Problem 1. At what points (if any) is the function continuous? Prove your answer using the o - E definition of continuity. f (2) = x TEQ 0 Problem 2. a) Prove that if f is continuous everywhere, then If | is continuous everywhere. -7 b) Give an example to show that the continuity of If | does not imply the continuity of f. c) Give an example of a function f such that f is continuous nowhere, but If | is continuous everywhere. Problem 3. Let f be continuous at c E R. Prove that if f(c) > 0, then there exists o > 0 such that f(x) > 0 for all x E (c - 8, c + 8)