Question

use the theorem on limits of rational functions to find the limit. if necessary, state that the limit does not exist. \\( \lim_{x \to -4} \frac{x^2 - 2}{4 - x} \\) select the correct choice below and, if necessary, fill in the answer box to complete your choice. \\( \bigcirc \\) a. \\( \lim_{x \to -4} \frac{x^2 - 2}{4 - x} = \square \\) (simplify your answer.) \\( \bigcirc \\) b. the limit does not exist

Explanation:

Step1: Check denominator at x=-4

Denominator: $4 - (-4) = 8 ≠ 0$

Step2: Substitute x=-4 into numerator

Numerator: $(-4)^2 - 2 = 16 - 2 = 14$

Step3: Calculate the limit

Limit = $\frac{14}{8} = \frac{7}{4}$

Answer:

A. $\lim_{x \to -4} \frac{x^2 - 2}{4 - x} = \frac{7}{4}$ (Simplify your answer)