Question

since the left and right limits are select , the limit is as follows. (if an answer does not exist, enter dne.)
$lim_{x
ightarrow - 6}\frac{5x + 30}{|x + 6|}=$

Explanation:

Step1: Analyze left - hand limit

When $x\to - 6^{-}$, $x + 6<0$, so $|x + 6|=-(x + 6)$. Then $\lim_{x\to - 6^{-}}\frac{5x + 30}{|x + 6|}=\lim_{x\to - 6^{-}}\frac{5(x + 6)}{-(x + 6)}=-5$.

Step2: Analyze right - hand limit

When $x\to - 6^{+}$, $x + 6>0$, so $|x + 6|=x + 6$. Then $\lim_{x\to - 6^{+}}\frac{5x + 30}{|x + 6|}=\lim_{x\to - 6^{+}}\frac{5(x + 6)}{x + 6}=5$.

Step3: Compare left and right limits

Since the left - hand limit ($-5$) and the right - hand limit ($5$) are not equal.

Answer:

DNE