Skip to main content
Mathematics

Top Questions

Ask Question
Interesting 31 Bountied Hot Week Month
68 votes
2 answers
2k views

coincidental (?) patterns in logs of repeating decimals, e.g. $\ln(2/3)$ vs. $\ln(0.6666666)$

Bill Dubuque's user avatar
Bill Dubuque
  • 281k
14 votes
6 answers
2k views

Do limits leave residual infinitesimals, or do they resolve exactly?

Yakk's user avatar
Yakk
  • 1,551
27 votes
5 answers
3k views

What explains this peak probability "gain" in the birthday problem?

Ilmari Karonen's user avatar
Ilmari Karonen
  • 26.8k
57 votes
2 answers
3k views

Are there non-zero real numbers equal to their "average decimal digit"?

Bill Dubuque's user avatar
Bill Dubuque
  • 281k
22 votes
5 answers
2k views

For what kind of problems was de Rham cohomology introduced?

J W's user avatar
J W
  • 2,306
9 votes
8 answers
2k views

Prove the following statement avoiding calculations as much as possible

preferred_anon's user avatar
preferred_anon
  • 17.7k
9 votes
4 answers
2k views

Can the irrationals be partitioned into dense, disjoint subsets?

Asaf Karagila's user avatar
Asaf Karagila♦
  • 405k
13 votes
5 answers
337 views

How to compute $\int_0^\infty\frac{dx}{(x^2+1)\sqrt{x^2-x+1}}$?

Claude Leibovici's user avatar
Claude Leibovici
  • 284k
21 votes
3 answers
522 views

The integral has a closed-form solution $\int_0^1\frac{1}{\sqrt{\frac1x+x}+\sqrt{\frac1x-x}} \, \mathrm{d}x$?

User's user avatar
User
  • 768
11 votes
4 answers
2k views

Why doesn't Cantor's diagonal argument prove only that the reals are not recursively enumerable?

SSequence's user avatar
SSequence
  • 1,012
10 votes
3 answers
2k views

How do you find the exact area enclosed by a closed curve?

worldsmithhelper's user avatar
worldsmithhelper
  • 256
14 votes
4 answers
1k views

Mathematically precise statement and proof of Maxwell relations?

Venkata Karthik Bandaru's user avatar
Venkata Karthik Bandaru
  • 1,444
30 votes
3 answers
2k views

Does taking countably-many "greedy" closed-ball bites from an open subset of "ice cream" in Euclidean space always leave a set of measure zero?

user76284's user avatar
user76284
  • 6,258
27 votes
1 answer
2k views

Is there a "true" value of BB(745)?

psmears's user avatar
psmears
  • 788
8 votes
5 answers
419 views

What would be the easiest way to solve the integral $-\int_{0}^{\pi/2} t \cos^{2n - 2}(t) \, dt$?

Ryszard Szwarc's user avatar
Ryszard Szwarc
  • 43.2k
9 votes
3 answers
1k views

Mathematical expectation of the area of ​triangle inside equilateral triangle

Rodrigo de Azevedo's user avatar
Rodrigo de Azevedo
  • 1
5 votes
3 answers
1k views

What is the probability that the graph remains connected?

Rodrigo de Azevedo's user avatar
Rodrigo de Azevedo
  • 1
11 votes
4 answers
262 views

How to show that $f_a(x) = \frac{1}{2\pi} \frac{2^{a-1}}{\Gamma(a)} \bigl|\Gamma\bigl(\frac{a+i x}{2}\bigr)\bigr|^2 e^{x(\tau - \pi/2)}$ is stable?

KStar's user avatar
KStar
  • 6,102
11 votes
1 answer
280 views

Does $f'(x) \sim g'(x)$ imply $f(x) \sim g(x)$

Question Number 2's user avatar
Question Number 2
  • 935
11 votes
1 answer
1k views

Is there a "coset test"?

KCd's user avatar
KCd
  • 53.8k
4 votes
5 answers
113 views

Evaluate $I\left(n\right)=\int_{0}^{\infty}\frac{1}{\left(e^{x}+e^{-x}\right)^{n}}\,\mathrm dx$

Letac Gérard's user avatar
Letac Gérard
  • 3,747
9 votes
4 answers
278 views

Proving $\lim_{q\to1^-}\sum_{k=0}^\infty(-1)^k\sin(xq^k)=\frac12\sin x$ with $0\le q<1$.

Daniel Smania's user avatar
Daniel Smania
  • 1,150
6 votes
4 answers
330 views

Domain of $f(f(x))$ where $f(x)=\frac1{1+x}$

Duong Ngo's user avatar
Duong Ngo
  • 1,796
25 votes
3 answers
483 views

How many continuous maps commute with $1 - |2x - 1|$ on $[0, 1]$?

Sara's user avatar
Sara
  • 495
8 votes
2 answers
287 views

Let $f(x) = x^3 - \frac{3}{2}x^2 + x + \frac{1}{4}$. Evaluate $\int_0^1 f^{2025}(x)\, dx. $

Mittens's user avatar
Mittens
  • 45.8k
18 votes
2 answers
460 views

Assigning numbers to letters such that the products of the letters in "zero", "one", ..., "eleven" give the named values (and "negative" gives $-1$)

Idran's user avatar
Idran
  • 103
-3 votes
6 answers
730 views

Find indeterminate $\lim_{x \to -8} \frac{\sqrt[]{1-x}-3}{2+\sqrt[3]{x}}$ without L'Hopital's theorem [closed]

user26872's user avatar
user26872
  • 20.1k
10 votes
2 answers
1k views

What is the average of many sinusoids with similar frequencies?

Random Math Enthusiast's user avatar
Random Math Enthusiast
  • 2,870
5 votes
4 answers
306 views

How to prove that $\tan 15^{\circ} \tan 25^{\circ} \tan 35^{\circ} \tan 85^{\circ}=1$?

Integreek's user avatar
Integreek
  • 7,794
8 votes
8 answers
285 views

How to evaluate $\lim\limits_{x \to 0^{+}} \frac{\sqrt{\sin x} - \sin \sqrt{x}}{x}$?

Ryszard Szwarc's user avatar
Ryszard Szwarc
  • 43.2k
7 votes
3 answers
232 views

How to prove $\int_{0}^{1}\frac{2x}{(1+x^2)\ln(\frac{1-x}{1+x})}dx=-\ln2$

TechColly y's user avatar
TechColly y
  • 125
9 votes
3 answers
462 views

If a stochastic matrix has unit permanent, is it a permutation matrix?

Fnacool's user avatar
Fnacool
  • 9,421
5 votes
3 answers
740 views

Least naturals with square average and cube product: $m+n = 2j^2, mn = k^3$

Bill Dubuque's user avatar
Bill Dubuque
  • 281k
3 votes
5 answers
341 views

How can $\emptyset = 0$ be in ZFC?

Michael Carey's user avatar
Michael Carey
  • 1,171
9 votes
3 answers
223 views

Is $\int_0^{\pi/4}\ln(1+\tan x)\mathrm dx = \int_0^{\pi/4}\frac{x}{\cos x(\cos x+\sin x)}\mathrm dx$ a coincidence or a connection?

Poonguzhali Annadurai's user avatar
Poonguzhali Annadurai
  • 913
9 votes
4 answers
349 views

A special case that Slutsky's theorem can be conversed

agriLec's user avatar
agriLec
  • 93
6 votes
4 answers
200 views

Is there any alternative to evaluate $\int_0^1\left(\sin ^{-1} x\right)^2 \ln x \,\mathrm dx$?

Nanayajitzuki's user avatar
Nanayajitzuki
  • 2,730
26 votes
1 answer
584 views

Enumerating all fractions by $x \mapsto x +1$ and $x \mapsto-\frac1x$.

mathmasterzach's user avatar
mathmasterzach
  • 483
3 votes
4 answers
210 views

What allows us to go from $3^{3x} = 3^9$ to $3x = 9$?

Ethan Bolker's user avatar
Ethan Bolker
  • 103k
8 votes
2 answers
715 views

Are there examples of functions that can be quadratically aproximated at certain points but not diffrentiable twice at those points?

Severin Schraven's user avatar
Severin Schraven
  • 22.4k
14 votes
2 answers
446 views

Evaluating of Multidimensional Integral

Gonçalo's user avatar
Gonçalo
  • 15.1k
6 votes
3 answers
548 views

Associativity of cartesian product demystification

Eric Towers's user avatar
Eric Towers
  • 70.3k
5 votes
3 answers
371 views

Question involving limits and area of region

K. Grammatikos's user avatar
K. Grammatikos
  • 12.6k
5 votes
2 answers
593 views

Is "being a local ring" a local property?

Derek Allums's user avatar
Derek Allums
  • 3,207
4 votes
2 answers
582 views

The term "finitely generated algebra"

Joshua Tilley's user avatar
Joshua Tilley
  • 9,886
6 votes
2 answers
739 views

"Calculus on Manifolds" by Michael Spivak vs "Introduction to Smooth Manifolds" by John M. Lee (Edited)

Diana Pestana's user avatar
Diana Pestana
  • 1,349
7 votes
3 answers
211 views

Is it hard to evaluate the integral $\int_0^{\frac{\pi}{4}} \tan ^{-1} \sqrt{\frac{1-\tan ^2 x}{2}} d x$ without Feynman’s trick?

Claude Leibovici's user avatar
Claude Leibovici
  • 284k
6 votes
3 answers
729 views

Why is this surface integral evaluating to zero?

Sammy Black's user avatar
Sammy Black
  • 28.3k

Looking for more? Browse the complete list of questions, or popular tags. Help us answer unanswered questions.