Question

simplify the function algebraically and find the limit. lim(x→3) (x² + 4x - 21)/(x² - 6x + 9) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim(x→3) (x² + 4x - 21)/(x² - 6x + 9)= (simplify your answer.) b. the limit does not exist.

Explanation:

Step1: Factor the numerator and denominator

$x^{2}+4x - 21=(x + 7)(x - 3)$ and $x^{2}-6x + 9=(x - 3)^{2}$

Step2: Simplify the function

$\lim_{x
ightarrow3}\frac{(x + 7)(x - 3)}{(x - 3)^{2}}=\lim_{x
ightarrow3}\frac{x + 7}{x - 3}$

Step3: Analyze the limit

As $x
ightarrow3$, the denominator approaches 0 and the numerator approaches 10. The limit does not exist.

Answer:

B. The limit does not exist.