Question

compute the following limit if it exists.
lim(x→7) (x² - 2x - 35)/(x - 7)
select the correct choice below and fill in any answer boxes within your choice.
a. lim(x→7) (x² - 2x - 35)/(x - 7) = (simplify your answer.)
b. the limit does not exist.

Explanation:

Step1: Factor the numerator

Factor $x^{2}-2x - 35$ as $(x - 7)(x+5)$. So the limit becomes $\lim_{x
ightarrow7}\frac{(x - 7)(x + 5)}{x - 7}$.

Step2: Simplify the function

Cancel out the common factor $(x - 7)$ (since $x
eq7$ when taking the limit), we get $\lim_{x
ightarrow7}(x + 5)$.

Step3: Evaluate the limit

Substitute $x = 7$ into $x+5$, we have $7+5=12$.

Answer:

A. $\lim_{x
ightarrow7}\frac{x^{2}-2x - 35}{x - 7}=12$