Question

find the limit, if it exists.

1. $lim_{x

ightarrow - 4}\frac{x^{2}+7x + 12}{x + 4}$

Explanation:

Step1: Factor the numerator

Factor $x^{2}+7x + 12$ as $(x + 3)(x+4)$. So the limit becomes $\lim_{x
ightarrow - 4}\frac{(x + 3)(x + 4)}{x + 4}$.

Step2: Simplify the function

Cancel out the common factor $(x + 4)$ (since $x
eq - 4$ when taking the limit), we get $\lim_{x
ightarrow - 4}(x + 3)$.

Step3: Evaluate the limit

Substitute $x=-4$ into $x + 3$. We have $-4+3=-1$.

Answer:

$-1$