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

$y=\left(5+8x^{-3}\right)\left(-5x^2+2-4x\right)$

$g\left(x\right)=\frac{x^2+5}{x^2+6x}$

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

$5x-2\left(x+3\right)\le x$

$\frac{dy}{dx}=\frac{x^3}{2y}$

$\frac{1}{3}ln\left(2x-1\right)+\frac{7}{6}ln\left(x+1\right)-\frac{1}{2}ln\left(x-1\right)$