Question

In Problems 8–12, use the accompanying graph of $y=f\left(x\right)$

Find$\underset{x\to -2}{\lim }f\left(x\right)$

Short answer

The value of the limit$\underset{x\to -2}{\lim }f\left(x\right)=2$

Step-by-step solution

Step 1. General formula

We know, to find the limit of a function,

$\underset{x\to c^{-}}{\lim }f\left(x\right)=\underset{x\to c^{+}}{\lim }f\left(x\right)=\underset{x\to c}{\lim }f\left(x\right)$

From the graph,

$$\begin{gathered} \underset{x\to -2^{-}}{\lim }f\left(x\right)=2 \\ \underset{x\to -2^{+}}{\lim }f\left(x\right)=2 \end{gathered}$$

Step 2. Value of the function

Therefore, it can be simplified as,

$$\begin{gathered} \underset{x\to -2^{-}}{\lim }f\left(x\right)=2=\underset{x\to -2^{+}}{\lim }f\left(x\right) \\ \underset{x\to -2}{\lim }f\left(x\right)=2 \end{gathered}$$