List questions from limsup-and-liminf

Published on 14 Nov 2021 - 13:50

450

Views

Limits, $\inf$ and $\sup$ of sets in a $\sigma$-algebra

Published on 17 Nov 2021 - 16:53

63

Views

Rare property of lim sup and lim inf?

Published on 18 Nov 2021 - 13:00

98

Views

Let $a_n>0$ be bounded and: $\limsup_{n\to\infty}\frac 1 {a_n}=\frac 1 {\liminf_{n\to\infty}a_n}$

Published on 07 Apr 2026 - 3:39

131

Views

$x_{n+1}=-1+\sqrt[n]{1+nx_n}$, $x_1>0$ limits

Published on 23 Nov 2021 - 16:37

212

Views

Fatou's lemma extension and dropping lim inf.

Published on 02 Dec 2021 - 3:48

180

Views

Proof explanation about why $\liminf_{n}X_{n}$ is a random variable

Published on 02 Apr 2026 - 13:41

79

Views

Solve $\int _0^x \sin (t^2) \text{d}t$ using MacLaurin series (for $x \in \mathbb{R}$)

Published on 06 Dec 2021 - 11:57

71

Views

Set of subsequence limits of $\{\sqrt n\}$

Published on 07 Dec 2021 - 15:29

129

Views

Example of a bounded sequence $(x_n)$ where $(\lim\sup x_n)^2\neq \lim \sup (x_n^2)$

Published on 10 Dec 2021 - 22:03

70

Views

How do I evaluate: $\limsup_{x\to0-}\frac{\sqrt{-x\sin^2(\ln |x|)}}{x}$?

Published on 12 Dec 2021 - 17:40

151

Views

Can L'Hôpital's rule be applied to the limit inferior of a sequence?

Published on 14 Dec 2021 - 11:31

145

Views

Supremum, limit and limsup

Published on 15 Dec 2021 - 11:46

130

Views

Show equivalence of definitons of $\limsup f(x)$

Published on 24 Dec 2021 - 14:47

61

Views

Show that $\limsup_{x\to p}f(x)$ is the unique element, which satisfies a certain condition.(follow-up question )

Published on 25 Dec 2021 - 16:48

List Question

convergent subsequence of bounded divergent sequence, and limit of $\sup$ and $\inf$

Limits, $\inf$ and $\sup$ of sets in a $\sigma$-algebra

Rare property of lim sup and lim inf?

Let $a_n>0$ be bounded and: $\limsup_{n\to\infty}\frac 1 {a_n}=\frac 1 {\liminf_{n\to\infty}a_n}$

$x_{n+1}=-1+\sqrt[n]{1+nx_n}$, $x_1>0$ limits

Fatou's lemma extension and dropping lim inf.

Proof explanation about why $\liminf_{n}X_{n}$ is a random variable

Solve $\int _0^x \sin (t^2) \text{d}t$ using MacLaurin series (for $x \in \mathbb{R}$)

Set of subsequence limits of $\{\sqrt n\}$

Example of a bounded sequence $(x_n)$ where $(\lim\sup x_n)^2\neq \lim \sup (x_n^2)$

How do I evaluate: $\limsup_{x\to0-}\frac{\sqrt{-x\sin^2(\ln |x|)}}{x}$?

Can L'Hôpital's rule be applied to the limit inferior of a sequence?

Supremum, limit and limsup

Show equivalence of definitons of $\limsup f(x)$

Show that $\limsup_{x\to p}f(x)$ is the unique element, which satisfies a certain condition.(follow-up question )

Trending Questions

Popular # Hahtags

Popular Questions