The following question is from Real Analysis. I need a detailed answer to the below question , reasoning and each steps for the correct answer and why other options are wrong.Also, please include any definations or theorems involved. if x ¢ 0,Let fn : [0, 1] –→ [0, 1] be defined by fn(x) = x * Xn(x) where Xn(x) =if x € |0,n(a) {fn} converges uniformly to 0 on [0, 1].(b) {fn} converges pointwise to 1 on [0, 1] but does not converge uniformly.(c) {fn} converges uniformly to 1 on [0, 1].(d) None of the above.

Name: The following question is from Real Analysis. I need a detailed answer
Uploaded: 2024-03-20T06:38:44.000Z
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Description: The following question is from Real Analysis. I need a detailed answer to the below question , reasoning and each steps for the correct answer and why other options are wrong.Also, please include any definations or theorems involved. if x ¢ 0,Let fn

Given that, fn:[0,1]→[0,1] and fn(x)=x×Xn where Xn=0x∉0,1n1x∈0,1n (a) is wrong because, fn(x) →0 if…

Math

Advanced Math

0 if x¢ 0, et fn : [0, 1] → [0, 1] be defined by fn(x) = x * Xn(x) where Xn(x) = 1 if x E 0, a) {fn} converges uniformly to 0 on [0, 1]. b) {fn} converges pointwise to 1 on [0, 1] but does not converge uniformly. =) {fn} converges uniformly to 1 on [0, 1]. H) None of the above

0 if x¢ 0, et fn : [0, 1] → [0, 1] be defined by fn(x) = x * Xn(x) where Xn(x) = 1 if x E 0, a) {fn} converges uniformly to 0 on [0, 1]. b) {fn} converges pointwise to 1 on [0, 1] but does not converge uniformly. =) {fn} converges uniformly to 1 on [0, 1]. H) None of the above

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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