Hottest Questions This Month

54

votes

15

answers

6k

views

Why does an exponential function eventually get bigger than a quadratic

modified Mar 4 at 19:44 Yves Daoust 196k

56

votes

5

answers

2k

views

If a two variable smooth function has two global minima, will it necessarily have a third critical point?

real-analysis multivariable-calculus differential-topology morse-theory

answered Mar 2 at 11:00 Thomas Rot 9,049

27

votes

8

answers

749

views

Collecting math websites

self-learning education connections learning

modified Feb 25 at 8:14 ZPlaya 507

31

votes

5

answers

588

views

Teacher claims this proof for $\frac{\csc\theta-1}{\cot\theta}=\frac{\cot\theta}{\csc\theta+1}$ is wrong. Why?

algebra-precalculus trigonometry proof-writing solution-verification

answered Feb 28 at 20:33 Benjamin Wang 2,164

28

votes

2

answers

977

views

Is this math game always winnable?

combinatorics card-games

modified Feb 16 at 21:54 AlexJaynMF 596

13

votes

7

answers

609

views

Divisibility by 7 Proof by Induction

discrete-mathematics induction

answered Feb 14 at 13:27 K.Raghuram Chakravorthy 73

17

votes

6

answers

513

views

Probability that a character kills the boss in a 3 versus 1 fight

probability

modified Feb 19 at 3:30 dan_fulea 19.1k

13

votes

4

answers

2k

views

Does the order of the Fibonacci sequence's initial values matter?

sequences-and-series generating-functions fibonacci-numbers

modified Feb 24 at 10:32 Marc van Leeuwen 101k

18

votes

5

answers

771

views

How to Evaluate $\int_{0}^{1} \frac{x^2 \ln(1-x^4)}{1+x^4}dx$?

integration sequences-and-series definite-integrals

modified Mar 3 at 1:04 Aaron Hendrickson 780

18

votes

3

answers

462

views

4 Color Theorem - What am I not seeing??

geometry coloring

modified Feb 26 at 9:30 Yves Daoust 196k

16

votes

2

answers

555

views

Determine if $x^3+y^3+z^3+t^3 = 10^{2021}$ has a solution

diophantine-equations mathematica

answered Feb 22 at 20:58 Adam Bailey 3,074

9

votes

7

answers

349

views

Prove $\int_0^\infty\frac{\ln x}{x^3-1}\mathrm{d}x=\frac{4\pi^2}{27}$

calculus integration improper-integrals

modified Feb 14 at 23:48 Quanto 51.9k

6

votes

7

answers

259

views

Prove that $\angle AEF =90^\circ$ given a square $ABCD$

geometry contest-math

modified Feb 9 at 15:07 TheSimpliFire 21.9k

7

votes

7

answers

354

views

Why does the definition of topological space require that the empty set be open?

general-topology definition

answered Feb 27 at 9:42 alper akyuz 657

3

votes

3

answers

323

views

if two computers are playing tic-tac-toe, but they are choosing their squares randomly, what is the chance for X to win? [closed]

probability

modified Mar 2 at 18:58 Artimis Fowl 1,711

11

votes

7

answers

314

views

Giving a 1-hour talk to highschool math club: any topic suggestion?

combinatorics discrete-mathematics graph-theory finite-fields recreational-mathematics

answered Mar 2 at 5:03 antkam 13.5k

8

votes

4

answers

452

views

Got $e^{-x}=\cos(ix)$ from Euler's formula. Where is my mistake?

algebra-precalculus trigonometry complex-numbers exponential-function

modified Feb 7 at 11:02 José Carlos Santos 321k

13

votes

5

answers

387

views

Find the minimum of $\sqrt{4y^2-12y+10}+\sqrt{18x^2-18x+5}+\sqrt{18x^2+4y^2-12xy+6x-4y+1}$

calculus maxima-minima

modified 8 hours ago Yuri Negometyanov 21.1k

10

votes

2

answers

2k

views

If a subset of the square grid can be tiled by $1\times n$ rectangles for every $n$, can it be tiled by infinite rays?

geometry logic tiling polyomino

modified Feb 22 at 23:23 RavenclawPrefect 8,003

12

votes

5

answers

254

views

Prove that $\frac{a^2}{a^2+bc}+\frac{b^2}{b^2+ac}+\frac{c^2}{c^2+ab}<2$

inequality contest-math

modified Feb 19 at 16:41 Especially Lime 33.2k

6

votes

4

answers

689

views

Why are abelian groups of interest? What is their usefulness?

group-theory abelian-groups motivation

modified 1 hour ago Ilmari Karonen 22.9k

8

votes

5

answers

284

views

Intuitively understanding why the volume of a cylinder of height $h$ and radius $R$ is $\pi R^2h$

volume solid-geometry

modified Feb 20 at 12:56 Asaf Karagila♦ 350k

10

votes

4

answers

519

views

Show that $\exists \delta > 0, \forall x \in ]0,\pi[, \exists n \in \Bbb N, |\sin(xk^n)|\ge \delta$.

real-analysis calculus sequences-and-series

modified Feb 15 at 20:11 NN2 2,367

30

votes

1

answer

521

views

How to evaluate double limit of multifactorial $\lim\limits_{k\to\infty}\lim\limits_{n\to 0} \sqrt[n]{n\underbrace{!!!!\cdots!}_{k\,\text{times}}}$

real-analysis limits factorial closed-form gamma-function

modified Feb 21 at 13:20 Start wearing purple 51.2k

3

votes

4

answers

191

views

Are $\exists ! (x,y)$ and $\exists ! x \exists ! y$ equivalent?

logic

modified Feb 11 at 17:05 Barry Cipra 74.3k

10

votes

4

answers

344

views

Prove $ \int_{5\pi/36}^{7\pi/36} \ln (\cot t )dt +\int_{\pi/36}^{3\pi/36} \ln (\cot t )dt = \frac49G $

calculus integration

modified Mar 4 at 11:29 ComplexYetTrivial 8,893

11

votes

4

answers

196

views

Solve this limit $\lim\limits_{x\to 1}\left(\dfrac{2017}{1-x^{2017}} -\dfrac{2018}{1-x^{2018}}\right)$

calculus limits

modified Feb 22 at 21:38 John Bentin 14.9k

9

votes

3

answers

994

views

Does a semicircle have 2 right angles?

geometry definition circles angle

modified Feb 28 at 1:49 Directions In Physics 81

6

votes

6

answers

183

views

Point within the interior of a given angle

geometry trigonometry euclidean-geometry reflection geometric-transformation

modified Feb 20 at 14:44 Aqua 79.3k

3

votes

3

answers

172

views

Calculating the integral with an undefined function f(x)

calculus integration analysis

modified 2 days ago robjohn♦ 307k

7

votes

4

answers

439

views

Binomial identity arising from Catalan recurrence.

summation recurrence-relations binomial-coefficients

modified Feb 18 at 8:46 Markus Scheuer 84.3k

7

votes

3

answers

185

views

Calculate $\int_0^{\infty} \frac{\cos 3x}{x^4+x^2+1} dx$

integration complex-analysis

modified Feb 15 at 6:02 Quanto 51.9k

7

votes

4

answers

214

views

Why does this pattern work: $1 \cdot{1} = 1, 11 \cdot{11} = 121, 111 \cdot{111} = 12321\ldots$

sequences-and-series number-theory arithmetic

answered Mar 2 at 15:40 a person 71

4

votes

5

answers

154

views

How to find minimum value of $\sqrt{(x+6)^2+25}+\sqrt{(x-6)^2+121}$? [duplicate]

calculus geometry algebra-precalculus

modified Mar 4 at 21:06 Intelligenti pauca 36.1k

14

votes

2

answers

277

views

Why does this Infinite Series have contradictory convergences?

calculus sequences-and-series

answered Feb 12 at 8:19 mag 1,499

8

votes

2

answers

491

views

Numbers of the kind $0.aaa\ldots =\frac{1}{aaa\ldots a}$

algebra-precalculus arithmetic rational-numbers decimal-expansion

answered Feb 8 at 18:49 lineage 226

6

votes

4

answers

172

views

meaning of topology on a finite set

general-topology

modified Feb 28 at 10:58 vitamin d 2,541

12

votes

3

answers

261

views

Is there a known closed form solution to $\int_0^1\frac{\ln(1+x^{2n})}{1+x^2} \,dx$?

definite-integrals closed-form

modified Feb 24 at 16:36 Quanto 51.9k

15

votes

2

answers

304

views

Is it possible to split the natural numbers into a finite number of sets so that no pair of numbers within a set adds up to a square?

elementary-set-theory square-numbers

modified Feb 24 at 22:55 quantus14 2,011

9

votes

2

answers

494

views

What is the deal with the three isomorphism theorems?

abstract-algebra

modified Feb 27 at 8:50 SSA 193

16

votes

2

answers

329

views

Let $f:\mathbb{R} \to \mathbb{R}$ continuous with $f(f(x))=e^x$, show that $\lim_{x\to \infty } \frac{f(x)}{x^n}=\infty$ (Brazilian Olympiad)

real-analysis limits contest-math

modified yesterday Martin R 64.2k

5

votes

4

answers

150

views

For different integers there exists an integer so that exactly one of the sums is prime.

elementary-number-theory prime-numbers

modified Feb 9 at 11:22 Paul123 168

4

votes

6

answers

142

views

Search for simpler (other) idea to show $(1.001)^{1000}>2$

calculus combinatorics algebra-precalculus elementary-number-theory inequality

answered Mar 4 at 16:44 Barry Cipra 74.3k

16

votes

2

answers

357

views

Given $n+1$ points, bound the product of the distances from one of them

real-analysis optimization real-numbers upper-lower-bounds

modified Feb 12 at 18:37 armand trepy 163

8

votes

4

answers

165

views

Why differentiate between continuous on $[a,b]$ and differentiable on $(a,b)$?

calculus limits derivatives

modified Feb 16 at 1:39 Jean-Claude Arbaut 19.8k

27

votes

1

answer

340

views

On the parity of $\left\lfloor{\frac{3^n}{2^n}}\right\rfloor$

number-theory

modified Mar 2 at 16:47 hgmath 1,130

6

votes

2

answers

155

views

“Introduction to Smooth Manifolds” - differential of a function query

differential-geometry smooth-manifolds differential-forms

answered Feb 8 at 17:56 Jack Lee 36.3k

3

votes

3

answers

325

views

What does it mean to equip a subset with the subspace topology?

general-topology

modified Feb 27 at 1:49 Kaj Hansen 31k

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