Answer
$\underset{x\to -2}{\mathop{\lim }}\,\left| x+2 \right|=0$, because as x-approaches $-2$, the value of $ f\left( x \right)$ gets closer to 0.
Work Step by Step
Consider the provided function, $ f\left( x \right)=\left| x+2 \right|$.
To plot the graph of the function $ f\left( x \right)=\left| x+2 \right|$ substitute different values of x in the equation $ f\left( x \right)=\left| x+2 \right|$ to get different values of $ f\left( x \right)$.
Now, consider the provided limit, $\underset{x\to -2}{\mathop{\lim }}\,\left| x+2 \right|$.
Consider the graph of the function $ f\left( x \right)=\left| x+2 \right|$.
To find $\underset{x\to -2}{\mathop{\lim }}\,\left| x+2 \right|$, examine the portion of the graph near $ x=-2$.
As x gets closer to $-2$, the value of $ f\left( x \right)$ gets closer to the y-coordinate of 0. This point $\left( -2,0 \right)$ is as shown in the above graph.
The point $\left( -2,0 \right)$ has a y-coordinate of 0.
Thus, $\underset{x\to -2}{\mathop{\lim }}\,\left| x+2 \right|=0$.
Hence the value of $\underset{x\to -2}{\mathop{\lim }}\,\left| x+2 \right|$ is 0.
