Question

Find the recursive formula for $I_m:=\int \frac{dx}{\sqrt{x^2+1}^m},\enspace \,m\in\mathbb{N}$

score 135 · Answer 1 · 2026-04-16 21:03:15

135

Views

Find the recursive formula for $I_m:=\int \frac{dx}{\sqrt{x^2+1}^m},\enspace \,m\in\mathbb{N}$

Published on 16 Apr 2026 - 21:03

score 99 · Answer 2 · 2026-04-16 12:17:53

99

Views

Prove that the following sequence $(\sin\frac{\pi k}{3})_{k=1}^\infty$ diverges

Published on 16 Apr 2026 - 12:17

score 315 · Answer 3 · 2026-04-12 05:21:32

315

Views

Inapproximability of the $k$-center problem

Published on 12 Apr 2026 - 5:21

score 32 · Answer 4 · 2026-04-14 17:04:51

32

Views

$X$ is a random variable with PDF $f$, with $f$ continuous at $x=a$. Then $\lim_{\varepsilon\to0^-}\frac{1}{\varepsilon}P(X\in(a,a+\varepsilon))=f(a)$

Published on 14 Apr 2026 - 17:04

score 38 · Answer 5 · 2026-04-09 08:45:04

38

Views

Composite function with integral

Published on 09 Apr 2026 - 8:45

score 129 · Answer 6 · 2026-04-13 13:02:43

129

Views

Proof: For $n \in \mathbb{Z_+}$, the set of all functions $f: \{1,...,n\} \to \mathbb{Z_+}$ is countable

Published on 13 Apr 2026 - 13:02

score 146 · Answer 7 · 2026-04-10 22:42:44

146

Views

Proving a self independent random variable can get only one value

Published on 10 Apr 2026 - 22:42

score 74 · Answer 8 · 2026-04-18 07:53:01

74

Views

A group of even order contains an element of order 2 : a proof by contradiction.

Published on 18 Apr 2026 - 7:53

score 1.1k · Answer 9 · 2026-04-14 06:16:54

1.1k

Views

A donut shop sells 12 types of donuts. A manager wants to buy six donuts, one for himself and 5 for his employees.

Published on 14 Apr 2026 - 6:16

score 74 · Answer 10 · 2026-04-11 06:36:04

74

Views

Bijection of a Generalised Cartesian Product

Published on 11 Apr 2026 - 6:36

score 54 · Answer 11 · 2026-04-13 09:10:54

54

Views

Show that the induced mapping $\hat{\phi}: X/\sim \to Y/\approx$ is continuous (Marsden, Ratiu, Abraham)

Published on 13 Apr 2026 - 9:10

score 236 · Answer 12 · 2026-04-15 18:05:10

236

Views

If $X_n\thicksim\text{Unif}\left\{\frac{1}{n},\frac{2}{n},\dots,\frac{n-1}{n},1\right\}$ then $X_n\overset{d}\to Z$ where $Z\thicksim\text{Unif}[0,1]$

Published on 15 Apr 2026 - 18:05

score 108 · Answer 13 · 2026-03-26 06:28:25

108

Views

How to prove that there is closure in NP for the reverse operation on strings?

Published on 26 Mar 2026 - 6:28

score 142 · Answer 14 · 2026-04-15 19:48:21

142

Views

If $ \lim_{x \to +\infty}f(x) = A $ and $ \lim_{x \to +\infty}f'(x) = B $, prove that $B = 0$

Published on 15 Apr 2026 - 19:48

score 54 · Answer 15 · 2026-04-11 05:23:56

54

Views

An exercise regarding the computation of partial derivatives and applying the Chain Rule

Published on 11 Apr 2026 - 5:23

List Question

Find the recursive formula for $I_m:=\int \frac{dx}{\sqrt{x^2+1}^m},\enspace \,m\in\mathbb{N}$

Prove that the following sequence $(\sin\frac{\pi k}{3})_{k=1}^\infty$ diverges

Inapproximability of the $k$-center problem

$X$ is a random variable with PDF $f$, with $f$ continuous at $x=a$. Then $\lim_{\varepsilon\to0^-}\frac{1}{\varepsilon}P(X\in(a,a+\varepsilon))=f(a)$

Composite function with integral

Proof: For $n \in \mathbb{Z_+}$, the set of all functions $f: \{1,...,n\} \to \mathbb{Z_+}$ is countable

Proving a self independent random variable can get only one value

A group of even order contains an element of order 2 : a proof by contradiction.

A donut shop sells 12 types of donuts. A manager wants to buy six donuts, one for himself and 5 for his employees.

Bijection of a Generalised Cartesian Product

Show that the induced mapping $\hat{\phi}: X/\sim \to Y/\approx$ is continuous (Marsden, Ratiu, Abraham)

If $X_n\thicksim\text{Unif}\left\{\frac{1}{n},\frac{2}{n},\dots,\frac{n-1}{n},1\right\}$ then $X_n\overset{d}\to Z$ where $Z\thicksim\text{Unif}[0,1]$

How to prove that there is closure in NP for the reverse operation on strings?

If $ \lim_{x \to +\infty}f(x) = A $ and $ \lim_{x \to +\infty}f'(x) = B $, prove that $B = 0$

An exercise regarding the computation of partial derivatives and applying the Chain Rule

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