Chapter 2.4, Problem 3E

3. Let $f\left(x\right)=\{\begin{array}{cc}3-x,& x<2\\ \frac{x}{2}+1,& x>2\end{array}$

1. Find ${\lim }_{x\to 2^{+}}f\left(x\right)$ and ${\lim }_{x\to 2^{-}}f\left(x\right)$ .

Does ${\lim }_{x\to 2}f\left(x\right)$ exist? If so, what is it? If not, why not?

Find ${\lim }_{x\to 4^{-}}f\left(x\right)$ and ${\lim }_{x\to 4^{+}}f\left(x\right)$ .

Does ${\lim }_{x\to 4}f\left(x\right)$ exist? If so, what is it? If not, why not?