Question

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

score 93 · Answer 1 · 2026-04-16 05:37:47

93

Views

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

Published on 16 Apr 2026 - 5:37

score 85 · Answer 2 · 2026-04-11 00:21:36

85

Views

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

Published on 11 Apr 2026 - 0:21

score 55 · Answer 3 · 2026-04-14 19:51:36

55

Views

Uniform continuity of oscillatory functions on an unbounded interval

Published on 14 Apr 2026 - 19:51

score 430 · Answer 4 · 2026-04-14 13:56:29

430

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 14 Apr 2026 - 13:56

score 79 · Answer 5 · 2026-04-16 09:21:02

79

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 16 Apr 2026 - 9:21

score 117 · Answer 6 · 2026-04-16 14:48:46

117

Views

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

Published on 16 Apr 2026 - 14:48

score 98 · Answer 7 · 2026-04-09 14:48:02

98

Views

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

Published on 09 Apr 2026 - 14:48

score 510 · Answer 8 · 2026-04-14 15:22:52

510

Views

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

Published on 14 Apr 2026 - 15:22

score 59 · Answer 9 · 2026-04-14 00:17:06

59

Views

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

Published on 14 Apr 2026 - 0:17

score 664 · Answer 10 · 2026-04-14 09:14:25

664

Views

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

Published on 14 Apr 2026 - 9:14

score 437 · Answer 11 · 2026-04-16 13:25:45

437

Views

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

Published on 16 Apr 2026 - 13:25

score 475 · Answer 12 · 2026-04-15 01:04:18

475

Views

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

Published on 15 Apr 2026 - 1:04

score 51 · Answer 13 · 2026-04-09 03:00:04

51

Views

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

Published on 09 Apr 2026 - 3:00

score 91 · Answer 14 · 2026-05-10 20:03:17

91

Views

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

Published on 10 May 2026 - 20:03

score 342 · Answer 15 · 2026-04-15 22:00:23

342

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 15 Apr 2026 - 22:00

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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