find the given limit. lim x→ - 2 x² - 5 / 2 - x select the correct choice below and, if necessary, fill in…

find the given limit. lim x→ - 2 x² - 5 / 2 - x select the correct choice below and, if necessary, fill in the answer box to complete your choice. o a. lim x→ - 2 x² - 5 / 2 - x = (simplify your answer.) o b. the limit does not exist.

find the given limit. lim x→ - 2 x² - 5 / 2 - x select the correct choice below and, if necessary, fill in the answer box to complete your choice. o a. lim x→ - 2 x² - 5 / 2 - x = (simplify your answer.) o b. the limit does not exist.

Answer

Explanation:

Step1: Substitute x = - 2

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

Step2: Calculate the numerator

When x = - 2, $x^{2}-5=(-2)^{2}-5=4 - 5=-1$.

Step3: Calculate the denominator

When x = - 2, $2-x=2-(-2)=2 + 2 = 4$.

Step4: Find the limit value

The limit $\lim_{x\rightarrow - 2}\frac{x^{2}-5}{2 - x}=\frac{-1}{4}=-\frac{1}{4}$.

Answer:

A. $\lim_{x\rightarrow - 2}\frac{x^{2}-5}{2 - x}=-\frac{1}{4}$