$\lim_{x\to\infty }\left(\sqrt{x^4+2x^3}-\left(x^2+x\right)\right)$

$\lim_{x\to\infty}\left(\frac{7x+8}{4x+3}\right)$

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

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

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

$\lim_{x\to\infty}\left(xsin\left(\frac{\pi}{x}\right)\right)$

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

$\lim_{x\to infinity}\left(\frac{1-\cos\left(x\right)}{x^2}\right)$