$\lim_{x\to\infty }\left(\sqrt{x^2-3x}-x\right)$

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

$\lim_{x\to\infty}\left(\frac{\sqrt{x^2+1}}{x}\right)$

$\lim_{x\to\infty}\left(\frac{ax^4+bx^2+c}{dx^3+ex^2+fx+g}\right)$

$\lim_{x\to\infty}\left(\frac{7x^2}{x-x^3}\right)$

$\lim_{x\to-3}\left(\frac{x^4-81}{x+3}\right)$

$\lim_{x\to-1}\left(\frac{12x^3+12x^2}{x^4-x^2}\right)$

$\lim_{x\to1}\left(\frac{x^3-1}{4x^3-x-3}\right)$