Math Problem Solver

The two-sided limit $\lim_{x \to -8}{\frac{2 + \sqrt[3]{x}}{3 - \sqrt{1 - x}}}$ does not exist because the directional limits from the right and the left result in different values.

Right limit:
$\displaystyle\lim_{x \to -8^+}\left(\frac{\sqrt[3]{x} + 2}{3 - \sqrt{1 - x}}\right) = \infty \operatorname{sign}{\left(2 + 2 \sqrt[3]{-1} \right)}$

Left limit:
$\displaystyle\lim_{x \to -8^-}\left(\frac{\sqrt[3]{x} + 2}{3 - \sqrt{1 - x}}\right) = - \infty \operatorname{sign}{\left(2 + 2 \sqrt[3]{-1} \right)}$