Question

To show $f$ is unifromly continuous if $|f(x)-g_{\epsilon}(x)|<\epsilon$.

score 90 · Answer 1 · 2018-08-27 13:33:37

90

Views

To show $f$ is unifromly continuous if $|f(x)-g_{\epsilon}(x)|<\epsilon$.

Published on 27 Aug 2018 - 13:33

score 82 · Answer 2 · 2018-08-28 23:02:40

82

Views

Is a Lipschitz continuous gradient function is a Lipschitz function as well?

Published on 28 Aug 2018 - 23:02

score 54 · Answer 3 · 2026-03-25 11:32:38

54

Views

Uniform continuity of oscillatory functions on an unbounded interval

Published on 25 Mar 2026 - 11:32

score 428 · Answer 4 · 2026-03-26 06:15:19

428

Views

Let $f$ be continuous real-valued function on $[0,1]$. Then, $F(x)=\max\{f(t):0\leq t\leq x\}$ is continuous

Published on 26 Mar 2026 - 6:15

score 76 · Answer 5 · 2018-09-07 16:25:13

76

Views

Let $f$ be a nonnegative continuous function on $[a,b]$, then $ \lim\limits_{n\to \infty} \left[\int^{b}_{a}f^{n}(x)dx\right]^{\frac{1}{n}}=M$

Published on 07 Sep 2018 - 16:25

score 113 · Answer 6 · 2018-09-08 06:12:55

113

Views

Let $f:[a,b]\to\Bbb{R}$ be continuous. Does $\max\{|f(x)|:a\leq x\leq b\}$ exist?

Published on 08 Sep 2018 - 6:12

score 95 · Answer 7 · 2018-09-11 16:11:58

95

Views

How to check whether $\sin (x \sin x)$ is uniformly continuous or not on $\mathbb R$.

Published on 11 Sep 2018 - 16:11

score 507 · Answer 8 · 2018-09-16 22:34:02

507

Views

Prove that a uniformly continuous function $f(x): \mathbb{R}_+ \rightarrow \mathbb{R}$ attains a maximum

Published on 16 Sep 2018 - 22:34

score 57 · Answer 9 · 2018-09-19 05:35:15

57

Views

Suppose $f$ is uniformly continuous on $[a,b]$. Does it mean $f$ is also uniformly continuous on $(a,b)$?

Published on 19 Sep 2018 - 5:35

score 662 · Answer 10 · 2018-09-19 21:47:11

662

Views

if $f$ convex, $f$ has bounded first derivative iff $f$ uniformly continuous

Published on 19 Sep 2018 - 21:47

score 434 · Answer 11 · 2018-09-23 04:37:25

434

Views

Proving that $f(x)= \sin (2\pi x [ x])$ is not uniformly continuous on $\mathbb{R}$

Published on 23 Sep 2018 - 4:37

score 472 · Answer 12 · 2018-09-23 05:59:04

472

Views

Proving $f(x)=\sqrt x$ is uniformly continuous on $[0,\infty )$ but is not Lipschitz.

Published on 23 Sep 2018 - 5:59

score 48 · Answer 13 · 2018-09-27 18:30:52

48

Views

Need clarification onto the intuition of why every continuous function on a compact set is uniformly continuous

Published on 27 Sep 2018 - 18:30

score 88 · Answer 14 · 2026-03-25 05:09:47

88

Views

How to formalize my intution of this theorem on continuous functions?

Published on 25 Mar 2026 - 5:09

score 339 · Answer 15 · 2018-10-10 17:10:07

339

Views

Prove $f(x)=\frac{3x+2}{2x-1}$ is uniformly continuous on $D_r= (-\infty, 1/2 -r] \cup [1/2 +r, \infty)$

Published on 10 Oct 2018 - 17:10

List Question

To show $f$ is unifromly continuous if $|f(x)-g_{\epsilon}(x)|<\epsilon$.

Is a Lipschitz continuous gradient function is a Lipschitz function as well?

Uniform continuity of oscillatory functions on an unbounded interval

Let $f$ be continuous real-valued function on $[0,1]$. Then, $F(x)=\max\{f(t):0\leq t\leq x\}$ is continuous

Let $f$ be a nonnegative continuous function on $[a,b]$, then $ \lim\limits_{n\to \infty} \left[\int^{b}_{a}f^{n}(x)dx\right]^{\frac{1}{n}}=M$

Let $f:[a,b]\to\Bbb{R}$ be continuous. Does $\max\{|f(x)|:a\leq x\leq b\}$ exist?

How to check whether $\sin (x \sin x)$ is uniformly continuous or not on $\mathbb R$.

Prove that a uniformly continuous function $f(x): \mathbb{R}_+ \rightarrow \mathbb{R}$ attains a maximum

Suppose $f$ is uniformly continuous on $[a,b]$. Does it mean $f$ is also uniformly continuous on $(a,b)$?

if $f$ convex, $f$ has bounded first derivative iff $f$ uniformly continuous

Proving that $f(x)= \sin (2\pi x [ x])$ is not uniformly continuous on $\mathbb{R}$

Proving $f(x)=\sqrt x$ is uniformly continuous on $[0,\infty )$ but is not Lipschitz.

Need clarification onto the intuition of why every continuous function on a compact set is uniformly continuous

How to formalize my intution of this theorem on continuous functions?

Prove $f(x)=\frac{3x+2}{2x-1}$ is uniformly continuous on $D_r= (-\infty, 1/2 -r] \cup [1/2 +r, \infty)$

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