IMathAS-libretexts

In which limits below can we use L'Hospital's Rule?

$\displaystyle \lim_{{{x}\rightarrow{0}}}\ \frac{{{7}{x}}}{{\cot{{x}}}}$
$\displaystyle \lim_{{{x}\rightarrow\infty}}\ \frac{{e}^{{x}}}{{x}}$
$\displaystyle \lim_{{{x}\rightarrow\infty}}\ \frac{{{8}{x}^{{2}}+{3}{x}+{6}}}{{{x}^{{2}}+{4}{x}-{9}}}$
$\displaystyle \lim_{{{x}\rightarrow\pi/{2}}}\ \frac{{\sin{{\left({2}{x}\right)}}}}{{{2}{x}-\pi}}$