3. For each n€ Z+ let fn : [0, 1] → R, fn(x) = 1/(1+x"). (a) Prove that (fn) converges uniformly. 1/2 (b) Compute the limit lim n→X S" fn, rigorously justifying your answer.
3. For each n€ Z+ let fn : [0, 1] → R, fn(x) = 1/(1+x"). (a) Prove that (fn) converges uniformly. 1/2 (b) Compute the limit lim n→X S" fn, rigorously justifying your answer.
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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![3. For each n€ Z+ let fn : [0, 1] → R, fn(x) = 1/(1+x").
(a) Prove that (fn) converges uniformly.
1/2
(b) Compute the limit lim
n→X
S"
fn, rigorously justifying your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2F4e416476-9c0f-4b9e-9ad0-621620570fad%2F1nrhfa8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. For each n€ Z+ let fn : [0, 1] → R, fn(x) = 1/(1+x").
(a) Prove that (fn) converges uniformly.
1/2
(b) Compute the limit lim
n→X
S"
fn, rigorously justifying your answer.
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