Question

$f(x)=f(x+1)$ for all x

score 104 · Answer 1 · 2018-05-14 04:54:54

104

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$f(x)=f(x+1)$ for all x

Published on 14 May 2018 - 4:54

score 41 · Answer 2 · 2026-03-26 04:52:40

41

Views

About the continuity of $x^3$.

Published on 26 Mar 2026 - 4:52

score 99 · Answer 3 · 2018-05-14 04:59:32

99

Views

Is my proof valid of: Suppose $f, g : X \to Y$ are continuous maps and $Y$ is Hausdorff. Show that the set $\{x\in X: f(x)=g(x)\}$ is closed in $X$.

Published on 14 May 2018 - 4:59

score 652 · Answer 4 · 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 4.8k · Answer 5 · 2026-03-25 17:17:25

4.8k

Views

C vs G continuity

Published on 25 Mar 2026 - 17:17

score 3.3k · Answer 6 · 2018-05-14 12:11:31

3.3k

Views

The function $f(x)=\tan^{-1}(x)$ is not uniformly continuous on $\Bbb{R}$

Published on 14 May 2018 - 12:11

score 35 · Answer 7 · 2026-03-25 10:58:17

35

Views

Bounds on the difference of sups in terms of the Hausdorff distance between feasible regions

Published on 25 Mar 2026 - 10:58

score 88 · Answer 8 · 2018-05-14 19:01:53

88

Views

Understanding a definition of continuity with a specific example

Published on 14 May 2018 - 19:01

score 2.4k · Answer 9 · 2018-05-14 20:21:32

2.4k

Views

Prove that $f(x)=\begin{cases}x& \text{if $x$ is rational},\\0 &\text{if $x$ is irrational}\end{cases}$ does not possess a derivative anywhere

Published on 14 May 2018 - 20:21

score 31 · Answer 10 · 2018-05-14 21:26:11

31

Views

Proof Verification and Help: Differentiation

Published on 14 May 2018 - 21:26

score 99 · Answer 11 · 2018-05-15 00:39:08

99

Views

Prove that for $x>0$, $\sin x<x$ and $\cos x>1-\frac{x^2}{2}$

Published on 15 May 2018 - 0:39

score 218 · Answer 12 · 2026-03-25 08:59:19

218

Views

Verify the Rolle's theorem when $f(x)=(x+1)^m(x-1)^n,\;\;-1\leq x\leq 1$

Published on 25 Mar 2026 - 8:59

score 158 · Answer 13 · 2026-03-26 03:18:46

158

Views

Proving uniform continuity given infinite limits and continuity

Published on 26 Mar 2026 - 3:18

score 160 · Answer 14 · 2026-03-25 20:10:53

160

Views

Prove that, any continuous and periodic function on $\Bbb{R}$ is uniformly continuous on $\Bbb{R}$.

Published on 25 Mar 2026 - 20:10

score 480 · Answer 15 · 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

List Question

$f(x)=f(x+1)$ for all x

About the continuity of $x^3$.

Is my proof valid of: Suppose $f, g : X \to Y$ are continuous maps and $Y$ is Hausdorff. Show that the set $\{x\in X: f(x)=g(x)\}$ is closed in $X$.

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$[0,1]$.

C vs G continuity

The function $f(x)=\tan^{-1}(x)$ is not uniformly continuous on $\Bbb{R}$

Bounds on the difference of sups in terms of the Hausdorff distance between feasible regions

Understanding a definition of continuity with a specific example

Prove that $f(x)=\begin{cases}x& \text{if $x$ is rational},\\0 &\text{if $x$ is irrational}\end{cases}$ does not possess a derivative anywhere

Proof Verification and Help: Differentiation

Prove that for $x>0$, $\sin x<x$ and $\cos x>1-\frac{x^2}{2}$

Verify the Rolle's theorem when $f(x)=(x+1)^m(x-1)^n,\;\;-1\leq x\leq 1$

Proving uniform continuity given infinite limits and continuity

Prove that, any continuous and periodic function on $\Bbb{R}$ is uniformly continuous on $\Bbb{R}$.

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

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