Chapter 2.3, Problem 126E

Piecewise Functions Let

$\begin{array}{l}f\left(x\right)=\{\begin{array}{cc}0,& \text{if }x\text{ is rational}\\ 1,& \text{if }x\text{ is irrational}\end{array}\\ \text{and}\\ g\left(x\right)=\{\begin{array}{cc}0,& \text{if }x\text{ is rational}\\ x,& \text{if }x\text{ is irrational}\end{array}\end{array}$

Find (if possible) $\underset{x\to 0}{\lim }f\left(x\right)$ and $\underset{x\to 0}{\lim }g\left(x\right)$.