Find the limit of $\frac{\log_{3}\left(x^2\right)}{e^x}$ as $x$ approaches $\infty $

Find the limit

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

Find the limit

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

Find the limit

$\lim_{x\to\infty}\left(x^8e^{-x^7}\right)$

Find the limit

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

Find the limit

$\lim_{x\to\infty}\left(\frac{\left(ln\left(x\right)\right)^2}{5x}\right)$

Find the limit

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

Find the limit

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