Question

Prove that $a_n=\sqrt[n]{f\left(\frac{1}{n} \right)^n+f\left(\frac{2}{n} \right)^n+\dots+f\left(\frac{n}{n} \right)^n}$ is convergent

score 132 · Answer 1 · 2026-04-16 23:19:06

132

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Prove that $a_n=\sqrt[n]{f\left(\frac{1}{n} \right)^n+f\left(\frac{2}{n} \right)^n+\dots+f\left(\frac{n}{n} \right)^n}$ is convergent

Published on 16 Apr 2026 - 23:19

score 36 · Answer 2 · 2026-04-17 04:22:55

36

Views

Checking Uniform Contuinity

Published on 17 Apr 2026 - 4:22

score 100 · Answer 3 · 2026-04-11 07:59:32

100

Views

Polynomial in two variables Lipschitz on compact set in $R^2$?

Published on 11 Apr 2026 - 7:59

score 3.9k · Answer 4 · 2026-04-14 19:14:33

3.9k

Views

If $f : [0,1) \rightarrow \mathbb{R}$ is uniformly continous, $f$ is bounded

Published on 14 Apr 2026 - 19:14

score 176 · Answer 5 · 2026-04-11 09:29:50

176

Views

Rudin's PMA, theorem 4.20. A continuous function which is not uniformly continuous on a set which is not closed

Published on 11 Apr 2026 - 9:29

score 390 · Answer 6 · 2026-04-09 00:05:15

390

Views

Confusion about definition of uniformly continuous function

Published on 09 Apr 2026 - 0:05

score 167 · Answer 7 · 2026-04-14 03:55:11

167

Views

Uniform continuity of the CDF of a continuous Random variable.

Published on 14 Apr 2026 - 3:55

score 114 · Answer 8 · 2026-04-15 18:12:51

114

Views

Functions $f: \mathbb{R}^n \to \mathbb{R}$ such that $|f(x) -f(y)| \le C \prod_{i=1}^n |x_i - y_i|^{\alpha_i}$

Published on 15 Apr 2026 - 18:12

score 4k · Answer 9 · 2026-04-16 08:49:05

4k

Views

Proving or disproving $e^{x^2}$ and $e^{-x^2}$ is uniformly continuous with $\epsilon - \delta$

Published on 16 Apr 2026 - 8:49

score 87 · Answer 10 · 2026-04-16 09:13:56

87

Views

Proving $ f:(0,1)\to R$ is uniformly continuous, where$ f(x)=1/(x+4)$ for all $x \in (0,1)$

Published on 16 Apr 2026 - 9:13

score 2k · Answer 11 · 2026-04-15 21:16:08

2k

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Prove uniform continuity of the composition of two uniformly continuous functions.

Published on 15 Apr 2026 - 21:16

score 81 · Answer 12 · 2026-04-15 20:21:57

81

Views

Integrability condition implies boundedness and limit is zero

Published on 15 Apr 2026 - 20:21

score 30 · Answer 13 · 2026-04-15 21:37:08

30

Views

Show that $\frac{n}{\sqrt{\pi}}\int_{\mathbb{R}}f(x-y)e^{-(ny)^2}dy$ is uniformly continuous.

Published on 15 Apr 2026 - 21:37

score 2.4k · Answer 14 · 2026-04-13 06:31:47

2.4k

Views

Proving that the exponential function is not uniformly continuous

Published on 13 Apr 2026 - 6:31

score 63 · Answer 15 · 2026-04-16 20:03:51

63

Views

Proving uniform continuity in $\frac{x-2}{3x-4}$

Published on 16 Apr 2026 - 20:03

List Question

Prove that $a_n=\sqrt[n]{f\left(\frac{1}{n} \right)^n+f\left(\frac{2}{n} \right)^n+\dots+f\left(\frac{n}{n} \right)^n}$ is convergent

Checking Uniform Contuinity

Polynomial in two variables Lipschitz on compact set in $R^2$?

If $f : [0,1) \rightarrow \mathbb{R}$ is uniformly continous, $f$ is bounded

Rudin's PMA, theorem 4.20. A continuous function which is not uniformly continuous on a set which is not closed

Confusion about definition of uniformly continuous function

Uniform continuity of the CDF of a continuous Random variable.

Functions $f: \mathbb{R}^n \to \mathbb{R}$ such that $|f(x) -f(y)| \le C \prod_{i=1}^n |x_i - y_i|^{\alpha_i}$

Proving or disproving $e^{x^2}$ and $e^{-x^2}$ is uniformly continuous with $\epsilon - \delta$

Proving $ f:(0,1)\to R$ is uniformly continuous, where$ f(x)=1/(x+4)$ for all $x \in (0,1)$

Prove uniform continuity of the composition of two uniformly continuous functions.

Integrability condition implies boundedness and limit is zero

Show that $\frac{n}{\sqrt{\pi}}\int_{\mathbb{R}}f(x-y)e^{-(ny)^2}dy$ is uniformly continuous.

Proving that the exponential function is not uniformly continuous

Proving uniform continuity in $\frac{x-2}{3x-4}$

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