Question

use the theorem on limits of rational functions to find the limit. if necessary, state that the limit does not exist. $lim_{x
ightarrow5}\frac{x^{2}-25}{x - 5}$ select the correct choice below and fill in the answer box within your choice. a. $lim_{x
ightarrow5}\frac{x^{2}-25}{x - 5}=square$ (simplify your answer.) b. the limit does not exist.

Explanation:

Step1: Factor the numerator

$x^{2}-25=(x + 5)(x - 5)$

Step2: Simplify the rational - function

$\lim_{x
ightarrow5}\frac{x^{2}-25}{x - 5}=\lim_{x
ightarrow5}\frac{(x + 5)(x - 5)}{x - 5}=\lim_{x
ightarrow5}(x + 5)$

Step3: Evaluate the limit

$\lim_{x
ightarrow5}(x + 5)=5+5 = 10$

Answer:

A. $\lim_{x
ightarrow5}\frac{x^{2}-25}{x - 5}=10$