Question

find the given limit.
lim(x→ - 7) (x^2 - 2)/(7 - x)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. lim(x→ - 7) (x^2 - 2)/(7 - x) = (simplify your answer.)
b. the limit does not exist.

Explanation:

Step1: Substitute x = - 7

Substitute x=-7 into $\frac{x^{2}-2}{7 - x}$.

Step2: Calculate the numerator

When x = - 7, $x^{2}-2=(-7)^{2}-2=49 - 2=47$.

Step3: Calculate the denominator

When x = - 7, $7 - x=7-(-7)=7 + 7 = 14$.

Step4: Find the limit value

The limit $\lim_{x
ightarrow - 7}\frac{x^{2}-2}{7 - x}=\frac{47}{14}$.

Answer:

A. $\lim_{x
ightarrow - 7}\frac{x^{2}-2}{7 - x}=\frac{47}{14}$