Question

evaluate the limit: $lim_{x
ightarrow - 7}\frac{x^{2}+x - 42}{x + 7}$

Explanation:

Step1: Factor the numerator

We factor $x^{2}+x - 42=(x + 7)(x-6)$. So the limit becomes $\lim_{x
ightarrow - 7}\frac{(x + 7)(x - 6)}{x + 7}$.

Step2: Simplify the function

Cancel out the common factor $(x + 7)$ (since $x
eq - 7$ when taking the limit), we get $\lim_{x
ightarrow - 7}(x - 6)$.

Step3: Evaluate the limit

Substitute $x=-7$ into $x - 6$, we have $-7-6=-13$.

Answer:

$-13$