University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.11 - Linearization and Differentials - Exercises - Page 200: 63


change in volume percent: $\frac{dV}{V}=40%$

Work Step by Step

We are given: $V=kr^4$ relative change for the function is shown by the relation: $\frac{dV}{V}$ $\frac{dV}{V}=\frac{4kr^3dr}{kr^4}$ $\frac{dV}{V}=\frac{4dr}{r}$ it is given that the increase in the value of r is 10%: so $dr=0.1r$ $\frac{dV}{V}=\frac{4\times0.1r}{r}=0.4$ $\frac{dV}{V}=0.4\times100=40%$ $\frac{dV}{V}=40%$
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