Mathematics 242 – Principles of Analysis Definitions Quiz 8 – November 19, 2004

Your Name:

1. (15) Let f : D → R and let c ∈ D. Give the precise definition of the statement “f is differentiable at c.”

2. (10) True or False: If h_{n} is any sequence such that lim_{n→∞} h_{n} = 0, c + h_{n} ∈ D for all n, and f is differentiable at c, then lim_{n→∞} f(c + h_{n}) = f(c). (Briefly) explain.