Question

Is $f:(0,\infty) \to \mathbb{R}$, $f(x):=x^{\sin(x)}$ uniformly continuous on $(0,1]$?

score 89 · Answer 1 · 2019-07-11 10:53:52

89

Views

Is $f:(0,\infty) \to \mathbb{R}$, $f(x):=x^{\sin(x)}$ uniformly continuous on $(0,1]$?

Published on 11 Jul 2019 - 10:53

score 125 · Answer 2 · 2019-07-12 15:36:01

125

Views

Why does $(f_{n})_{n}$ equicontinuous and $f_{n}$ uniformly continuous not imply $ (f_{n})_{n}$ uniformly equicontinuous

Published on 12 Jul 2019 - 15:36

score 427 · Answer 3 · 2026-03-26 07:58:38

427

Views

Show that $f$ Satisfies the Lipschitz Condition

Published on 26 Mar 2026 - 7:58

score 311 · Answer 4 · 2019-07-22 10:55:46

311

Views

Characterization of real-valued $C^1$ functions on $[0,1]$

Published on 22 Jul 2019 - 10:55

score 472 · Answer 5 · 2019-07-28 03:52:56

472

Views

Continuous approximation of an indicator function of a closed set.

Published on 28 Jul 2019 - 3:52

score 2.6k · Answer 6 · 2026-03-24 19:49:57

2.6k

Views

Pointwise convergence of uniformly continuous functions to zero, but not uniformly

Published on 24 Mar 2026 - 19:49

score 45 · Answer 7 · 2019-07-29 01:35:15

45

Views

For $x^{2}$, how does one show that the $\delta$ which works at $-N$ or $N$ works anywhere else in $[-N,N]$?

Published on 29 Jul 2019 - 1:35

score 58 · Answer 8 · 2026-03-27 08:45:59

58

Views

For $f(x)=\sin(\frac{1}{x})$, how would $\delta>0$ change after switching the interval $(0,1)$ to $(0,1]$?

Published on 27 Mar 2026 - 8:45

score 33 · Answer 9 · 2019-07-30 23:32:33

33

Views

Example of a function such that $A$ and $\alpha$ depend on $\epsilon$ from Spivak's Calculus

Published on 30 Jul 2019 - 23:32

score 55 · Answer 10 · 2019-07-31 07:07:52

55

Views

A problem on uniform continuity .

Published on 31 Jul 2019 - 7:07

score 52 · Answer 11 · 2019-08-05 08:40:05

52

Views

Uniformly continuous functions in terms of limits

Published on 05 Aug 2019 - 8:40

score 39 · Answer 12 · 2019-08-12 10:37:07

39

Views

Can the measure of $\{ x \in \Omega : 0 < f_n(x) < k_n\}$ be bounded by $C/n$ if $f_n$ converges to a non-positive function?

Published on 12 Aug 2019 - 10:37

score 25 · Answer 13 · 2019-08-12 14:10:02

25

Views

How to proceed for the following problem in uniform continuity

Published on 12 Aug 2019 - 14:10

score 167 · Answer 14 · 2019-08-18 19:35:16

167

Views

Is $f(x,y)=\frac{1}{x^2+y^2+1}$ uniformly continuous?

Published on 18 Aug 2019 - 19:35

score 217 · Answer 15 · 2019-08-19 01:34:08

217

Views

Show $\frac{\sin(x^{3})}{x}$ is uniformly continuous on $[0,\infty)$.

Published on 19 Aug 2019 - 1:34

List Question

Is $f:(0,\infty) \to \mathbb{R}$, $f(x):=x^{\sin(x)}$ uniformly continuous on $(0,1]$?

Why does $(f_{n})_{n}$ equicontinuous and $f_{n}$ uniformly continuous not imply $ (f_{n})_{n}$ uniformly equicontinuous

Show that $f$ Satisfies the Lipschitz Condition

Characterization of real-valued $C^1$ functions on $[0,1]$

Continuous approximation of an indicator function of a closed set.

Pointwise convergence of uniformly continuous functions to zero, but not uniformly

For $x^{2}$, how does one show that the $\delta$ which works at $-N$ or $N$ works anywhere else in $[-N,N]$?

For $f(x)=\sin(\frac{1}{x})$, how would $\delta>0$ change after switching the interval $(0,1)$ to $(0,1]$?

Example of a function such that $A$ and $\alpha$ depend on $\epsilon$ from Spivak's Calculus

A problem on uniform continuity .

Uniformly continuous functions in terms of limits

Can the measure of $\{ x \in \Omega : 0 < f_n(x) < k_n\}$ be bounded by $C/n$ if $f_n$ converges to a non-positive function?

How to proceed for the following problem in uniform continuity

Is $f(x,y)=\frac{1}{x^2+y^2+1}$ uniformly continuous?

Show $\frac{\sin(x^{3})}{x}$ is uniformly continuous on $[0,\infty)$.

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