Question

What must a function satisfy in order to say that a certain limit exists?

score 83 · Answer 1 · 2014-05-19 18:55:30

83

Views

What must a function satisfy in order to say that a certain limit exists?

Published on 19 May 2014 - 18:55

score 41 · Answer 2 · 2014-05-20 14:12:17

41

Views

Limit of a sequence of roots

Published on 20 May 2014 - 14:12

score 72 · Answer 3 · 2014-05-22 18:18:59

72

Views

Definition of $\limsup$

Published on 22 May 2014 - 18:18

score 199 · Answer 4 · 2014-05-28 04:50:23

199

Views

Interchaging $P(\mathrm{limsup})$ with $P(\mathrm{limit})$ for $P$ a probability measure.

Published on 28 May 2014 - 4:50

score 114 · Answer 5 · 2014-06-03 20:13:24

114

Views

Show that $\limsup_{n\rightarrow\infty} \|x_n\|^{\frac{1}{n}}=1$

Published on 03 Jun 2014 - 20:13

score 98 · Answer 6 · 2014-06-04 14:27:22

98

Views

Prove $\{Z=0\}\subset\limsup\limits_{n}\{X_n<\epsilon\}$

Published on 04 Jun 2014 - 14:27

score 89 · Answer 7 · 2014-06-05 15:58:51

89

Views

A couple of inequalities (explanation needed), how to show $\liminf_{k \to 0}k^{-1}\int(\nabla u - \nabla v)\nabla (T_k(b(u)-b(v))) \geq 0$

Published on 05 Jun 2014 - 15:58

score 604 · Answer 8 · 2014-06-08 07:13:29

604

Views

$\int_0^1f(x)dx=1, \int_0^1xf(x)dx=\frac16$ minimum value of $\int_0^1f^2(x) dx$?

Published on 08 Jun 2014 - 7:13

score 80 · Answer 9 · 2014-06-09 12:25:36

80

Views

If $a_n \geq b_n$ and $b_n \to 0$, does $\liminf a_n \geq 0$?

Published on 09 Jun 2014 - 12:25

score 4k · Answer 10 · 2014-06-09 16:32:54

4k

Views

Complement of limsup E_n

Published on 09 Jun 2014 - 16:32

score 119 · Answer 11 · 2014-06-09 16:32:58

119

Views

Help with understanding a proof about differentiating a real power series

Published on 09 Jun 2014 - 16:32

score 899 · Answer 12 · 2014-06-11 10:36:11

899

Views

When can I interchange $\liminf$ and integral?

Published on 11 Jun 2014 - 10:36

score 110 · Answer 13 · 2014-06-15 11:03:21

110

Views

Find $\lim_{k \rightarrow \infty} \sup a_k$ and $\lim_{k \rightarrow \infty} \inf (a_k)$, with $a_k=(\frac{1}{k})_{k \in \mathbb{N}}$

Published on 15 Jun 2014 - 11:03

score 479 · Answer 14 · 2014-06-15 11:36:44

479

Views

Show that if $(a_k)_{k \in \mathbb{N}}, (b_k)_{k \in \mathbb{N}}$ are bounded, then $\lim \sup(a_k + b_k) \leq \lim \sup(a_k)+\lim \sup (b_k)$

Published on 15 Jun 2014 - 11:36

score 364 · Answer 15 · 2014-06-15 13:24:55

364

Views

Show that if $\limsup_{k \rightarrow \infty} \sqrt[k]{|a_k|} < 1$ then $\sum_{k=0}^\infty a_k$ converges absolutely.

Published on 15 Jun 2014 - 13:24

List Question

What must a function satisfy in order to say that a certain limit exists?

Limit of a sequence of roots

Definition of $\limsup$

Interchaging $P(\mathrm{limsup})$ with $P(\mathrm{limit})$ for $P$ a probability measure.

Show that $\limsup_{n\rightarrow\infty} \|x_n\|^{\frac{1}{n}}=1$

Prove $\{Z=0\}\subset\limsup\limits_{n}\{X_n<\epsilon\}$

A couple of inequalities (explanation needed), how to show $\liminf_{k \to 0}k^{-1}\int(\nabla u - \nabla v)\nabla (T_k(b(u)-b(v))) \geq 0$

$\int_0^1f(x)dx=1, \int_0^1xf(x)dx=\frac16$ minimum value of $\int_0^1f^2(x) dx$?

If $a_n \geq b_n$ and $b_n \to 0$, does $\liminf a_n \geq 0$?

Complement of limsup E_n

Help with understanding a proof about differentiating a real power series

When can I interchange $\liminf$ and integral?

Find $\lim_{k \rightarrow \infty} \sup a_k$ and $\lim_{k \rightarrow \infty} \inf (a_k)$, with $a_k=(\frac{1}{k})_{k \in \mathbb{N}}$

Show that if $(a_k)_{k \in \mathbb{N}}, (b_k)_{k \in \mathbb{N}}$ are bounded, then $\lim \sup(a_k + b_k) \leq \lim \sup(a_k)+\lim \sup (b_k)$

Show that if $\limsup_{k \rightarrow \infty} \sqrt[k]{|a_k|} < 1$ then $\sum_{k=0}^\infty a_k$ converges absolutely.

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