Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.4 Tangent Planes and Linear Approximations - 14.4 Exercises - Page 976: 39

Answer

$0.059 ohm$

Work Step by Step

Write the differential form such as: $dR=\dfrac{\partial R}{\partial R_1} \times dR_1 + \dfrac{\partial R}{\partial R_2} \times dR_2+ \dfrac{\partial R}{\partial R_3} \times dR_3$ $\triangle R=\dfrac{\partial R}{\partial R_1} \times \triangle R_1 + \dfrac{\partial R}{\partial R_2} \times \triangle R_2+ \dfrac{\partial R}{\partial R_3} \times \triangle R_3$ Need to plug the values. $\triangle R=[\dfrac{(11.7647)^2}{(25)^2}] (0.125)+ [\dfrac{(11.7647)^2}{(40)^2}] (0.2)+ [\dfrac{(11.7647)^2}{(50)^2}] (0.25)=(138.408) (0.0002+0.000125+0.0001)$ Thus, we get $dR =\dfrac{1}{17} \approx 0.059$ ohm
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