Two students, Lucy and Rita, are approximating b a f (t) dt, where f is a positive and increasing on the interval [a, b]. Rita computes R5 = 33.5 and Lucy computes L5 = 30.5. Tracy arrives and averages Lucy's and Rita's results to get T5. (a) Even though she hasn't yet studied the error bounding formula, Lucy claims that the error in her result is no bigger than 3, i.e. |L5 I| < 3. (Rita makes a similar claim.) Explain (without using the error bounding formulas) how you know that they are both right. (b) Tracy claims that there is an even smaller bound for the error |T5 I|. What's the smallest number E for which you can be sure that |T5 I| < E? Explain. (c) Tracy claims that if f (t) is linear she has the exact answer. Do you agree? Explain why, using a picture. (d) Tracy claims that T5 = L5 R5 2 is geometrically equivalent to approximating the area corresponding to b a f (t) dt by five trapezoids. Explain. (e) Suppose f (t) is not only positive and increasing on [a, b], but also concave down on [a