Question

Let the bisection method be applied to a continuous function, resulting in intervals $[a_0, b_0], [a_1, b_1],$ and so on. Let

score 644 · Answer 1 · 2018-02-19 19:41:45

644

Views

Let the bisection method be applied to a continuous function, resulting in intervals $[a_0, b_0], [a_1, b_1],$ and so on. Let

Published on 19 Feb 2018 - 19:41

score 246 · Answer 2 · 2026-03-25 04:59:48

246

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Let $F:\mathbb{R}^2\to \mathbb{R}$ be of class $C^2$, with $F(0, 0) = 0$ and $DF(0, 0) =\begin{bmatrix}2 & 3\end{bmatrix}$.

Published on 25 Mar 2026 - 4:59

score 38 · Answer 3 · 2026-04-04 05:16:40

38

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Trouble with exercise about smoothness of unit normal

Published on 04 Apr 2026 - 5:16

score 47 · Answer 4 · 2018-02-20 05:20:18

Let $c_n$ be an increasing sequence such that $c_n \leq d_n$ for all $n$ and $d_n \rightarrow L$. Show $c_n$ has a limit and $\lim c_n \leq L$.

score 1.2k · Answer 5 · 2026-04-01 02:33:04

1.2k

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Connection between Analytic and harmonic

Published on 01 Apr 2026 - 2:33

score 1.1k · Answer 6 · 2018-02-20 12:47:26

1.1k

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Consequence of convergence of indicator function to zero in probability.

Published on 20 Feb 2018 - 12:47

score 153 · Answer 7 · 2018-02-20 16:42:50

153

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$I_n= \int_{-1}^1 (1 − x^2 )^n \cos(ax) \mathrm dx$

Published on 20 Feb 2018 - 16:42

score 29 · Answer 8 · 2018-02-20 17:39:31

29

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Complex functions in a subset that has a accumulation points.

Published on 20 Feb 2018 - 17:39

score 106 · Answer 9 · 2026-03-26 08:02:17

106

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$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

Published on 26 Mar 2026 - 8:02

score 30 · Answer 10 · 2018-02-20 18:54:11

30

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Given $c_n \rightarrow L$ and $d_n$ lies between $c_n, c_{n+1}$, show $d_n \rightarrow L$.

Published on 20 Feb 2018 - 18:54

score 227 · Answer 11 · 2026-04-03 17:03:01

227

Views

$Var[w]=O(\log\log(N))$ where $w(n)$ is the no of prime divisors of $n$

Published on 03 Apr 2026 - 17:03

score 93 · Answer 12 · 2026-03-29 13:46:40

93

Views

prove that $\mathbb{Q}$ can not be $G_{\delta}$ set in $\mathbb{R}$.

Published on 29 Mar 2026 - 13:46

score 133 · Answer 13 · 2018-02-20 20:41:05

133

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Sum of series $\sum_1 \frac{\cos(x)^{n-1}}{n!}$

Published on 20 Feb 2018 - 20:41

score 235 · Answer 14 · 2018-02-20 20:53:28

Given $a_n, b_n$ are both convergent sequences such that $a_n \leq b_n$ for all $n$, show $\lim_{n\to\infty} a_n \leq \lim_{n\to\infty} b_n$.

score 114 · Answer 15 · 2026-04-03 04:56:40

114

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What is the value of $i^{i^{i^{\cdots}}}$

Published on 03 Apr 2026 - 4:56

List Question

Let the bisection method be applied to a continuous function, resulting in intervals $[a_0, b_0], [a_1, b_1],$ and so on. Let

Let $F:\mathbb{R}^2\to \mathbb{R}$ be of class $C^2$, with $F(0, 0) = 0$ and $DF(0, 0) =\begin{bmatrix}2 & 3\end{bmatrix}$.

Trouble with exercise about smoothness of unit normal

Let $c_n$ be an increasing sequence such that $c_n \leq d_n$ for all $n$ and $d_n \rightarrow L$. Show $c_n$ has a limit and $\lim c_n \leq L$.

Connection between Analytic and harmonic

Consequence of convergence of indicator function to zero in probability.

$I_n= \int_{-1}^1 (1 − x^2 )^n \cos(ax) \mathrm dx$

Complex functions in a subset that has a accumulation points.

$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

Given $c_n \rightarrow L$ and $d_n$ lies between $c_n, c_{n+1}$, show $d_n \rightarrow L$.

$Var[w]=O(\log\log(N))$ where $w(n)$ is the no of prime divisors of $n$

prove that $\mathbb{Q}$ can not be $G_{\delta}$ set in $\mathbb{R}$.

Sum of series $\sum_1 \frac{\cos(x)^{n-1}}{n!}$

Given $a_n, b_n$ are both convergent sequences such that $a_n \leq b_n$ for all $n$, show $\lim_{n\to\infty} a_n \leq \lim_{n\to\infty} b_n$.

What is the value of $i^{i^{i^{\cdots}}}$

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