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4. Prove that does not converge uniformly on S = [1,∞). Hint: n=1 Use Lemma 17.5 from Bartle and the pointwise limit in problem 3.

4. Prove that does not converge uniformly on S = [1,∞). Hint: n=1 Use Lemma 17.5 from Bartle and the pointwise limit in problem 3.

Advanced Engineering Mathematics
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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Real Analysis II Only problem ONLY Q4. Use hint from Q3
3. Find the pointwise limit of 12 on S = [1, ∞). Hint: Define L € R by L = 1/2 (L = 2 but you don't need its exact value to do this problem.) n=1 4. Prove that does not converge uniformly on S = [1, ∞). Hint: Use Lemma 17.5 from Bartle and the pointwise limit in problem 3.
Transcribed Image Text:3. Find the pointwise limit of 12 on S = [1, ∞). Hint: Define L € R by L = 1/2 (L = 2 but you don't need its exact value to do this problem.) n=1 4. Prove that does not converge uniformly on S = [1, ∞). Hint: Use Lemma 17.5 from Bartle and the pointwise limit in problem 3.
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Here, we do not know the Lemma from the Bartle, So I am giving the general proof of same. 

 

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