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)"! *
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)"! *
Transcribed Image Text: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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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2807574b-9831-41a7-9a11-b07d270a0553%2Fd9db5717-e953-4b57-b7a4-1e6ce791f055%2Fbaxalh_processed.jpeg&w=3840&q=75)
