find the given limit.\nlim(x→ - 7) (x^2 - 2)/(7 - x)\nselect the correct choice below and, if necessary…
find the given limit.\nlim(x→ - 7) (x^2 - 2)/(7 - x)\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. lim(x→ - 7) (x^2 - 2)/(7 - x) = (simplify your answer.)\nb. the limit does not exist.
Answer
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 $\lim_{x\rightarrow - 7}\frac{x^{2}-2}{7 - x}=\frac{47}{14}$.
Answer:
A. $\lim_{x\rightarrow - 7}\frac{x^{2}-2}{7 - x}=\frac{47}{14}$