Question

use the theorem on limits of rational functions to find the limit. if necessary, state that the limit does not exist. lim(x→ - 4) (x² - 5)/(4 - x) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim(x→ - 4) (x² - 5)/(4 - x)= (simplify your answer.) b. the limit does not exist.

Explanation:

Step1: Substitute x = - 4

Substitute x=-4 into $\frac{x^{2}-5}{4 - x}$.

Step2: Calculate value

$\frac{(-4)^{2}-5}{4-(-4)}=\frac{16 - 5}{4 + 4}=\frac{11}{8}$.

Answer:

A. $\lim_{x
ightarrow - 4}\frac{x^{2}-5}{4 - x}=\frac{11}{8}$