Question

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

$\underset{x\to 0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}{e}^x& ifx>0\\ 1-x& ifx\le 0\end{array}\right.$

Short answer

the limit of a given function at x=0 is 0

Step-by-step solution

step1. Given information 

The given function $\underset{x\to 0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}{e}^x& ifx>0\\ 1-x& ifx\le 0\end{array}\right.$

step2. Explanation about the existence of a limit of the given function 

To find the limit we have to draw the graph of its

We know that at the limit point as x-factor is near to limit points so that time y tends to a specific value, that specific value is the value of the function at the limit point

so according to the question, we can see in the pieces of both graphs when x is near 0, then y approach 1 in both pieces of the graph

Thus the limit of the given function is evaluated by 1