Let a be increasing in [a, b]. Suppose a sequence of real continuous functions in [a, b] converges pointwise to a continuous function f. Furthemore, it is true that fn(x) < fn+1(x), Væ E [a, b], Vn E N. Prove that: 1. {f1, f2, f3, - ..}C R(a) 2. Så fda = lim,0Så fnda 3. lim, 00 Så lfn – f\da = 0
Let a be increasing in [a, b]. Suppose a sequence of real continuous functions in [a, b] converges pointwise to a continuous function f. Furthemore, it is true that fn(x) < fn+1(x), Væ E [a, b], Vn E N. Prove that: 1. {f1, f2, f3, - ..}C R(a) 2. Så fda = lim,0Så fnda 3. lim, 00 Så lfn – f\da = 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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![Let a be increasing in [a, b]. Suppose a sequence of real continuous functions in
[a, b] converges pointwise to a continuous function f. Furthemore, it is true that
fn (x) < fn+1(x), Væ € [a, b], Vn E N.
Prove that:
1. {f1, f2, f3, … . .} C R(a)
2. Si fda = lim,å fnda
3. lim,00 Sa lfn – f|da = 0
%3D
Note: Show all your work. Nothing is trivial.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2d8f98a-e204-4834-bafa-04734716e97b%2F907edbb0-e8b4-4af1-b6b4-2d078e29a738%2Fnsgyzaa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let a be increasing in [a, b]. Suppose a sequence of real continuous functions in
[a, b] converges pointwise to a continuous function f. Furthemore, it is true that
fn (x) < fn+1(x), Væ € [a, b], Vn E N.
Prove that:
1. {f1, f2, f3, … . .} C R(a)
2. Si fda = lim,å fnda
3. lim,00 Sa lfn – f|da = 0
%3D
Note: Show all your work. Nothing is trivial.
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