Question

question topic(s)/section(s): 1.6 determining limits using algebraic manipulation
$lim_{x
ightarrow - 4}\frac{x^{2}-2x - 24}{2x + 8}$
1
-10
dne
-5
clear my selection

Explanation:

Step1: Factor the numerator

Factor $x^{2}-2x - 24$ as $(x - 6)(x+4)$. So the limit becomes $\lim_{x
ightarrow - 4}\frac{(x - 6)(x + 4)}{2x+8}$.

Step2: Factor the denominator

Factor $2x + 8$ as $2(x + 4)$. Then the limit is $\lim_{x
ightarrow - 4}\frac{(x - 6)(x + 4)}{2(x + 4)}$.

Step3: Cancel out common factors

Cancel out the common factor $(x + 4)$ (since $x
eq - 4$ when taking the limit), we get $\lim_{x
ightarrow - 4}\frac{x - 6}{2}$.

Step4: Substitute the value of x

Substitute $x=-4$ into $\frac{x - 6}{2}$, we have $\frac{-4-6}{2}=\frac{-10}{2}=-5$.

Answer:

D. -5