MATH 1A Lecture 10: 15 Limit Definitions

 Proof Prove Theorem 9.18. (Him for Property I: If the limit equals r < 1. choose a real number R such that r < R < 1. By the definitions of the limit there exists some N > 0 such that

such that f'(x) > 0 for all 2, "(x) < 0 for x < 0, 5. Sketch the graph of a function and f"(x) > 0 for 3 > 0. (10)

(b) Find values of a that would make the following function continuous everywhere, or determine that no such value exists. In the latter case, write DNE as answer. 22 +2 g(x) = {2+1 if x < 0 if 0 <<<1 if >1. lar3 Answer