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…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Does the sequence Pn=(120e0.7n)/(4+e0.7n) converge? If so what's the limit?
Prove using the ϵ−n0 definition that the sequence Xn=(9−7n)/(8−13n) converges, and find its limit.
Suppose that ∞ n = 0 anxn converges to a function y such that y'' − 2y' + y = 0 where y(0) = 0 and y'(0) = 1. Find a formula that relates an + 2, an + 1, and
Let x1 > 1 and xn+1 = 2 − 1 / xn for n ≥ 2. Show that ( xn ) converges and find its limit.
Show that the sequence {cn} = {(−1)n 1/ n! } converges, and find its limit
(i) Let gn(x) =1/n(1 + x2) For any fixed x ∈ R, we can see that limgn(x) = 0 so that g(x) = 0 is the pointwise limit of the sequence (gn) on R. Is this convergence uniform? The observation that 1/(1 + x2) ≤ 1 for all x ∈ R implies that .
. Let gn = nχ[1/n,2/n] and g = 0. Show thatZ 20g 6= limn→∞ Z 20gn.Does the sequence (gn) converge uniformly to g? Does the Monotone Convergence Theoremapply? Does Fatou’s Lemma apply?
Find the pointwise limit f(x) for {nxe-nx} for x ∈ (0, +inf)). Does the sequence converge uniformly for x ∈ (0, +inf))? If yes, what is the uniform norm of fn(x)-f(x) on (0, +inf)?
Suppose that fn : [0, 1] → R is defined by fn(x) = x n. If 0 ≤ x < 1, then xn → 0 as n → ∞, while if x = 1, then x n → 1 as n → ∞. So fn → f pointwise where Although each fn is continuous on [0, 1], their pointwise limit f is not (it is discontinuous at 1). Thus, pointwise convergence does not, in general, preserve continuity.
Use two different methods to find the limit where m > 0, n > 0, and x > 0
Give an example of a sequence of differentiable functions {f_n: (-1,1)—>R} that converges uniformly but for which {f’_n(0)} is unbounded.
1. Use the definition of the limit ( epsolon - delta ) to show thatlim of 1/z as z approaches -i2. Give the condition which ensure that |ez| < 1 where z in C.

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

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.