$\lim_{x\to\infty }\left(x^{\frac{4}{x}}\right)$

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

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

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

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

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

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

$\lim_{x\to\infty}\left(x^{\frac{4}{x}}\right)$