11. Let a, b ER with a < b, and let {fr} be a uniformity convergent sequence of continuous real- valued functions on [a,b). Prove that the taking the limit and integrating can be exchanged in this case.i.e., S [limn-co fn (x)]dx = lim, -co S, fn (x)dx xp(x)"! *

11. Let a, b ER with a < b, and let {fr} be a uniformity convergent sequence of continuous real- valued functions on [a,b). Prove that the taking the limit and integrating can be exchanged in this case.i.e., S [limn-co fn (x)]dx = lim, -co S, fn (x)dx xp(x)"! *

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Description: Course: Real AnalysisPlease do your own and type neat and clean 11. Let a, b ER with a < b, and let {fr} be a uniformity convergent sequence of continuous real-valued functions on [a,bl. Prove that the taking the limit and integrating can be exchange

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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Course: Real Analysis

Please do your own and type neat and clean

11. Let a, b ER with a < b, and let {fr} be a uniformity convergent sequence of continuous real-
valued functions on [a,bl. Prove that the taking the limit and integrating can be exchanged in
this case.i.e.,
wwwenww
S limn-co fn (x)]dx = lim, -co S, fn (x)dx
n-00

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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