J i ,,,, ' " W 'i' i ' ' *' i'vw\" if ,,,,,,,, PRELAB: In the lab, we will learn the following theorem. Theorem. Let f and g be continuous, and suppose that 0 S g (33') E f (I) for c110. S it. Then (1) If [:0 f (11:) (1:2: is convergent, then so is L00 g (:23) (1.1:. (2) If L100 9 (3:) dx is divergent, then so is 1:0}.(37) dx. To work with this theorem, we need to practice working with inequalities. In particular, we would like to deve10p a technique for contructing useful inequalities. Consider the following: Exercise 1. For 2 g as, it is true that (1.1) Let's work through the proof to see why (1.1) is true. We will start with the assumption that 2 S :c. We then use a more simple, true inequality, along with a step-bystep process, to build up to (1.1). (1) To start, we know that when 2 S a: we must have 0