MATH 19A Study Guide - Midterm Guide: Irrational Number, Joule, Rational Number
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The exercises below should give you an idea of the type and di culty of problem to expect on the midterm. I will provide (partial) solutions/answers to the questions. Some exam questions will come directly from the homework: determine whether the following statements are true or false. We proved in class that di erentiability at a implies continuity at a. We showed in class that this function is continuous at 0 but not di erentiable at 0. (3) false. (f g)(cid:48) = f g(cid:48) + f(cid:48)g. (4) false. We gave a sketch in class of the fact that the limit goes not exist. The set x = [0, ) is a closed set but x2 does not achieve its maximum on x. Only when the domain of a continuous function is compact can we say for sure that the function achieves its extreme values. (6) false. Take f (x) = g(x) = x and a = 0.
