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PinkyWay
  • Member for 4 years, 5 months
  • Last seen this week
  • Imagination
18 votes
1 answer
331 views

Removal of an arbitrary point of the boundary of a closed and connected $A\subseteq\Bbb R^2$ so the new set remains connected

12 votes
5 answers
575 views

Without calculating the square roots, determine which of the numbers:$a=\sqrt{7}+\sqrt{10}\;\;,\;\; b=\sqrt{3}+\sqrt{19}$ is greater.

11 votes
2 answers
158 views

Finding the smallest $\alpha>0$ for which $\exists\beta(\alpha)>0$ so that $\sqrt{1+x}+\sqrt{1-x}\le 2-\frac{x^\alpha}\beta,\forall x\in[0,1]$.

10 votes
1 answer
1k views

Prove: Three tangents to a parabola form a triangle with an orthocenter on the directrix and a circumcircle passing through the focus

9 votes
2 answers
160 views

Solution verification:$\lim_{x\to 2}\frac{\ln(x-1)}{3^{x-2}-5^{-x+2}}$

7 votes
2 answers
231 views

Finding $\lim_{n\to\infty}{\frac{n}{a^{n+1}}\left(a+\frac{a^2}{2}+\frac{a^3}{3}+\cdots+\frac{a^n}{n}\right)}$ where $a>1$

6 votes
1 answer
93 views

Languages, students, interpretation of $AA^{\tau}\;\&\;A^{\tau}A$

5 votes
1 answer
76 views

Necessary & sufficient conditions on the parameters in a recursive sequence

5 votes
4 answers
161 views

Proof by induction:$\frac{3}{5}\cdot\frac{7}{9}\cdot\frac{11}{13}\cdots\frac{4n-1}{4n+1}<\sqrt{\frac{3}{4n+3}}$

5 votes
1 answer
168 views

Show $A$ is Hermitian and find the orthonormal basis for $V$ in which $A$ is diagonalizable.

5 votes
1 answer
343 views

Property of a semicyclic quadrilateral

5 votes
1 answer
178 views

Proving that for any 3 infinite sequences $\{a_n\},\{b_n\},\{c_n\}$ in $\Bbb N,\exists p,q\in\Bbb N$ s. t. $a_p\ge a_q,b_p\ge b_q,c_p\ge c_q.$

5 votes
0 answers
92 views

Taylor series of the function $f(x)=\ln\left[(3x+4)^{x+2}\right]$ and its convergence interval

5 votes
1 answer
105 views

If $f^{-1}(c)$ is closed $\forall c\in\Bbb R$ and if for each $c\in\Bbb R$ between $f(x)$ & $f(y)$ there is $z\in[x,y]$ s.t. $f(z)=c,f$ is continuous.

5 votes
1 answer
319 views

$2n$ people around the table, ways to place exactly $r$ out of $n$ men next to their wives given that $n$ women are already sitting at the table

5 votes
1 answer
162 views

Bounded convex sets $A,B\subseteq\Bbb R^n,n\ge 2$ with a common point, but disjoint boundaries

5 votes
1 answer
277 views

Oscillation of the function at each point

5 votes
1 answer
138 views

Proving $\lim_{n\to\infty}f_n(x)$ doesn't exist for any $x\in[0,1],$ where $(f_n)_{n\in\Bbb N}$ is the Typewriter sequence

4 votes
1 answer
166 views

Are $[0,1)\times\Bbb R$ and $[0,1)\times\Bbb Q$ similar?

4 votes
1 answer
211 views

Integrability of the function on the intersection of the Lebesgue measure $0$

4 votes
2 answers
73 views

Solid enclosed by the paraboloid $\frac{y^2}{b^2}+\frac{z^2}{c^2}=2\frac{x}a$ and the plane $x=a.$

4 votes
1 answer
76 views

Computing $I=\iint_D\sqrt{\frac{1-x^2-y^2}{1+x^2+y^2}}dxdy$

4 votes
1 answer
256 views

Existence of a unique function $f:\Bbb R^2\setminus\{(0,0)\}\to\Bbb R, f(x,y)^3=xy\cos(xyf(x,y))-x^2y^2f(x,y), (x,y)\in\Bbb R^2\setminus\{(0,0)\}.$

4 votes
3 answers
147 views

Finding: $\gcd\left(2^{200}-2^{100},2^{200}+2^{101}\right)$ and $\gcd\left(3^{202}-3^{101},3^{202}+3^{102}\right)$

4 votes
1 answer
249 views

Limit: ratio of the digit product and the number itself

4 votes
2 answers
115 views

$\cos(x)=\frac{1}{n}, n=2k+1, k\in \mathbb Z_+$

4 votes
1 answer
119 views

Questions on $A^mBA^n=I$ and $\small B=\left[\begin{smallmatrix}1&-1&3&1\\1&1&2&1\\2&-1&3&2\\-1&-2&1&2\end{smallmatrix}\right]$

4 votes
1 answer
443 views

Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction

3 votes
2 answers
182 views

Construction of a group of complex numbers [duplicate]

3 votes
2 answers
187 views

Yugoslavia team selection for IMO 1987 (functions) [closed]

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