Calculus Examples

$lim_{x \to 0} \frac{x (x^{2} - 1)}{x^{2}}$

Step 1

Cancel the common factors.

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Step 1.1

Factor $x$ out of $x^{2}$ .

$lim_{x \to 0} \frac{x (x^{2} - 1)}{x \cdot x}$

Step 1.2

Cancel the common factor.

$lim_{x \to 0} \frac{x (x^{2} - 1)}{x \cdot x}$

Step 1.3

Rewrite the expression.

$lim_{x \to 0} \frac{x^{2} - 1}{x}$

Step 2

Since the function approaches $\infty$ from the left and $- \infty$ from the right, the limit does not exist.

$Does not exist$