If $0<x<1$ for some $x \in \mathbb{R}$, prove that $\frac{1}{x(1-x)}\geq 4$.
89125
Prove that $r \in R$ such that $0 \lt r \lt 1$ then $\frac{1}{r (1 - r)} \ge 4$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
91877
Let $|x|\leq1, |y|\leq 1$. Show that$0 \leq x^{2}+y^{2} -2x^{2} y^{2}+2xy \sqrt{1-x^{2}} \sqrt{1-y^{2}} \leq 1$
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
149201
What does $\lim_{x\to4} \frac{1}{x-4}$ equal?
152223
If $0<r<1$ show that $r^n$ goes to $0$ as $n$ goes to 1.
90556
Proof of the unbounded-ness of $\sum_{n\geq 1}\frac{1}{n}\sin\frac{x}{n}$
63526
Proving that $(\sup_{x\in R}|f'(x)|)^2\leq 4\sup_{x\in R}|f(x)|\cdot\sup_{x\in R}|f''(x)|$.
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
112565
Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{9}{a+b+c} : (a, b, c) > 0$
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
67851
Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
148494
How does one prove that $\frac{1}{2}\cdot\frac{3}{4}\cdots \frac{2n-1}{2n}\leq \frac{1}{\sqrt{3n+1}}?$