Calculus Examples

$lim_{x \to 5} \frac{1}{x - 5}$

Step 1

Change the two-sided limit into a left sided limit.

$lim_{x \to 5^{-}} \frac{1}{x - 5}$

Step 2

Since the numerator is positive and the denominator $x - 5$ approaches zero and is less than zero for $x$ near $5$ to the left, the function decreases without bound.

$- \infty$