Calculus Examples

$lim_{x \to 1} \frac{(x - 1) (x - 2)}{{(x - 1)}^{3}}$

Step 1

Cancel the common factors.

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Step 1.1

Factor $x - 1$ out of ${(x - 1)}^{3}$ .

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

Step 1.2

Cancel the common factor.

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

Step 1.3

Rewrite the expression.

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

Step 2

Since the numerator is negative and the denominator ${(x - 1)}^{2}$ approaches zero and is greater than zero for $x$ near $1$ on both sides, the function decreases without bound.

$- \infty$