Does $\lim _{x \rightarrow-8} \frac{|x+8|}{x+8}$
exist?

Name: Does $\lim _{x \rightarrow-8} \frac{|x+8|}{x+8}$ exist?
Brand: Quizplus
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Question

Does $\lim _{x \rightarrow-8} \frac{|x+8|}{x+8}$
 exist?

Quizplus · Accepted Answer

The limit does not exist because the function $\frac{|x+8|}{x+8}$ behaves differently on the left side and the right side of $x = -8$. For $x > -8$, the expression simplifies to $1$, and for $x < -8$, it simplifies to $-1$, leading to a discontinuity at $x = -8$.

Does lim⁡x→−8∣x+8∣x+8\lim _{x \rightarrow-8} \frac{|x+8|}{x+8}limx→−8​x+8∣x+8∣​ Exist

Does $\lim _{x \rightarrow-8} \frac{|x+8|}{x+8}$ Exist