Prove $0\leqq x^{2}+ y^{2}- 2\,x^{2}y^{2}+ 2\,xy\sqrt{1- x^{2}}\sqrt{1- y^{2}}\leqq 1$
91877
Let $|x|\leq1, |y|\leq 1$. Show that$0 \leq x^{2}+y^{2} -2x^{2} y^{2}+2xy \sqrt{1-x^{2}} \sqrt{1-y^{2}} \leq 1$
104498
Show that $x^3y^3(x^3+y^3) \leq 2$
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
155341
Proving or disproving inequality $ \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y} \ge x + y + z $
58969
A proof for the inequality $\sum_{i=0}^{t-2}{\frac{1}{t+3i}} \leq \frac{1}{2} $ for all $t \geq 2$
156881
How prove this inequality $I=\int_{0}^{\sqrt{2\pi}}\sin{x^2}dx>0$
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
8027
How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
18477
$(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$ for $n$ integer, $n\geq 2$, $W\gt 0$ and $a$ constant, real, $0\lt a\lt 1$
139711
prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
83531
Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
120954
Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$
52157
Prove that $d(n)\leq 2\sqrt{n}$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$