Real Analysis IIOnly problem ONLY Q4. Use hint from Q3 3. Find the pointwise limit of 12 on S = [1, ∞). Hint: Define L € Rby L = 1/2 (L = 2 but you don't need its exact value to do thisproblem.)n=14. Prove thatdoes not converge uniformly on S = [1, ∞). Hint:Use Lemma 17.5 from Bartle and the pointwise limit in problem 3.

Here, we do not know the Lemma from the Bartle, So I am giving the general proof of same.

Answered: 4. Prove that does not converge…

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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter5: Graphs And The Derivative

Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test

Problem 61E

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Question

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.

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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