Question

Limit at infinity of the differential implies uniform continuity

score 217 · Answer 1 · 2019-08-21 16:25:41

Limit at infinity of the differential implies uniform continuity

Published on 21 Aug 2019 - 16:25

score 82 · Answer 2 · 2019-08-22 21:11:35

If $f:R \to R$ is a continuous function and there are $a \geq 0$ and $b \geq 0$ such that $\|f(x)\| \leq a\|x\| + b$ then $f$ is uniformly continuous.

score 48 · Answer 3 · 2019-08-25 06:53:01

48

Views

Finding example of a function having the required property.

Published on 25 Aug 2019 - 6:53

score 337 · Answer 4 · 2019-08-25 18:46:49

337

Views

Prove that the function $\sqrt{x^2+y^2}\sin \frac{1}{\sqrt{x^2+y^2}}$ is uniformly continuous in $\mathbb R^2$

Published on 25 Aug 2019 - 18:46

score 78 · Answer 5 · 2019-08-26 10:06:01

78

Views

Compactness hypothesis in Heine's theorem

Published on 26 Aug 2019 - 10:06

score 115 · Answer 6 · 2019-08-27 18:16:37

115

Views

Prove that $f_n$ converges uniformly to $f$ on $[a,b)$

Published on 27 Aug 2019 - 18:16

score 35 · Answer 7 · 2019-08-30 04:35:53

35

Views

Restriction of an everywhere continuous to open, closed and bounded subsets and uniform continuity.

Published on 30 Aug 2019 - 4:35

score 98 · Answer 8 · 2019-09-02 03:01:40

98

Views

Show that $~f~$ is uniformly continuous on all of $~\mathbb R~$.

Published on 02 Sep 2019 - 3:01

score 115 · Answer 9 · 2019-09-02 21:40:59

115

Views

uniform continuity of $f$ on $[0,\infty)$ when $\lim_{x\rightarrow\infty}f(x)/x=1$.

Published on 02 Sep 2019 - 21:40

score 203 · Answer 10 · 2019-09-03 14:37:27

203

Views

Different conditions for Continuity and Uniform Continuity of a function on Union of Sets

Published on 03 Sep 2019 - 14:37

score 85 · Answer 11 · 2019-09-03 17:27:35

85

Views

Is this function uniformly continuous or just continuous?

Published on 03 Sep 2019 - 17:27

score 340 · Answer 12 · 2019-09-06 15:03:44

340

Views

Definition of uniformity in different contexts

Published on 06 Sep 2019 - 15:03

score 411 · Answer 13 · 2019-09-07 09:27:36

411

Views

Uniform continuity of the function $x\log(\frac{1}{x})$ on$ (0,\infty)$.

Published on 07 Sep 2019 - 9:27

score 265 · Answer 14 · 2026-03-27 00:10:51

265

Views

If f is a continuous function then is the derivative bounded?

Published on 27 Mar 2026 - 0:10

score 71 · Answer 15 · 2019-09-13 03:30:46

71

Views

This function isn't uniformly continuous, but how?

Published on 13 Sep 2019 - 3:30

List Question

Limit at infinity of the differential implies uniform continuity

If $f:R \to R$ is a continuous function and there are $a \geq 0$ and $b \geq 0$ such that $\|f(x)\| \leq a\|x\| + b$ then $f$ is uniformly continuous.

Finding example of a function having the required property.

Prove that the function $\sqrt{x^2+y^2}\sin \frac{1}{\sqrt{x^2+y^2}}$ is uniformly continuous in $\mathbb R^2$

Compactness hypothesis in Heine's theorem

Prove that $f_n$ converges uniformly to $f$ on $[a,b)$

Restriction of an everywhere continuous to open, closed and bounded subsets and uniform continuity.

Show that $~f~$ is uniformly continuous on all of $~\mathbb R~$.

uniform continuity of $f$ on $[0,\infty)$ when $\lim_{x\rightarrow\infty}f(x)/x=1$.

Different conditions for Continuity and Uniform Continuity of a function on Union of Sets

Is this function uniformly continuous or just continuous?

Definition of uniformity in different contexts

Uniform continuity of the function $x\log(\frac{1}{x})$ on$ (0,\infty)$.

If f is a continuous function then is the derivative bounded?

This function isn't uniformly continuous, but how?

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