Question

Graph each function. Use the graph to find the indicated limit, if it exists.

$\underset{x\to 2}{\lim }f\left(x\right),f\left(x\right)=1-x^2$

Short answer

The limit is$-3$.

Step-by-step solution

Step 1. Given Information  

We are given a function $f\left(x\right)=1-x^2$and we need to graph the function and find $\underset{x\to 2}{\lim }f\left(x\right)$.

Step 2. Plotting the graph 

So, the graph of the function $f\left(x\right)=1-x^2$is

Step 3. Finding the limit  

To find the value of $\underset{x\to 2}{\lim }f\left(x\right)$we need to find the value of the function at $x=2$.

role="math" localid="1646978216414" $$\begin{gathered} f\left(x\right)=1-x^2 \\ \Rightarrow f\left(2\right)=1-{\left(2\right)}^2 \\ \Rightarrow f\left(2\right)=-3 \\ \therefore \underset{x\to 2}{\lim }f\left(x\right)=-3 \end{gathered}$$