Chapter 2.6, Problem 78E

Continuity of the absolute value function Prove that the absolute value function |x| is continuous for all values of x. (Hint: Using the definition of the absolute value function, compute $\underset{x\to 0^{-}}{\lim }\left|x\right|$ and $\underset{x\to 0^{+}}{\lim }\left|x\right|$.)