Chapter 11.3, Problem 73E

Solution

To check: The given statement is true or false

Limit exist. So, the answer is False.

Given information:

  $f\left(x\right)=\left\{\begin{array}{l}x+2\text{if}x\le 3\\ 8-x\text{if}x>3\end{array}\right.$ then $\underset{x\to 3}{{\displaystyle \lim }}f\left(x\right)$ undefined

Calculation:

  $\begin{array}{c}\underset{x\to 3^{{}^{-}}}{{\displaystyle \lim }}f\left(x\right)=x+2\\ =3+2\\ =5\end{array}$

And,

  $\begin{array}{c}\underset{x\to 3^{+}}{{\displaystyle \lim }}f\left(x\right)=8-x\\ =8-3\\ =5\end{array}$

Therefore, the statement is false.