Question

Convergence in probability vs almost surely using Borel-Cantelli Lemma

score 89 · Answer 1 · 2026-04-11 06:59:46

89

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Convergence in probability vs almost surely using Borel-Cantelli Lemma

Published on 11 Apr 2026 - 6:59

score 145 · Answer 2 · 2026-04-18 11:12:27

145

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Prove that if $\left|\begin{smallmatrix} 1 & 1 & 1\\ x & y & z\\ f(x) & f(y) & f(z)\end{smallmatrix}\right|\ge 0,$ then $f$ is convex.

Published on 18 Apr 2026 - 11:12

score 125 · Answer 3 · 2026-04-12 13:59:54

125

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Totals homework

Published on 12 Apr 2026 - 13:59

score 71 · Answer 4 · 2026-04-16 05:55:05

71

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Given any $\varepsilon > 0$, it is possible to cover $\textbf{Q}$ by a countable number of intervals whose total length is less than $\varepsilon$.

Published on 16 Apr 2026 - 5:55

score 612 · Answer 5 · 2026-04-13 17:12:26

612

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Problem in finding $\delta$ to prove that $\lim_{x\to a}[\lim_{y\to b}f(x,y)]=\lim_{y\to b}[\lim_{x\to a}f(x,y)]=L$

Published on 13 Apr 2026 - 17:12

score 28 · Answer 6 · 2026-04-16 15:11:10

28

Views

Finite dimension of $X/M$ and closed complement

Published on 16 Apr 2026 - 15:11

score 36 · Answer 7 · 2026-04-14 20:00:25

36

Views

Equivalence for a subspace to be bounded on a Banach space

Published on 14 Apr 2026 - 20:00

score 99 · Answer 8 · 2026-04-14 14:42:44

99

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Using residue theorem to calculate integral $\int\limits_0^{2\pi} \frac{dx}{10+6\sin x}$ - where is my mistake?

Published on 14 Apr 2026 - 14:42

score 278 · Answer 9 · 2026-04-12 14:43:51

278

Views

Condition for an operator to have closed Image

Published on 12 Apr 2026 - 14:43

score 126 · Answer 10 · 2026-04-16 09:10:18

126

Views

Using residue theorem to calculate $\int\limits_{-\infty}^{\infty} \frac{\cos(2x)\,dx}{(x^2+2x+2)^2}$

Published on 16 Apr 2026 - 9:10

score 693 · Answer 11 · 2026-04-15 07:04:28

693

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No. of ways to choose $k$ objects from $n$ $(n\ge k)$ distinct objects with replacement, order doesn't matter.

Published on 15 Apr 2026 - 7:04

score 38 · Answer 12 · 2026-04-15 08:09:52

38

Views

IB HL Math, proving that a function is greater than $1$, for all $x>0$

Published on 15 Apr 2026 - 8:09

score 42 · Answer 13 · 2026-04-15 12:47:06

42

Views

Limit of $\frac{S_n}{n}$, for $S_n \sim N(0, n)$ - prerequisite to convergence in probability

Published on 15 Apr 2026 - 12:47

score 49 · Answer 14 · 2026-04-16 05:44:12

49

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Finding the number of solutions to $\sin^2x+2\cos^2x+3\sin x\cos x=0$ with $0\leq x<2\pi$

Published on 16 Apr 2026 - 5:44

score 71 · Answer 15 · 2026-04-13 14:27:24

71

Views

Subset of $[a,b]$ with measure $b-a$ is dense (proof verification)

Published on 13 Apr 2026 - 14:27

List Question

Convergence in probability vs almost surely using Borel-Cantelli Lemma

Prove that if $\left|\begin{smallmatrix} 1 & 1 & 1\\ x & y & z\\ f(x) & f(y) & f(z)\end{smallmatrix}\right|\ge 0,$ then $f$ is convex.

Totals homework

Given any $\varepsilon > 0$, it is possible to cover $\textbf{Q}$ by a countable number of intervals whose total length is less than $\varepsilon$.

Problem in finding $\delta$ to prove that $\lim_{x\to a}[\lim_{y\to b}f(x,y)]=\lim_{y\to b}[\lim_{x\to a}f(x,y)]=L$

Finite dimension of $X/M$ and closed complement

Equivalence for a subspace to be bounded on a Banach space

Using residue theorem to calculate integral $\int\limits_0^{2\pi} \frac{dx}{10+6\sin x}$ - where is my mistake?

Condition for an operator to have closed Image

Using residue theorem to calculate $\int\limits_{-\infty}^{\infty} \frac{\cos(2x)\,dx}{(x^2+2x+2)^2}$

No. of ways to choose $k$ objects from $n$ $(n\ge k)$ distinct objects with replacement, order doesn't matter.

IB HL Math, proving that a function is greater than $1$, for all $x>0$

Limit of $\frac{S_n}{n}$, for $S_n \sim N(0, n)$ - prerequisite to convergence in probability

Finding the number of solutions to $\sin^2x+2\cos^2x+3\sin x\cos x=0$ with $0\leq x<2\pi$

Subset of $[a,b]$ with measure $b-a$ is dense (proof verification)

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