lim(x→-8) (2 + ∛x)/(3 - √(1 - x))
You asked:
Evaluate the expression: \(\lim_{x \to -8}{\frac{2 + \sqrt[3]{x}}{3 - \sqrt{1 - x}}}\)
MathBot Answer:
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:
\(\displaystyle\lim_{x \to -8^-}\left(\frac{\sqrt[3]{x} + 2}{3 - \sqrt{1 - x}}\right) = - \infty \operatorname{sign}{\left(2 + 2 \sqrt[3]{-1} \right)}\)