Use the graph below to find $\lim _ { x \rightarrow - 2 } \frac { | x + 2 | } { x + 2 }$, if it exists.

A) $- 1$
B) $- 2$
C) 2
D) 1
E) The limit does not exist.

Question

Use the graph below to find $\lim _ { x \rightarrow - 2 } \frac { | x + 2 | } { x + 2 }$, if it exists.

A) $- 1$ 
B) $- 2$ 
C) 2 
D) 1 
E) The limit does not exist.

Quizplus · Accepted Answer

As $x$ approaches $-2$ from the left, $\dfrac{|x+2|}{x+2}$ approaches $1$. However, as $x$ approaches $-2$ from the right, $\dfrac{|x+2|}{x+2}$ approaches $-1$. Therefore, the limit does not exist.

Use the Graph Below to Find lim⁡x→−2∣x+2∣x+2\lim _ { x \rightarrow - 2 } \frac { | x + 2 | } { x + 2 }limx→−2​x+2∣x+2∣​

Use the Graph Below to Find $\lim _ { x \rightarrow - 2 } \frac { | x + 2 | } { x + 2 }$