$\lim_{x\to0}\left(\frac{\left(3^x-1\right)}{\left(2^x-1\right)}\right)$

$5-8x>-3$

$\frac{d}{dx}\frac{2x+3}{x+12}$

$\cot^2x+\csc^2x=2\csc\left(x\right)-1$

$\lim_{x\to\infty}\left(\frac{-2x^2-4x+6}{x^2+3x}\right)$

$\lim_{x\to\infty}\left(\frac{1}{2\sin\left(x\right)}\right)$

$\cos x=\sin x\cot x$