Question

Show $f$ is bounded on $[a,\infty)$ if continuous there and $\lim\limits_{x\to\infty}f(x)$ exists

score 3.5k · Answer 1 · 2012-12-06 16:19:56

3.5k

Views

Show $f$ is bounded on $[a,\infty)$ if continuous there and $\lim\limits_{x\to\infty}f(x)$ exists

Published on 06 Dec 2012 - 16:19

score 23.7k · Answer 2 · 2012-12-06 20:23:11

23.7k

Views

How do I prove a uniformly continuous function preserves Cauchy sequences?

Published on 06 Dec 2012 - 20:23

score 1.8k · Answer 3 · 2013-01-10 02:00:33

1.8k

Views

Continuity, uniform continuity and preservation of Cauchy sequences in metric spaces.

Published on 10 Jan 2013 - 2:00

score 1.2k · Answer 4 · 2013-02-03 13:04:20

1.2k

Views

Show $f$ is continuous at $(0,0)$ if $f(x,y) = \frac{x^3\sin(x+y) - y^4\ln(x^2+y^2)}{x^2+y^2}$ for $(x,y) \neq (0,0)$ and $f(0,0)=0$

Published on 03 Feb 2013 - 13:04

score 330 · Answer 5 · 2013-02-03 17:21:55

330

Views

If $p$ is a non-zero real polynomial then the map $x\mapsto \frac{1}{p(x)}$ is uniformly continuous over $\mathbb{R}$

Published on 03 Feb 2013 - 17:21

score 3.5k · Answer 6 · 2013-02-15 19:34:12

3.5k

Views

Every uniformly continuous real function has at most linear growth at infinity

Published on 15 Feb 2013 - 19:34

score 390 · Answer 7 · 2013-03-01 03:45:46

390

Views

Prove $I:C([0,1])\rightarrow C([0,1])$ defined by $I(f)(x)=\int_0^x f(t)dt$ is uniformly continuous

Published on 01 Mar 2013 - 3:45

score 585 · Answer 8 · 2013-03-23 18:05:48

585

Views

Why $f(x) = \frac{d(x,A)}{d(x,A)+d(x,B)}$ is uniform continuous?

Published on 23 Mar 2013 - 18:05

score 8.5k · Answer 9 · 2013-03-28 05:34:50

8.5k

Views

Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?

Published on 28 Mar 2013 - 5:34

score 22.8k · Answer 10 · 2013-03-29 06:49:36

22.8k

Views

product of two uniformly continuous functions is uniformly continuous

Published on 29 Mar 2013 - 6:49

score 360 · Answer 11 · 2013-03-30 07:14:08

360

Views

uniform continuity on $[0, +\infty)$

Published on 30 Mar 2013 - 7:14

score 60 · Answer 12 · 2020-08-01 13:28:01

60

Views

How do I show $f(x)$ is uniformly continuous.

Published on 01 Aug 2020 - 13:28

score 1.3k · Answer 13 · 2020-08-01 16:55:27

1.3k

Views

prove that a function $f$ is uniformly continuous if and only if there exists a modulus of continuity for $f$

Published on 01 Aug 2020 - 16:55

score 35 · Answer 14 · 2020-08-02 13:44:20

35

Views

Is $f: [5,8] \rightarrow \mathbb{R}$ defined by $f(x) = \cos^3(x + 1)$ uniformly continuous?

Published on 02 Aug 2020 - 13:44

score 62 · Answer 15 · 2020-08-03 08:19:17

62

Views

Looking for $f$ with a uniform derivative

Published on 03 Aug 2020 - 8:19

List Question

Show $f$ is bounded on $[a,\infty)$ if continuous there and $\lim\limits_{x\to\infty}f(x)$ exists

How do I prove a uniformly continuous function preserves Cauchy sequences?

Continuity, uniform continuity and preservation of Cauchy sequences in metric spaces.

Show $f$ is continuous at $(0,0)$ if $f(x,y) = \frac{x^3\sin(x+y) - y^4\ln(x^2+y^2)}{x^2+y^2}$ for $(x,y) \neq (0,0)$ and $f(0,0)=0$

If $p$ is a non-zero real polynomial then the map $x\mapsto \frac{1}{p(x)}$ is uniformly continuous over $\mathbb{R}$

Every uniformly continuous real function has at most linear growth at infinity

Prove $I:C([0,1])\rightarrow C([0,1])$ defined by $I(f)(x)=\int_0^x f(t)dt$ is uniformly continuous

Why $f(x) = \frac{d(x,A)}{d(x,A)+d(x,B)}$ is uniform continuous?

Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?

product of two uniformly continuous functions is uniformly continuous

uniform continuity on $[0, +\infty)$

How do I show $f(x)$ is uniformly continuous.

prove that a function $f$ is uniformly continuous if and only if there exists a modulus of continuity for $f$

Is $f: [5,8] \rightarrow \mathbb{R}$ defined by $f(x) = \cos^3(x + 1)$ uniformly continuous?

Looking for $f$ with a uniform derivative

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