24.6 Let fn(x) = (x − 1)² for x = [0, 1]. (a) Does the sequence (fn) converge pointwise on the set [0, 1]? If so, give the limit function. (b) Does (fn) converge uniformly on [0, 1]? Prove your assertion.
24.6 Let fn(x) = (x − 1)² for x = [0, 1]. (a) Does the sequence (fn) converge pointwise on the set [0, 1]? If so, give the limit function. (b) Does (fn) converge uniformly on [0, 1]? Prove your assertion.
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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![**24.6** Let \( f_n(x) = \left(x - \frac{1}{n}\right)^2 \) for \( x \in [0, 1] \).
(a) Does the sequence \((f_n)\) converge pointwise on the set \([0, 1]\)? If so, give the limit function.
(b) Does \((f_n)\) converge uniformly on \([0, 1]\)? Prove your assertion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F833bf7b1-3e6b-4749-8e88-54090320a3f5%2F92ce511a-eac7-4292-a814-549b18e3f857%2Fsd6y1up_processed.png&w=3840&q=75)
Transcribed Image Text:**24.6** Let \( f_n(x) = \left(x - \frac{1}{n}\right)^2 \) for \( x \in [0, 1] \).
(a) Does the sequence \((f_n)\) converge pointwise on the set \([0, 1]\)? If so, give the limit function.
(b) Does \((f_n)\) converge uniformly on \([0, 1]\)? Prove your assertion.
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