\lim_{x \to (0)} \frac{1}{\sqrt[3]{x}} - 3
You asked:
Evaluate the expression: \(\lim_{x \to 0}{\frac{1}{\sqrt[3]{x}} - 3}\)
MathBot Answer:
The two-sided limit \(\lim_{x \to 0}{\frac{1}{\sqrt[3]{x}} - 3}\) does not exist because the directional limits from the right and the left result in different values.
Right limit:
\(\displaystyle\lim_{x \to 0^+}\left(-3 + \frac{1}{\sqrt[3]{x}}\right) = \infty\)
Left limit:
\(\displaystyle\lim_{x \to 0^-}\left(-3 + \frac{1}{\sqrt[3]{x}}\right) = - \infty \left(-1\right)^{\frac{2}{3}}\)