Question

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

$\underset{x\to 2}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}{x}^2& ifx\le 2\\ 2x-1& ifx>2\end{array}\right.$

Short answer

limit of the given function (at x=2) doesn't exist

Step-by-step solution

Step1. Given information 

The given function $\underset{x\to 2}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}{x}^2& ifx\le 2\\ 2x-1& ifx>2\end{array}\right.$

Step2. Calculations of the limit of the 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

According to the question when x is near 2

the first segment of the graph is near 3 but the second segment tends to be 4

The value of both parts of the graph is different at the same value, so on this value limit of the given function doesn't exist