Question

simplify the function algebraically and find the limit
lim(x→5) (x² + 2x - 35)/(x² - 10x + 25)
simplify the given limit.
lim(x→5) (x² + 2x - 35)/(x² - 10x + 25)=lim(x→5) ((x + 7)/(x - 5)) (type an expression using x as the variable. simplify your answer.)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. lim(x→5) (x² + 2x - 35)/(x² - 10x + 25)= (simplify your answer.)
b. the limit does not exist

Explanation:

Step1: Factor the numerator and denominator

$x^{2}+2x - 35=(x + 7)(x - 5)$ and $x^{2}-10x + 25=(x - 5)^{2}$

Step2: Simplify the function

$\lim_{x
ightarrow5}\frac{(x + 7)(x - 5)}{(x - 5)^{2}}=\lim_{x
ightarrow5}\frac{x + 7}{x - 5}$

Step3: Evaluate the limit

As $x
ightarrow5$, the denominator approaches 0 and the numerator approaches 12. The limit does not exist.

Answer:

B. The limit does not exist