$\lim_{x\to\infty }\left(\sqrt{x^2-5x+6}-x\right)$

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

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

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

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

$\lim_{x\to\infty}\left(\frac{ln\left(x\right)}{\sqrt{x}}\right)$

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

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