Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 9 - Multiveriable Calculus - 9.5 Total Differentials and Approximations - 9.5 Exercises - Page 502: 1

Answer

dz=0.12

Work Step by Step

We are given $z=f(x,y)=2x^{2}+4xy+y^{2}$ $f_{x}(x,y)=4x+4y$ $f_{y}(x,y)=4x+2y$ By the definition $dz=f_{x}(x,y).dx+f_{y}(x,y)dy=$ $dz=(4x+4y)dx+(4x+2y)dy$ $dz=[4\times5+4\times(-1)]\times0.03+[4\times5+2\times(-1)]\times(-0.02)=0.12$
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