric on X. If In → x in (X,d) and an iscontinuous at to E [a, b] for each n > 1, prove that x is also continuous at to.%3Dii) Let In (t)convergent in B [0, 1] with the sup metric?t", for all t e [0, 1] and all integers n > 1. Is the sequence {¤n}

Answered: Image /qna-images/answer/34f3c50a-94ba-40a9-ac1e-e8f68823ba0d.jpg

Answered: 4. i) Let X = B [a, b] and let d be the…

4. i) Let X = B [a, b] and let d be the sup metric on X. If n → x in (X,d) and an is continuous at to E ſa, b) for each n > 1, prove that z is also continuous at to. %3D

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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4. i) Let X = B[a, b] and let d be the sup metric on X. If In → x in (X,d) and an is
continuous at to E [a, b] for each n > 1, prove that x is also continuous at to.
%3D
ii) Let In (t)
convergent in B [0, 1] with the sup metric?
t", for all t e [0, 1] and all integers n > 1. Is the sequence {¤n}

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