$\lim_{y\to\infty }\left(\frac{2y^2-3y+5}{y^2-5y+2}\right)$

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

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

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

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

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

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

$\lim_{x\to\infty}\left(xe^{-x}\right)$