$\lim_{x\to-2}\left(\frac{4x^2+16}{-2x^2-8x}\right)$

$\lim_{t\to-\infty}\left(\frac{\sqrt[3]{3t^3-1}-2}{t-5}\right)$

$\frac{20xy}{24x}$

$\lim_{x\to0}\left(\frac{x^2+2}{2-2\sin\left(x\right)}\right)^{\frac{2}{x}}$

$\int x^{-13}dx$

$x^2+2ax-15ax^2$

$\frac{dy}{dx}\sqrt{xy+3}$