Chapter 1.3, Problem 112E

(a)

To determine

To prove: If $\underset{x\to c}{\lim }\left|f\left(x\right)\right|=0$, then $\underset{x\to c}{\lim }f\left(x\right)=0$, where c be a real number.

(b)

To determine

To prove: The expression $\underset{x\to c}{\lim }\left|f\left(x\right)\right|=\left|L\right|$.