72. (a) Show that the absolute value function F(x)=|x| is continuous everywhere.

72.
(a) Show that the absolute value function F(x)=|x| is continuous everywhere.
(b) Prove that if f is a continuous function on an interval, then so is |f|.
(c) Is the converse of the statement in part (b) also true? In other words, if |f| is continuous, does it follow that f is continuous? If so, prove it. If not, find a counterexample.

Calculus: Early Transcendentals
Chapter 2: Limits and Derivatives
Section 2.5: Continuity
Problem 72

10/1/2024 - 5,263 Subscribers - 1,188,683 Views