find the given limit. lim x→−1 x² - 3 / 1 - x select the correct choice below and, if necessary, fill in the…

find the given limit. lim x→−1 x² - 3 / 1 - x select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim x→−1 x² - 3 / 1 - x = (simplify your answer.) b. the limit does not exist.

find the given limit. lim x→−1 x² - 3 / 1 - x select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim x→−1 x² - 3 / 1 - x = (simplify your answer.) b. the limit does not exist.

Answer

Explanation:

Step1: Substitute x = - 1

Substitute (x=-1) into (\frac{x^{2}-3}{1 - x}). We get (\frac{(-1)^{2}-3}{1-(-1)}).

Step2: Simplify the numerator and denominator

First, simplify the numerator: ((-1)^{2}-3=1 - 3=-2). Then, simplify the denominator: (1-(-1)=1 + 1 = 2).

Step3: Calculate the fraction

(\frac{-2}{2}=-1).

Answer:

A. (\lim_{x\rightarrow - 1}\frac{x^{2}-3}{1 - x}=-1)