Question

Let $I = [0 , 1]$; let $Q = I \times I$. Define $f: Q \to \mathbb{R}$ by letting $f(x , y) = 1 /q$ if y is rational and $x = p/q$

score 2.2k · Answer 1 · 2026-04-17 14:20:18

2.2k

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Let $I = [0 , 1]$; let $Q = I \times I$. Define $f: Q \to \mathbb{R}$ by letting $f(x , y) = 1 /q$ if y is rational and $x = p/q$

Published on 17 Apr 2026 - 14:20

score 2.3k · Answer 2 · 2026-05-10 16:12:08

2.3k

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Why are there two separate branches of calculus?

Published on 10 May 2026 - 16:12

score 70 · Answer 3 · 2026-04-16 02:38:02

70

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Find the derivatives of the following function and calculate $f'(1)$.

Published on 16 Apr 2026 - 2:38

score 70 · Answer 4 · 2026-04-16 14:59:01

70

Views

$x^2$ vs $x^3$ as example of function with non smooth inverse

Published on 16 Apr 2026 - 14:59

score 64 · Answer 5 · 2026-05-10 15:03:27

64

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Show that: $ \int_{1}^{3}\int_{0}^{x-1} f_{x}(x,y)dydx = -\frac{4}{3}$

Published on 10 May 2026 - 15:03

score 123 · Answer 6 · 2026-05-11 06:54:07

123

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Formal Definition Of Limit with Sequence

Published on 11 May 2026 - 6:54

score 98 · Answer 7 · 2026-04-12 14:20:48

98

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What is the operator norm of the following?

Published on 12 Apr 2026 - 14:20

score 46 · Answer 8 · 2026-04-16 07:19:06

46

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Solving a weird system of ODEs: $-(\lambda_i+\delta)v_i(x)+\mu_iv_i(x) +\frac{1}{2}\sigma_i^2 v_i''(x) +\lambda_iv_{3-i}(x)=0, ~~~~~i=1,2$

Published on 16 Apr 2026 - 7:19

score 78 · Answer 9 · 2026-04-16 06:48:12

78

Views

Showing that $\int_0^{ \frac \pi 2} \cos^{2n+1}(x) dx \ = \frac{4^n(n!)²}{(2n+1)!}$?

Published on 16 Apr 2026 - 6:48

score 1.4k · Answer 10 · 2026-04-29 12:52:46

1.4k

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Multivariate Faà di Bruno's formula

Published on 29 Apr 2026 - 12:52

score 117 · Answer 11 · 2026-04-15 09:11:19

117

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Find limit of a random variable: $\lim_\limits{s\to\infty} s^n P(|Y| > s)$.

Published on 15 Apr 2026 - 9:11

score 327 · Answer 12 · 2026-05-14 22:09:59

327

Views

If $\,a_n\searrow 0\,$ and $\,\sum_{n=1}^\infty a_n<\infty,\,$ does this imply that $\,n\log n\, a_n\to 0$?

Published on 14 May 2026 - 22:09

score 111 · Answer 13 · 2026-04-15 00:49:13

111

Views

Finding the point on $6x^2+y^2=262090$ that is nearest to the point $(1045,0)$

Published on 15 Apr 2026 - 0:49

score 301 · Answer 14 · 2026-04-10 10:53:23

301

Views

Fundamental theorem of calculus with 2-variables integrand

Published on 10 Apr 2026 - 10:53

score 63 · Answer 15 · 2026-05-10 15:03:14

Question about the proof of $\liminf_{n\rightarrow\infty}(a_{n})+\liminf_{n\rightarrow\infty}(b_{n})\leq\liminf_{n\rightarrow\infty}(a_{n}+b_{n})$

List Question

Let $I = [0 , 1]$; let $Q = I \times I$. Define $f: Q \to \mathbb{R}$ by letting $f(x , y) = 1 /q$ if y is rational and $x = p/q$

Why are there two separate branches of calculus?

Find the derivatives of the following function and calculate $f'(1)$.

$x^2$ vs $x^3$ as example of function with non smooth inverse

Show that: $ \int_{1}^{3}\int_{0}^{x-1} f_{x}(x,y)dydx = -\frac{4}{3}$

Formal Definition Of Limit with Sequence

What is the operator norm of the following?

Solving a weird system of ODEs: $-(\lambda_i+\delta)v_i(x)+\mu_iv_i(x) +\frac{1}{2}\sigma_i^2 v_i''(x) +\lambda_iv_{3-i}(x)=0, ~~~~~i=1,2$

Showing that $\int_0^{ \frac \pi 2} \cos^{2n+1}(x) dx \ = \frac{4^n(n!)²}{(2n+1)!}$?

Multivariate Faà di Bruno's formula

Find limit of a random variable: $\lim_\limits{s\to\infty} s^n P(|Y| > s)$.

If $\,a_n\searrow 0\,$ and $\,\sum_{n=1}^\infty a_n<\infty,\,$ does this imply that $\,n\log n\, a_n\to 0$?

Finding the point on $6x^2+y^2=262090$ that is nearest to the point $(1045,0)$

Fundamental theorem of calculus with 2-variables integrand

Question about the proof of $\liminf_{n\rightarrow\infty}(a_{n})+\liminf_{n\rightarrow\infty}(b_{n})\leq\liminf_{n\rightarrow\infty}(a_{n}+b_{n})$

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