Question

1. find the limit, if it exists. $lim_{x

ightarrow4}\frac{x - 4}{x^{2}-2x - 8}$

Explanation:

Step1: Factor the denominator

Factor $x^{2}-2x - 8$ as $(x - 4)(x+2)$. So the limit becomes $\lim_{x
ightarrow4}\frac{x - 4}{(x - 4)(x + 2)}$.

Step2: Simplify the function

Cancel out the common factor $(x - 4)$ (since $x
eq4$ when taking the limit), we get $\lim_{x
ightarrow4}\frac{1}{x + 2}$.

Step3: Substitute the value of x

Substitute $x = 4$ into $\frac{1}{x+2}$, we have $\frac{1}{4+2}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$