Precalculus Examples

$\frac{lim_{x \to 1} \sqrt[3]{x} - \sqrt{x^{2} - x} - 1}{x - 1}$

Step 1

Because there is a gap in the domain of $\sqrt[3]{x} - \sqrt{x^{2} - x} - 1$ to the left of $1$ , the limit does not exist.

$\frac{Does not exist}{x - 1}$

Step 2

The limit does not exist.

$Does not exist$