Calcular $L = \displaystyle\lim_{\begin{array}{l}x \rightarrow 1\\ y \rightarrow 1\end{array}} \dfrac{\sqrt[3]{xy} - 1}{\sqrt{xy} - 1}$.
$L = \displaystyle\lim_{\begin{array}{l}x \rightarrow 1\\ y \rightarrow 1\end{array}} \dfrac{\left(\sqrt[3]{xy} - 1\right)\left(\sqrt{xy} + 1\right)}{xy - 1} = \displaystyle\lim_{\begin{array}{l}x \rightarrow 1\\ y \rightarrow 1\end{array}} \dfrac{\cancel{\left(\sqrt[3]{xy} - 1\right)}\left(\sqrt{xy} + 1\right)}{\cancel{\left(\sqrt[3]{xy} - 1\right)}\left(\sqrt[3]{x^2 y^2} + \sqrt[3]{xy} + 1\right)} = \fbox{$\dfrac{2}{3}$}$
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