Question

Show that the function $f:[a,\infty] \to \mathbb R$ defined by $x \mapsto \frac{1}{x}$ for $a$ a positive number is uniformly continuous.

score 72 · Answer 1 · 2021-01-04 09:52:32

72

Views

Show that the function $f:[a,\infty] \to \mathbb R$ defined by $x \mapsto \frac{1}{x}$ for $a$ a positive number is uniformly continuous.

Published on 04 Jan 2021 - 9:52

score 246 · Answer 2 · 2021-01-04 17:01:04

246

Views

Let $g(x)=\sin(x)$ and $f(x)=x$,show that the function $fg$ defined by $(fg)(x)=f(x)g(x)$ is not uniformly continuous on $\mathbb R$.

Published on 04 Jan 2021 - 17:01

score 59 · Answer 3 · 2021-01-08 05:56:11

59

Views

Bounding uniformly continuous functions

Published on 08 Jan 2021 - 5:56

score 44 · Answer 4 · 2021-01-08 18:56:06

44

Views

Non-uniformly continous function

Published on 08 Jan 2021 - 18:56

score 343 · Answer 5 · 2021-01-09 14:16:49

343

Views

How to prove this problem about uniform continuity

Published on 09 Jan 2021 - 14:16

score 123 · Answer 6 · 2026-04-01 11:43:32

123

Views

Prove or disprove: function is uniformly continuous

Published on 01 Apr 2026 - 11:43

score 96 · Answer 7 · 2021-01-10 13:11:31

96

Views

Uniformly continuous $f$ such that $\lim_{n \to +\infty}f(nx) = 0 \implies \lim_{x \to +\infty} f(x)= 0$

Published on 10 Jan 2021 - 13:11

score 37 · Answer 8 · 2021-01-11 10:37:20

37

Views

Is this argument for uniform continuity good?

Published on 11 Jan 2021 - 10:37

score 21 · Answer 9 · 2021-01-15 20:24:00

21

Views

A standard name for an “inversely (uniformly) continuous” map

Published on 15 Jan 2021 - 20:24

score 65 · Answer 10 · 2021-01-16 10:55:09

65

Views

What properties does this function have?

Published on 16 Jan 2021 - 10:55

score 72 · Answer 11 · 2021-01-17 10:53:47

72

Views

Prove that $f(x)=e^{\frac{1}{x}}$ is uniformly continuous.

Published on 17 Jan 2021 - 10:53

score 299 · Answer 12 · 2021-01-23 18:06:01

299

Views

Every uniformly continuous function $\mathbb Q\to \mathbb Z$ is constant.

Published on 23 Jan 2021 - 18:06

score 198 · Answer 13 · 2021-01-24 14:37:41

198

Views

A counter example on uniform continuity

Published on 24 Jan 2021 - 14:37

score 110 · Answer 14 · 2021-01-24 17:55:09

110

Views

Uniform continuity choosing delta problem

Published on 24 Jan 2021 - 17:55

score 88 · Answer 15 · 2021-01-25 09:02:12

88

Views

Are the integrals uniformly continuous and differentiable on $\mathbb{R}$?

Published on 25 Jan 2021 - 9:02

List Question

Show that the function $f:[a,\infty] \to \mathbb R$ defined by $x \mapsto \frac{1}{x}$ for $a$ a positive number is uniformly continuous.

Let $g(x)=\sin(x)$ and $f(x)=x$,show that the function $fg$ defined by $(fg)(x)=f(x)g(x)$ is not uniformly continuous on $\mathbb R$.

Bounding uniformly continuous functions

Non-uniformly continous function

How to prove this problem about uniform continuity

Prove or disprove: function is uniformly continuous

Uniformly continuous $f$ such that $\lim_{n \to +\infty}f(nx) = 0 \implies \lim_{x \to +\infty} f(x)= 0$

Is this argument for uniform continuity good?

A standard name for an “inversely (uniformly) continuous” map

What properties does this function have?

Prove that $f(x)=e^{\frac{1}{x}}$ is uniformly continuous.

Every uniformly continuous function $\mathbb Q\to \mathbb Z$ is constant.

A counter example on uniform continuity

Uniform continuity choosing delta problem

Are the integrals uniformly continuous and differentiable on $\mathbb{R}$?

Trending Questions

Popular # Hahtags

Popular Questions