Calculus Examples

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

Step 1

Consider the limit with the constant multiple $- 1$ removed.

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

Step 2

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

$\infty$

Step 3

Since the function $\frac{1}{{(x - 1)}^{2}}$ approaches $\infty$ , the negative constant $- 1$ times the function approaches $- \infty$ .

$- \infty$