Příklad 2.42

Spočtěte \(\Large\lim_{x\to\infty}\frac{e^{4x}}{\ln{x}}\)

$$\Large \begin{aligned}

&\lim_{x\to\infty}\frac{e^{4x}}{\ln{x}} \

=& \lim_{x\to\infty}\frac{\infty}{\infty} \

\\ &\text{It's L'Hospital Time:} \\

=& \lim_{x\to\infty}\frac{4e^{4x}}{\frac{1}{x}} \

=& \lim_{x\to\infty}4xe^{4x} \

=& \lim_{x\to\infty}\infty \

=& \boxed{\infty}

\end{aligned} $$