Prove that $|\sin x-x |\le \frac{1}{6}|x|^3$
124208
Proof $|\sin(x) - x| \le \frac{1}{3.2}|x|^3$
85944
Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $
52427
Prove, $\sqrt{n} \le (n!)^\frac{1}{n} \le \frac{n+1}{2} $
118884
The sine inequality $\frac2\pi x \le \sin x \le x$ for $0<x<\frac\pi2$
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
16418
Showing that $\frac{f(x)-f(x-h)}{h} \le f'(x) \le \frac{f(x+h)-f(x)}{h}$ given that f' is increasing
120954
Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$
103757
how can I prove that $\frac{\arctan x}{x }< 1$?
49054
Show that $\left | \sin a - \sin b \right | \leq \left | a-b \right |$
124026
Prove $\int^\infty_0\frac x{e^x-1}dx=\frac{\pi^2}{6}$
133428
How prove this inequality $\frac{a}{b+3}+\frac{b}{c+3}+\frac{c}{d+3}+\frac{d}{a+3}\le 1$
42545
If $ a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}<1$
113593
How can I prove that $\frac{n^2}{x_1+x_2+\dots+x_n} \le \frac{1}{x_1}+ \frac{1}{x_2} +\dots+ \frac{1}{x_n}$?
133880
$|\sin^2x-\sin^2y|\le K|x-y|$ find K
75653
Prove that $|f ''|\ge 4$
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
3820
Prove that $||x|-|y||\le |x-y|$