Thomas' Calculus 13th Edition

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

Chapter 2: Limits and Continuity - Section 2.1 - Rates of Change and Tangents to Curves - Exercises 2.1 - Page 47: 15

Answer

a) PQ1 = 43 m/sec PQ2= 46 m/sec PQ3 = 49 m/sec PQ4 = 50 m/sec b.) 50 m/sec

Work Step by Step

a.) The points Q1, Q2, Q3, Q4 should be estimates and its okay if you have different answers. the y axis is distance (m) and x axis is elapsed time (sec), So slope will be speed(m/sec) Slope PQ1 = $\frac{Δy}{Δx}$ = $\frac{650 - 220}{20-10}$ = $\frac{430}{10}$ = 43 m/sec Slope PQ2 = $\frac{Δy}{Δx}$ = $\frac{650 - 380}{20-14}$ = $\frac{270}{6}$ = 45 m/sec Slope PQ3 = $\frac{Δy}{Δx}$ = $\frac{650 - 480}{20-16.5}$ = $\frac{170}{3.5}$ = 48.6 m/sec ~ 49 m/sec Slope PQ4 = $\frac{Δy}{Δx}$ = $\frac{650 - 550}{20-18}$ = $\frac{100}{2}$ = 50 m/sec b.) We are deducing the answer from part a, the limits are approaching 50 m/sec. So this is the best estimate.
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