Question

Proving sequence is Cauchy sequence

score 237 · Answer 1 · 2026-04-14 23:42:10

237

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Proving sequence is Cauchy sequence

Published on 14 Apr 2026 - 23:42

score 488 · Answer 2 · 2026-04-16 13:13:03

488

Views

Prove that $f(ax + (1-a)y) = \frac{1}{y-x}\int_x^y f(t)dt$ implies $a = \frac{1}{2}$

Published on 16 Apr 2026 - 13:13

score 88 · Answer 3 · 2026-04-12 12:55:19

88

Views

Checking of convergence of a given sequence.

Published on 12 Apr 2026 - 12:55

score 94 · Answer 4 · 2026-04-11 23:52:36

94

Views

Polynomial of degree less or equal 2

Published on 11 Apr 2026 - 23:52

score 73 · Answer 5 · 2026-04-16 00:59:39

73

Views

$\lim_{n \to \infty}\mu(\{x\ |\ f(a)\le f(x)<f (a)+1/n\})=0$ implies continuity a.e.?

Published on 16 Apr 2026 - 0:59

score 645 · Answer 6 · 2026-04-13 17:51:31

645

Views

How $f_{yx} = f_{xy}$?

Published on 13 Apr 2026 - 17:51

score 57 · Answer 7 · 2026-04-12 09:50:16

57

Views

How to write a segment in topology

Published on 12 Apr 2026 - 9:50

score 172 · Answer 8 · 2026-04-16 23:23:56

172

Views

Proving that if $\lim\limits_{x\to\infty} xf(x)=0$ and $\lim\limits_{x\to\infty}xf''(x)=0$ , then $\lim\limits_{x\to\infty}xf'(x)=0$. (using Taylor)

Published on 16 Apr 2026 - 23:23

score 164 · Answer 9 · 2026-04-16 04:48:04

164

Views

Compute $\lim_{n\to\infty}\int_0^{\pi/2} \sin(x^n)dx$

Published on 16 Apr 2026 - 4:48

score 181 · Answer 10 · 2026-04-11 09:22:57

181

Views

A question about Rademacher system

Published on 11 Apr 2026 - 9:22

score 55 · Answer 11 · 2026-04-15 23:08:35

55

Views

On the uniform convergence of a sequence of functions

Published on 15 Apr 2026 - 23:08

score 90 · Answer 12 · 2026-04-14 05:11:29

90

Views

If $f$ is continuous and $f(x)=\int_{0}^{x} f(t)dt$, prove $f=0$ without FTC. Small issue with solution.

Published on 14 Apr 2026 - 5:11

score 60 · Answer 13 · 2026-04-14 07:01:49

60

Views

How can I understand/visualise this (finite) set?

Published on 14 Apr 2026 - 7:01

score 90 · Answer 14 · 2026-04-22 17:43:26

90

Views

If $X$ is finite dimensional, what is an explicit metric inducing the weak topology on $X?$

Published on 22 Apr 2026 - 17:43

score 120 · Answer 15 · 2026-04-13 11:48:49

120

Views

Prove that, even if a sequence isn't monotonic, it still converges and has limit.

Published on 13 Apr 2026 - 11:48

List Question

Proving sequence is Cauchy sequence

Prove that $f(ax + (1-a)y) = \frac{1}{y-x}\int_x^y f(t)dt$ implies $a = \frac{1}{2}$

Checking of convergence of a given sequence.

Polynomial of degree less or equal 2

$\lim_{n \to \infty}\mu(\{x\ |\ f(a)\le f(x)<f (a)+1/n\})=0$ implies continuity a.e.?

How $f_{yx} = f_{xy}$?

How to write a segment in topology

Proving that if $\lim\limits_{x\to\infty} xf(x)=0$ and $\lim\limits_{x\to\infty}xf''(x)=0$ , then $\lim\limits_{x\to\infty}xf'(x)=0$. (using Taylor)

Compute $\lim_{n\to\infty}\int_0^{\pi/2} \sin(x^n)dx$

A question about Rademacher system

On the uniform convergence of a sequence of functions

If $f$ is continuous and $f(x)=\int_{0}^{x} f(t)dt$, prove $f=0$ without FTC. Small issue with solution.

How can I understand/visualise this (finite) set?

If $X$ is finite dimensional, what is an explicit metric inducing the weak topology on $X?$

Prove that, even if a sequence isn't monotonic, it still converges and has limit.

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