Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - 14.4 Exercises - Page 947: 39

Answer

$0.059~ohm$

Work Step by Step

The differential form can be evaluated as follows: $dR=\dfrac{\partial R}{\partial R_1} dR_1 + \dfrac{\partial R}{\partial R_2} dR_2+ \dfrac{\partial R}{\partial R_3} dR_3$ Re-write as: $\triangle R=\dfrac{\partial R}{\partial R_1} \triangle R_1 + \dfrac{\partial R}{\partial R_2} \triangle R_2+ \dfrac{\partial R}{\partial R_3} \triangle R_3$ Plug in the given data, we have $\triangle R=\dfrac{(11.7647)^2}{(25)^2} \times 0.125+ \dfrac{(11.7647)^2}{(40)^2} \times 0.2+ \dfrac{(11.7647)^2}{(50)^2} \times 0.25=138.408 \times (0.0002+0.000125+0.0001)$ Hence, we have $dR =\dfrac{1}{17} \approx~0.059 ohm$
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