Show $0< \frac{2x}{\pi} < \sin x$
105622
How to show $ \sin x \geq \frac{2x}{\pi}, x \in [0, \frac{\pi}{2}]$?
70974
How can zero divided by $i$ be $2\pi$?
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
150601
The limit of $\sin(1/x)$ as $x\to 0$ does not exists
35529
Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$
32823
Prove $\forall n \in \mathbb{N}: \int_{0}^{\frac{\pi}{2}} |\frac{\sin(nx)}{x}|dx \geq \frac{2}{\pi}\sum_{k=1}^{n}\frac{1}{k}$
150917
Show that $\lim_{n\to \infty}\sin{n\pi x} =0$ if $x\in \mathbb{Z},$ but the limit fails to exist if $x\notin \mathbb{Z}.$
70715
How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?
118884
The sine inequality $\frac2\pi x \le \sin x \le x$ for $0<x<\frac\pi2$
25797
Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $
149102
Evaluating $\lim_{x \to 0} x\sin\left(\frac{1}{x}\right)$ or showing it does not exist
118687
Prove an inequality with a $\sin$ function: $\sin(x) > \frac2\pi x$ for $0<x<\frac\pi2$
113765
$\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
106868
Prove that $x+\frac1{4x} ≥ 1$ for $x>0$
68774
Proving that $f(x)$ is less than or equal to $1+\pi/4$
117587
$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$
149827
show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$