Thomas' Calculus 13th Edition

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

Chapter 14: Partial Derivatives - Section 14.6 - Tangent Planes and Differentials - Exercises 14.6 - Page 834: 22


$\approx 0.1732$

Work Step by Step

As we know that, $u=\dfrac{v}{|v|}$ Now, $u=\dfrac{\lt 1,1,1 \gt}{\sqrt{1^2+1^2+(1)^2}}=\lt \dfrac{1}{\sqrt 3},\dfrac{1}{\sqrt 3},\dfrac{1}{\sqrt 3} \gt$ Here, $dh=(\nabla h \cdot u) ds$ Thus, $dh=[\sqrt 3](0.1)\approx 0.1732$
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