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Interesting 45 Bountied Hot Week Month
12 votes
2 answers
1k views

(Why) Does Algebraic Topology only deal with topological spaces up to homotopy?

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anomaly
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14 votes
7 answers
516 views

Finding circle tangent to a line and intersecting a given point

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Dr. Michael W. Ecker
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25 votes
6 answers
648 views

$P$ is a point in $\triangle ABC$, with $\angle PBC=\angle PCB=24^\circ$, $\angle ABP=30^\circ$, $\angle ACP=54^\circ$. What is the $\angle BAP$?

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dfnu
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6 votes
4 answers
516 views

Is an argument valid if assuming its premises and conclusion leads to no contradiction?

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ryang
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25 votes
3 answers
614 views

Crazy fact(?) about circles drawn on base of triangle between cevians: they always fit, no matter what their order?

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orangeskid
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9 votes
9 answers
815 views

How to rationalize the denominator $\frac{1}{1 + \sqrt[3]{5} - \sqrt[3]{25}}$

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MathFail
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14 votes
3 answers
531 views

Evaluate $\int_{-\infty}^\infty \frac{\sin{(x\sin{x})}}{x^2}dx$.

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Random Variable
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10 votes
6 answers
380 views

How might I figure out the $n$th term, and the general Maclaurin/Taylor series, for $\sin^3 x$?

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Alex Jones
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9 votes
10 answers
688 views

What is the simple way to solve the equation $x+\sqrt{a+\sqrt{x}}=a$ for all real $x$?

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dan_fulea
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5 votes
3 answers
795 views

Formal Definition of Cardinality

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Vivaan Daga
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16 votes
4 answers
731 views

Incorrect reasoning during Taylor series derivation?

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Hopeful Whitepiller
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9 votes
4 answers
400 views

Solving the Fresnel-type integral $\int_{0}^{\infty} \cos(x\sqrt{x^2+2}) \,\mathrm{d}x$ in an elementary way.

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Angelo
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11 votes
4 answers
395 views

Finding $\displaystyle \lim_{n \rightarrow \infty} \sqrt{n} \int_0^1 \left(\frac{\sin t}{t}\right)^n dt$

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River Li
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67 votes
1 answer
2k views

How to prove this recurrence relation for generalized "rounding up to $\pi$"?

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Thomas Lehéricy
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18 votes
2 answers
1k views

Probability of Sisyphus laboring forever

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Darren Cook
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6 votes
8 answers
177 views

Find the max/min value of $x^2+y^2$ subject to $3x^2+5xy+3y^2=1$

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lone student
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5 votes
3 answers
632 views

Is a parabola really a conic section?

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John Alexiou
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5 votes
6 answers
187 views

Evaluating $ \int \frac{ 1 } { \sin x - \cos x - 1} dx$

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Quanto
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8 votes
2 answers
783 views

Does a recursive definition of a variable make sense at all?

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Robert Z
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9 votes
10 answers
470 views

How to solve for $y$ in $(1+x)dy-ydx=0$?

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Sangchul Lee
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5 votes
4 answers
575 views

Solve this trigonometry problem without using trigonometric functions.

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Robert Z
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4 votes
3 answers
668 views

Categories where every morphism is a monomorphism

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Zhen Lin
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4 votes
5 answers
214 views

Why inner automorphisms; why conjugation? Why not closure under other automorphims?

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Alex Provost
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6 votes
4 answers
204 views

Compute integral $\int^\infty_{-\infty}\frac{1}{\big(\frac89x^2+\frac23\big)\sqrt{\frac{x^2}{3}+1}}~dx$

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MathFail
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5 votes
6 answers
201 views

Integrating $ (x^2+2x+3)^{-2}$

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Mostafa
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5 votes
4 answers
286 views

With the epsilon-delta definition of continuity, are the rationals continuous?

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Arthur Filippi
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7 votes
4 answers
503 views

An open set containing a closed ball should contain an open ball between them

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Paul Frost
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4 votes
4 answers
230 views

How to show that $x^2 \ge \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \dots$?

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Leucippus
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6 votes
6 answers
169 views

Find $\,\lim\limits_{t\to0^+}t\!\int_{t^2}^t\frac{\cos(x)}{x^{3/2}}\,\mathrm{d}x$

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xpaul
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3 votes
7 answers
199 views

how to solve $\lim_{x\to0}\frac{e^x-e^{-x}-2x}{x^3}$ without L'Hospital rule or Taylor series

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robjohn♦
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3 votes
6 answers
150 views

Find all real numbers $a$ for equation $x^3 + ax^2 + 51x + 2023=0$, has two equal roots.

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boojum
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4 votes
5 answers
165 views

Extending an adjunction using colimits

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Zhen Lin
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3 votes
3 answers
332 views

Are there non cyclic subgroup of the set of nonzero rationals under multiplication?

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egreg
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5 votes
5 answers
197 views

How to prove $x + 3 = (x + 1)^2 \Leftarrow x=-2\;\text{or}\;1 \,? \quad \sqrt{x+3}=x+1 \Leftarrow x=1 \, ? \quad x^2 = x \Leftarrow x=0 \; $?

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Stinking Bishop
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6 votes
4 answers
310 views

Evaluating $\int_0^\pi \sin^2(3x+\cos^45x)dx$ (2023 MIT Integration Bee #16)

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conan
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12 votes
3 answers
223 views

Integrating the exponential of distance to a convex bounded set

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Christophe Leuridan
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7 votes
1 answer
279 views

Why does this trig equation have only 2 solutions and not 4?

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Nicolás A.
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4 votes
5 answers
156 views

Prove that $e^{-x^2}<\frac{1}{x^3}$, if $x>0$

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Ryszard Szwarc
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14 votes
2 answers
669 views

Evaluating $\sqrt{x+\sqrt{\sqrt{x+\sqrt{\sqrt{\sqrt{x+...}}}}}}$

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MokutekiJ
  • 132
3 votes
2 answers
372 views

How does every vector space have at least two subspaces?

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b00n heT
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6 votes
2 answers
370 views

Is this a new representation of (some) Bernoulli numbers?

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Peter Luschny
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7 votes
3 answers
473 views

Teacher needs help with an integral involving trig identities that a student found online

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Learningstill
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4 votes
3 answers
349 views

is real analysis just a bunch of proofs of theorems in calculus?

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Ahmed
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4 votes
3 answers
210 views

Use of $\sum_{r=1}^{\infty} \frac{1}{r^2} = \frac{\pi^2}{6} $ in evaluating $I$

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robjohn♦
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9 votes
3 answers
198 views

Prove : $\int_{{π}/{4}}^{{π}/{2}} e^{\cos x + \cos^2{x}}\mathrm dx>\sqrt2$

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Claude Leibovici
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7 votes
4 answers
190 views

Is there a formula for $\sum_{j=1}^n \binom{m j}{m}$, where $m$ is an integer?

Freddie's user avatar
Freddie
  • 186
6 votes
3 answers
146 views

Is there any simple method to evaluate $\int \frac{\tan (3 x)}{\tan(x)+\sec(x)} d x$?

MathFail's user avatar
MathFail
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8 votes
1 answer
387 views

Australian Mathematics Competition Year 7-8 Question 21

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Will Octagon Gibson
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