Question

Finding limit of a convergent sequence

score 49 · Answer 1 · 2018-04-11 11:59:14

49

Views

Finding limit of a convergent sequence

Published on 11 Apr 2018 - 11:59

score 752 · Answer 2 · 2018-04-15 15:00:17

752

Views

Proving a sequence of functions is not uniformly convergent

Published on 15 Apr 2018 - 15:00

score 56 · Answer 3 · 2018-04-20 18:09:54

56

Views

Convergence of sequence of function $\frac{|x|^n}{n+|x|^n}$

Published on 20 Apr 2018 - 18:09

score 116 · Answer 4 · 2018-04-24 22:22:35

116

Views

Issue with pointwise limit to the indicator function on $\mathbb{Q}$.

Published on 24 Apr 2018 - 22:22

score 322 · Answer 5 · 2018-04-28 05:39:26

322

Views

Show that $f_n(x)= \frac{\sin^2(n^{\alpha}x)}{nx}$ is not uniformly convergent for $\alpha \geq 1$ and $x \neq 0$

Published on 28 Apr 2018 - 5:39

score 109 · Answer 6 · 2018-05-01 13:11:05

109

Views

Pointwise convergence and continuity problem

Published on 01 May 2018 - 13:11

score 34 · Answer 7 · 2018-05-07 18:25:18

34

Views

Normed spaces: Sequence of functions/convergence

Published on 07 May 2018 - 18:25

score 38 · Answer 8 · 2018-05-07 18:44:47

38

Views

Convergence of sequence of functions.

Published on 07 May 2018 - 18:44

score 2.8k · Answer 9 · 2018-05-10 21:42:57

2.8k

Views

Show that the sum of reciprocal products equals $n$

Published on 10 May 2018 - 21:42

score 389 · Answer 10 · 2018-05-12 14:44:59

389

Views

If $f_n \rightarrow f$ is a sequence of $L^p$ and $g_n \rightarrow g$ a bounded sequence of $L^{\infty}$ then $f_ng_n \rightarrow fg$ in $L^p$

Published on 12 May 2018 - 14:44

score 44 · Answer 11 · 2018-05-13 16:02:47

44

Views

Find the limit function for the sequence of function problem

Published on 13 May 2018 - 16:02

score 651 · Answer 12 · 2018-05-14 10:02:20

651

Views

Let, $g$ be a cont. func. on $[0,1]$,$g(1)=0$,$\{f_n\}$ be a seq. of func. on $[0,1]$, $f_n (x)=x^n g(x)$. Prove,$\{f_n\}$ converge unif'ly on$[0,1]$.

Published on 14 May 2018 - 10:02

score 218 · Answer 13 · 2018-05-15 08:59:30

218

Views

Taylor Expansion for Sequence of Functions

Published on 15 May 2018 - 8:59

score 477 · Answer 14 · 2018-05-15 21:53:47

477

Views

Let $f_n \to f$ pointwise on $[0,1]$. If $f_n, f$ are continuous, is it true that $\int_0^1 f_n(x) dx \to \int_0^1 f(x)dx$?

Published on 15 May 2018 - 21:53

score 71 · Answer 15 · 2018-05-18 01:18:10

Family of functions over compact have derivative with the same Lipschitz constant. Do the functions themselves have the same Lipschitz constant?

List Question

Finding limit of a convergent sequence

Proving a sequence of functions is not uniformly convergent

Convergence of sequence of function $\frac{|x|^n}{n+|x|^n}$

Issue with pointwise limit to the indicator function on $\mathbb{Q}$.

Show that $f_n(x)= \frac{\sin^2(n^{\alpha}x)}{nx}$ is not uniformly convergent for $\alpha \geq 1$ and $x \neq 0$

Pointwise convergence and continuity problem

Normed spaces: Sequence of functions/convergence

Convergence of sequence of functions.

Show that the sum of reciprocal products equals $n$

If $f_n \rightarrow f$ is a sequence of $L^p$ and $g_n \rightarrow g$ a bounded sequence of $L^{\infty}$ then $f_ng_n \rightarrow fg$ in $L^p$

Find the limit function for the sequence of function problem

Let, $g$ be a cont. func. on $[0,1]$,$g(1)=0$,$\{f_n\}$ be a seq. of func. on $[0,1]$, $f_n (x)=x^n g(x)$. Prove,$\{f_n\}$ converge unif'ly on$[0,1]$.

Taylor Expansion for Sequence of Functions

Let $f_n \to f$ pointwise on $[0,1]$. If $f_n, f$ are continuous, is it true that $\int_0^1 f_n(x) dx \to \int_0^1 f(x)dx$?

Family of functions over compact have derivative with the same Lipschitz constant. Do the functions themselves have the same Lipschitz constant?

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