Calculus Examples

$lim_{x \to 5} \frac{x^{2} - 5 x - 50}{x^{2} - 15 x + 50}$

Step 1

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

$lim_{x \to 5^{-}} \frac{x^{2} - 5 x - 50}{x^{2} - 15 x + 50}$

Step 2

Since the numerator is negative and the denominator $x^{2} - 15 x + 50$ approaches zero and is greater than zero for $x$ near $5$ to the left, the function decreases without bound.

$- \infty$