Encontrar $L = \displaystyle\lim_{x \rightarrow \infty} \left(\sqrt{x^6 + 5x^3} - x^3\right)$.

$L = \displaystyle\lim_{x \rightarrow \infty} \left(\dfrac{\cancel{x^6} + 5x^3 - \cancel{x^6}}{\sqrt{x^6 + 5x^3} + x^3}\right) = \displaystyle\lim_{x \rightarrow \infty} \left(\dfrac{5}{\sqrt{\dfrac{x^6 + 5x^3}{x^6}} + \dfrac{x^3}{x^3}}\right) =$

 

$= \displaystyle\lim_{x \rightarrow \infty} \left(\dfrac{5}{\sqrt{1 + \cancelto{0}{\dfrac{5}{x^3}}} + 1}\right) = \fbox{$\dfrac{5}{2}$}$