Question

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

$\underset{x\to 0}{\lim }f\left(x\right),f\left(x\right)=e^x$

Short answer

The limit is$-1$.

Step-by-step solution

Step 1. Given Information  

We are given a function $f\left(x\right)=e^x$and we need to graph the function and find$\underset{x\to 0}{\lim }f\left(x\right)$.

Step 2. Plotting the graph 

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

Step 3. Finding the limit   

To find the value of $\underset{x\to 0}{\lim }{e}^x$we need to find the value of the function at $x=0$.

$$\begin{gathered} f\left(x\right)=e^x \\ \Rightarrow f\left(0\right)=e^x \\ \Rightarrow f\left(0\right)=e^x \\ \therefore \underset{x\to 0}{\lim }f\left(x\right)=1 \end{gathered}$$