Question

use the theorem on limits of rational functions to find the limit. if necessary, state that the limit does not exist. $lim_{x
ightarrow - 3}\frac{x^{2}-9}{x + 3}$ select the correct choice below and fill in the answer box within your choice. a. $lim_{x
ightarrow - 3}\frac{x^{2}-9}{x + 3}=$ (simplify your answer.) b. the limit does not exist.

Explanation:

Step1: Factor the numerator

$x^{2}-9=(x + 3)(x - 3)$

Step2: Simplify the function

$\lim_{x
ightarrow - 3}\frac{x^{2}-9}{x + 3}=\lim_{x
ightarrow - 3}\frac{(x + 3)(x - 3)}{x+3}=\lim_{x
ightarrow - 3}(x - 3)$

Step3: Evaluate the limit

$\lim_{x
ightarrow - 3}(x - 3)=-3-3=-6$

Answer:

A. -6