Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 5: Integrals - Section 5.1 - Area and Estimating with Finite Sums - Exercises 5.1 - Page 258: 19

Answer

A) UPPER ESTIMATE =758 GAL lOWER ESTIMATE = 543 gal b) upper estimate=2363 gal Lower Estimate=1693 gal c) worst case=31.4 best case=32.4

Work Step by Step

Since the leakage is increasing, an upper estimate uses right endpoints and a lower estimate uses left endpoints: (a) upper estimate (70)(1) (97)(1) (136)(1) (190)(1) (265)(1)= 758 gal, lower estimate (50)(1) (70)(1) (97)(1) (136)(1) (190)(1) = 543 gal. (b) upper estimate (70 97 136 190 265 369 516 720) = 2363 gal, lower estimate (50 70 97 136 190 265 369 516) = 1693 gal. (c) worst case: 2363 720t 25,000 t =31.4 hrs; best case: 1693 720t 25,000 t= 32.4 hrs
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