I need to prove that these statements are false. If E fk is a series of continuous functions converging to a continuous function on D,then the convergence is uniform.If E fk is absolutely uniformly convergent on some domain D, then E Mk with M,fn(x) converges.supxeD

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Answered: If E fk is a series of continuous…

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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If E fk is a series of continuous functions converging to a continuous function on D, then the convergence is uniform. If E fk is absolutely uniformly convergent on some domain D, then Mk with M, supxeD fn (x) converges.