mja
  • Member for 6 years, 5 months
  • Last seen more than a month ago
  • USA
1 answers
15 votes
548 views
6 bookmarks
Solving $\sin^{2015}x+\cos^{2015}x=\frac12$
4 answers
14 votes
1k views
10 bookmarks
If $u_{n+1}\le u_n+u_n^2$ and $\sum u_n$ converges, prove that $\lim\limits_{n\to +\infty}(n\cdot u_n)=0$
2 answers
7 votes
310 views
5 bookmarks
In tetrahedron ABCD, prove that $r<\frac{AB\cdot CD}{2AB+2CD}$
1 answers
7 votes
323 views
3 bookmarks
Evaluating $\int\sqrt{\frac{1-x^2}{1+x^2}}\mathrm dx$
2 answers
7 votes
143 views
4 bookmarks
Given $a,b,c\ge1;abc\ge8$. Proving that $\sqrt{a^2-1}+\sqrt{b^2-1}+\sqrt{c^2-1}\ge 3\sqrt3$
4 answers
6 votes
181 views
2 bookmarks
Showing that $\left (\frac{\sin x}{x} \right )^3\geq \cos^{2}x$
3 answers
6 votes
74 views
1 bookmarks
Prove that $3x-x^3<\frac2{\sin2x}$
3 answers
5 votes
275 views
3 bookmarks
Prove that $\measuredangle AQP+\measuredangle NAP=90^o$
2 answers
5 votes
1k views
5 bookmarks
Calculate $S=3\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}-\sqrt[3]{2}-\sqrt[3]{20}+\sqrt[3]{25}$
2 answers
4 votes
90 views
Solve $\cos \frac{4x}{3}=\cos x+1$
1 answers
4 votes
173 views
When does $f\left [g\left (x \right ) \right ]=g\left [ f\left ( x \right ) \right ]$ have roots.
2 answers
3 votes
141 views
Find $a$ such that $83359654581 ... 10843035531 ^ a \equiv 1 \pmod{32003240081}$
2 answers
3 votes
81 views
3 bookmarks
Proving that $\tan^n\angle A + \tan^n\angle B + \tan^n\angle C \ge 3 + \frac{3n}{2}$
2 answers
3 votes
740 views
2 bookmarks
Given $a, b,c,d$ non-negative and $a+b+c+d=4$. Prove that $a^3b+b^3c+c^3d+d^3a+23abcd \le 27.$
3 answers
3 votes
142 views
2 bookmarks
Given $x\in \left(0; \frac\pi2\right)$. Prove that $\sin x>\frac{2x}{\pi}$
2 answers
3 votes
232 views
5 bookmarks
Prove that $\left (1+\frac ba \right )\left (1+\frac ac \right )\left ( 1+ \frac cb\right )\ge 4+3\sqrt2$
2 answers
2 votes
9k views
How to find modulus square root?
1 answers
2 votes
55 views
Given $2$ sets: $A:=\{1, 2,3\}$ and $B:=\{a, b, c\}.$ Are $A$ and $B$ equivalent?
1 answers
2 votes
36 views
1 bookmarks
Does $\int_1^{+\infty} \frac{1}{\ln^2(x+1)}dx$ convergent?
4 answers
2 votes
89 views
Prove that $\tan x < \frac{4}{\pi}x,\forall x\in \left( 0;\frac{\pi}{4} \right)$
2 answers
2 votes
89 views
2 bookmarks
Find min of $M=\frac{1}{2+\cos2A}+\frac{1}{2+\cos2B}+\frac{1}{2-\cos2C}$
1 answers
2 votes
946 views
1 bookmarks
Prove that $\sum_{k=1}^{n} \frac1{\sin^2 \frac{\left( 2k-1\right)\pi}{4n+2}}=2n\left( n+1\right)$
2 answers
1 votes
85 views
1 bookmarks
Does $\int_{-\infty}^{+\infty}\frac{2xdx}{x^2+1}$ converge?
5 answers
1 votes
79 views
Maclaurin expansion of $y=\frac{1+x+x^2}{1-x+x^2}$ to $x^4$
3 answers
1 votes
101 views
1 bookmarks
Calculus $\int_0^{+\infty}\frac{\sin^2x}x\mathrm dx$
1 answers
0 votes
76 views
Is $\lim\limits_{n\to\infty}a_n=\lim\limits_{n\to\infty}b_n=c$ true?
2 answers
0 votes
30 views
Find Maclaurin expansion of $y=2^x$ to $x^4$
2 answers
0 votes
301 views
Find period of $y=\sin\frac1x$
1 answers
0 votes
574 views
Does a function ( $f(x)$ )is convex iff $f''(x)>0$?
1 answers
0 votes
76 views
1 bookmarks
Find triangle $ABC$ satisfies $1+2\sqrt{2}\sin\frac{B}{2}\sin\frac{C}{2}=\cos B+\cos C$