Question

(Expectation)Consider the joint density $f(x,y)=c(x−y)e^{−x}, 0 \le y \le x$.

score 459 · Answer 1 · 2026-03-25 11:06:32

459

Views

(Expectation)Consider the joint density $f(x,y)=c(x−y)e^{−x}, 0 \le y \le x$.

Published on 25 Mar 2026 - 11:06

score 107 · Answer 2 · 2026-04-13 02:01:13

107

Views

Evaluating improper integrals with the help of contour integrals.

Published on 13 Apr 2026 - 2:01

score 175 · Answer 3 · 2026-04-17 06:24:42

Find a model and a non-model of a theory $T=\{\mathtt{(∀x)¬E(x, x),(∀x)(∀y)(E(x, y)→E(y, x)),(∀x)(∃y)ϕ(x, y)}\}$ over language $L$ where $L=(E)$

score 41 · Answer 4 · 2026-04-16 10:45:22

41

Views

Are there derivatives of the following functions or not? Justify your answer. In the case of a positive answer and calculate the derivatives.

Published on 16 Apr 2026 - 10:45

score 52 · Answer 5 · 2026-04-15 00:32:42

52

Views

($C^1$ Function)False or true? (justify) a) Let $f: X \to \mathbb R$. If $f'(x) = 0, \forall x \in X$, then $f'$ is constant...

Published on 15 Apr 2026 - 0:32

score 57 · Answer 6 · 2026-03-29 00:06:36

57

Views

(extremum)Let $f: \mathbb R \to \mathbb R$ be a polynomial function ...

Published on 29 Mar 2026 - 0:06

score 1.1k · Answer 7 · 2026-04-15 18:16:44

1.1k

Views

(convex function) Let $f: [a,b] \to \mathbb R$ twice differentiable, and $f''(x) \ge 0$, $\forall x \in [a,b]$....

Published on 15 Apr 2026 - 18:16

score 166 · Answer 8 · 2026-04-15 21:13:03

166

Views

Is formula $\mathtt{(∃x)(∀y)ϕ(x,y)}$ provable or refutable from $\mathtt{T}$ (in a Sound & Complete Proof System using the Axioms of $\mathtt{T}$)?

Published on 15 Apr 2026 - 21:13

score 202 · Answer 9 · 2026-04-12 17:35:54

202

Views

Evaluating $\int_0^\infty e^{-ax}\cos(bx)dx$ and $\int_0^\infty e^{-ax}\sin(bx)dx$ for $a>0$ using complex analysis.

Published on 12 Apr 2026 - 17:35

score 32 · Answer 10 · 2026-04-11 18:07:34

32

Views

Finding a vector maximising and minimising the inner product on two others vectors

Published on 11 Apr 2026 - 18:07

score 68 · Answer 11 · 2026-04-13 05:43:57

68

Views

Determine the location of a logistics center which is optimally close to its providers

Published on 13 Apr 2026 - 5:43

score 71 · Answer 12 · 2026-04-12 22:09:09

71

Views

How to quickly find unique values of $\sin x$ given that $\sin (nx) = k$, where $-1\le k\le 1$ and $n\in\mathbb N$?

Published on 12 Apr 2026 - 22:09

score 60 · Answer 13 · 2026-04-18 13:09:26

60

Views

Conceptual problems in measure theory.

Published on 18 Apr 2026 - 13:09

score 46 · Answer 14 · 2026-04-10 14:56:25

46

Views

Confusion regarding pole of a complex function.

Published on 10 Apr 2026 - 14:56

score 343 · Answer 15 · 2026-04-14 18:13:22

343

Views

The N-barrel problem. From some national math olympiad.

Published on 14 Apr 2026 - 18:13

List Question

(Expectation)Consider the joint density $f(x,y)=c(x−y)e^{−x}, 0 \le y \le x$.

Evaluating improper integrals with the help of contour integrals.

Find a model and a non-model of a theory $T=\{\mathtt{(∀x)¬E(x, x),(∀x)(∀y)(E(x, y)→E(y, x)),(∀x)(∃y)ϕ(x, y)}\}$ over language $L$ where $L=(E)$

Are there derivatives of the following functions or not? Justify your answer. In the case of a positive answer and calculate the derivatives.

($C^1$ Function)False or true? (justify) a) Let $f: X \to \mathbb R$. If $f'(x) = 0, \forall x \in X$, then $f'$ is constant...

(extremum)Let $f: \mathbb R \to \mathbb R$ be a polynomial function ...

(convex function) Let $f: [a,b] \to \mathbb R$ twice differentiable, and $f''(x) \ge 0$, $\forall x \in [a,b]$....

Is formula $\mathtt{(∃x)(∀y)ϕ(x,y)}$ provable or refutable from $\mathtt{T}$ (in a Sound & Complete Proof System using the Axioms of $\mathtt{T}$)?

Evaluating $\int_0^\infty e^{-ax}\cos(bx)dx$ and $\int_0^\infty e^{-ax}\sin(bx)dx$ for $a>0$ using complex analysis.

Finding a vector maximising and minimising the inner product on two others vectors

Determine the location of a logistics center which is optimally close to its providers

How to quickly find unique values of $\sin x$ given that $\sin (nx) = k$, where $-1\le k\le 1$ and $n\in\mathbb N$?

Conceptual problems in measure theory.

Confusion regarding pole of a complex function.

The N-barrel problem. From some national math olympiad.

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