Question

Show $f_{n}(x) = n \sin(\frac{x}{n})$ converges point wise on the compact set $[-R,R]$

score 52 · Answer 1 · 2019-07-27 01:18:44

52

Views

Show $f_{n}(x) = n \sin(\frac{x}{n})$ converges point wise on the compact set $[-R,R]$

Published on 27 Jul 2019 - 1:18

score 23 · Answer 2 · 2019-07-27 02:16:41

23

Views

Interpretation of a piece wise function with regards to point wise functional convergence.

Published on 27 Jul 2019 - 2:16

score 143 · Answer 3 · 2019-08-04 13:04:27

143

Views

Uniform convergence of the series $\sum_{n=1}^\infty\frac{x}{(1+x)^n}$

Published on 04 Aug 2019 - 13:04

score 58 · Answer 4 · 2019-08-06 19:55:30

58

Views

$\{g_n\}$ be uniformly bounded sequence of functions on $[0,1]$ and converges pointwise to $g$.

Published on 06 Aug 2019 - 19:55

score 67 · Answer 5 · 2019-08-06 23:38:55

67

Views

Give an example of $h$ and $h_n$ where h is not continuous at $0$.

Published on 06 Aug 2019 - 23:38

score 144 · Answer 6 · 2019-08-11 15:19:24

144

Views

Uniform convergence of exponential function

Published on 11 Aug 2019 - 15:19

score 156 · Answer 7 · 2019-08-14 06:24:11

156

Views

If a sequence of functions $\{f_n\}$ be uniformly convergent on $[a,b]$, would it be uniformly convergent of $(a,b)$?

Published on 14 Aug 2019 - 6:24

score 880 · Answer 8 · 2019-08-14 18:53:45

880

Views

Validity of interchanging limit and integral under non-uniform convergence!!

Published on 14 Aug 2019 - 18:53

score 64 · Answer 9 · 2019-08-18 14:17:51

64

Views

How to deduce the sup of a function sequence $f_n$ without computing the derivative?

Published on 18 Aug 2019 - 14:17

score 411 · Answer 10 · 2019-08-19 19:11:57

411

Views

Does $(f_n)=(n\sin(\frac{x}{n})-x)$ converge uniformly on $[-a,a]$ for $a\geq0$?

Published on 19 Aug 2019 - 19:11

score 157 · Answer 11 · 2019-08-20 06:15:05

157

Views

Uniformly bounded sequence of non-decreasing functions has a convergent subsequence

Published on 20 Aug 2019 - 6:15

score 56 · Answer 12 · 2019-08-22 14:29:48

56

Views

$f_n(x) \rightharpoonup0$ in $L^1(\mathbb{R})$ where $f_n(x) = f(-x+n^3)$

Published on 22 Aug 2019 - 14:29

score 239 · Answer 13 · 2019-08-24 18:58:22

239

Views

Study the uniform convergence of the functional sequence $f_n(x)=\sqrt{n+1}\sin^nx\cos x$

Published on 24 Aug 2019 - 18:58

score 23 · Answer 14 · 2019-08-28 09:41:09

23

Views

Pointwise Convergence Of Sequence Of Real Functions

Published on 28 Aug 2019 - 9:41

score 287 · Answer 15 · 2019-08-29 07:35:22

287

Views

Limit and Integration are interchangeable

Published on 29 Aug 2019 - 7:35

List Question

Show $f_{n}(x) = n \sin(\frac{x}{n})$ converges point wise on the compact set $[-R,R]$

Interpretation of a piece wise function with regards to point wise functional convergence.

Uniform convergence of the series $\sum_{n=1}^\infty\frac{x}{(1+x)^n}$

$\{g_n\}$ be uniformly bounded sequence of functions on $[0,1]$ and converges pointwise to $g$.

Give an example of $h$ and $h_n$ where h is not continuous at $0$.

Uniform convergence of exponential function

If a sequence of functions $\{f_n\}$ be uniformly convergent on $[a,b]$, would it be uniformly convergent of $(a,b)$?

Validity of interchanging limit and integral under non-uniform convergence!!

How to deduce the sup of a function sequence $f_n$ without computing the derivative?

Does $(f_n)=(n\sin(\frac{x}{n})-x)$ converge uniformly on $[-a,a]$ for $a\geq0$?

Uniformly bounded sequence of non-decreasing functions has a convergent subsequence

$f_n(x) \rightharpoonup0$ in $L^1(\mathbb{R})$ where $f_n(x) = f(-x+n^3)$

Study the uniform convergence of the functional sequence $f_n(x)=\sqrt{n+1}\sin^nx\cos x$

Pointwise Convergence Of Sequence Of Real Functions

Limit and Integration are interchangeable

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