Question

$ \frac{\ln(x)}{x} $ show this function is not continuous uniformly

score 57 · Answer 1 · 2017-11-01 17:48:15

57

Views

$ \frac{\ln(x)}{x} $ show this function is not continuous uniformly

Published on 01 Nov 2017 - 17:48

score 57 · Answer 2 · 2017-11-03 19:22:56

57

Views

If $f_m \geq 0$ on $[0,T]$, $f_m$ is continuous on $[0,T]$ and $\int_0^T f_m(t)dt \to 0$ as $m \to \infty$ then $f_m(t)\to 0$ as $m \to \infty$.

Published on 03 Nov 2017 - 19:22

score 136 · Answer 3 · 2017-11-04 18:33:16

136

Views

Show that $f:\mathbb{R}\to \mathbb{R}$ with $f(tx) = tf(x)$ for all $x,t\in \mathbb{R}$ is continuous.

Published on 04 Nov 2017 - 18:33

score 843 · Answer 4 · 2017-11-05 13:06:48

843

Views

Is the pasting lemma also true in case of uniform continuity?

Published on 05 Nov 2017 - 13:06

score 1.1k · Answer 5 · 2017-11-07 07:27:57

1.1k

Views

Proving that $x^{\frac{1}{n}}$ is uniformly continuous over $[0, \infty)$ with the usual metric

Published on 07 Nov 2017 - 7:27

score 815 · Answer 6 · 2017-11-07 07:45:09

815

Views

Proving uniform continuity of function on a half-open interval whose derivative has a limit at the boundary

Published on 07 Nov 2017 - 7:45

score 28 · Answer 7 · 2017-11-08 01:51:36

28

Views

Let ${f_n}$ be a sequence of functions $E\to \mathbb{R}$ and suppose $E= \cup _{k=1} \;E_k$ for some sets $E_k$

Published on 08 Nov 2017 - 1:51

score 185 · Answer 8 · 2017-11-10 02:46:07

185

Views

Proving uniform continuity of $g(x)=\sqrt{x^2 + 1}$ on $(0, 1)$

Published on 10 Nov 2017 - 2:46

score 93 · Answer 9 · 2017-11-10 16:07:33

93

Views

Continuity on Compacts subsets is equivalent to Uniform Continuity (proof using Lebesgue Covering Lemma)?

Published on 10 Nov 2017 - 16:07

score 156 · Answer 10 · 2017-11-11 11:28:53

156

Views

Studying the uniform continuity of $f(x) =x^2$ on the set of real numbers.

Published on 11 Nov 2017 - 11:28

score 116 · Answer 11 · 2017-11-14 16:51:29

116

Views

Studying uniform continuity.

Published on 14 Nov 2017 - 16:51

score 345 · Answer 12 · 2026-03-29 08:45:09

345

Views

Example of $f$ continuous on a totally bounded metric space $X$, where $f(X)$ isn't totally bounded

Published on 29 Mar 2026 - 8:45

score 212 · Answer 13 · 2017-11-16 03:39:01

212

Views

Is $t\sin\left(\frac1t\right)$ uniformly continuous on $(0,1)$?

Published on 16 Nov 2017 - 3:39

score 820 · Answer 14 · 2026-03-31 19:14:21

820

Views

$C^1$ function $f$ with bounded gradient such that $\frac{f(x)}{1+|x|}$ is unbounded

Published on 31 Mar 2026 - 19:14

score 99 · Answer 15 · 2017-11-20 20:45:57

99

Views

The order of growth of $F(x)=\int_0^x f(t)dt$ if $f$ is uniformly continuous

Published on 20 Nov 2017 - 20:45

List Question

$ \frac{\ln(x)}{x} $ show this function is not continuous uniformly

If $f_m \geq 0$ on $[0,T]$, $f_m$ is continuous on $[0,T]$ and $\int_0^T f_m(t)dt \to 0$ as $m \to \infty$ then $f_m(t)\to 0$ as $m \to \infty$.

Show that $f:\mathbb{R}\to \mathbb{R}$ with $f(tx) = tf(x)$ for all $x,t\in \mathbb{R}$ is continuous.

Is the pasting lemma also true in case of uniform continuity?

Proving that $x^{\frac{1}{n}}$ is uniformly continuous over $[0, \infty)$ with the usual metric

Proving uniform continuity of function on a half-open interval whose derivative has a limit at the boundary

Let ${f_n}$ be a sequence of functions $E\to \mathbb{R}$ and suppose $E= \cup _{k=1} \;E_k$ for some sets $E_k$

Proving uniform continuity of $g(x)=\sqrt{x^2 + 1}$ on $(0, 1)$

Continuity on Compacts subsets is equivalent to Uniform Continuity (proof using Lebesgue Covering Lemma)?

Studying the uniform continuity of $f(x) =x^2$ on the set of real numbers.

Studying uniform continuity.

Example of $f$ continuous on a totally bounded metric space $X$, where $f(X)$ isn't totally bounded

Is $t\sin\left(\frac1t\right)$ uniformly continuous on $(0,1)$?

$C^1$ function $f$ with bounded gradient such that $\frac{f(x)}{1+|x|}$ is unbounded

The order of growth of $F(x)=\int_0^x f(t)dt$ if $f$ is uniformly continuous

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