Chapter 11.2, Problem 85E

To determine

To Graph:

Function for which $f\left(2\right)$ is defined but the limit of $f\left(x\right)$ as $x$ approaches $2$ does not exist.

Explanation of Solution

Graph:

The graph for the Function for which $f\left(2\right)$ is defined but the limit of $f\left(x\right)$ as $x$ approaches $2$ does not exist is as below:

  

Interpretation:

The function is defined at a point but limit of the function is not defined at the point.

By the addition of the limit of the function, it is defined only when the value of function is similar as the value of $x$ approaches $2$ from left and right.

Consider the given question:

  $f\left(x\right)=\{\begin{array}{l}4xx<2\\ x+2x\ge 2\end{array}$

The discounts curve suggests that the limit of the function is not defined the point $x=2$ but the values of the function is defined.