Příklad 2.14

Spočtěte \(\Large\lim_{x\to0^+}\sqrt[4]{x^3}\ln^2{x}\)

$$\Large \begin{aligned}

&\lim_{x\to0^+}\sqrt[4]{x^3}\ln^2{x} \

=& \lim_{x\to0^+}x^\frac{3}{4}\ln^2{x} \

=& \lim_{x\to0^+}x^\frac{3}{4}\ln^2{x} \

=& \lim_{x\to0^+}x^\frac{3}{4} \cdot \lim_{x\to0^+}\ln^2{x} \

=& \;0^\frac{3}{4} \cdot \left(\lim_{x\to0^+}\ln{x}\right)^2 \

=& \;0 \cdot \left(\infty\right)^2 \

=& \;\boxed{0} \

\end{aligned} $$