Question

Finding limit of a convergent sequence

score 51 · Answer 1 · 2026-03-27 05:19:45

51

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Finding limit of a convergent sequence

Published on 27 Mar 2026 - 5:19

score 753 · Answer 2 · 2026-02-23 01:20:50

753

Views

Proving a sequence of functions is not uniformly convergent

Published on 23 Feb 2026 - 1:20

score 57 · Answer 3 · 2026-02-23 01:21:44

57

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

Published on 23 Feb 2026 - 1:21

score 118 · Answer 4 · 2026-04-08 06:03:40

118

Views

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

Published on 08 Apr 2026 - 6:03

score 323 · Answer 5 · 2026-02-23 01:23:46

323

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 23 Feb 2026 - 1:23

score 112 · Answer 6 · 2026-03-23 21:40:20

112

Views

Pointwise convergence and continuity problem

Published on 23 Mar 2026 - 21:40

score 35 · Answer 7 · 2026-02-23 01:20:02

35

Views

Normed spaces: Sequence of functions/convergence

Published on 23 Feb 2026 - 1:20

score 40 · Answer 8 · 2026-03-27 06:46:09

40

Views

Convergence of sequence of functions.

Published on 27 Mar 2026 - 6:46

score 2.8k · Answer 9 · 2026-02-23 01:22:14

2.8k

Views

Show that the sum of reciprocal products equals $n$

Published on 23 Feb 2026 - 1:22

score 390 · Answer 10 · 2026-02-23 01:23:46

390

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 23 Feb 2026 - 1:23

score 45 · Answer 11 · 2026-02-23 01:17:11

45

Views

Find the limit function for the sequence of function problem

Published on 23 Feb 2026 - 1:17

score 652 · Answer 12 · 2026-02-23 01:23:46

652

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 23 Feb 2026 - 1:23

score 220 · Answer 13 · 2026-03-27 05:14:29

220

Views

Taylor Expansion for Sequence of Functions

Published on 27 Mar 2026 - 5:14

score 480 · Answer 14 · 2026-03-24 03:50:54

480

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 24 Mar 2026 - 3:50

score 72 · Answer 15 · 2026-02-23 01:21:42

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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