Calculus 8th Edition

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

Chapter 14 - Partial Derivatives - 14.1 Functions of Several Variables - 14.1 Exercises - Page 940: 14


The domain is $\mathcal{D}=\left\{(x,y)|y\leq\frac{1}{3}x\right\}$ and it is shown in the figure below

Work Step by Step

The argument of every even order root has to be positive so we need that $x-3y\ge0$ which gives $3y\le x$ and finally $y\le\frac{1}{3}x.$ We can now write for the domain $$\mathcal{D}=\left\{(x,y)|y\le\frac{x}{3}\right\}.$$ Geometrically, this is the region of $xy$ plane under the line $y=\frac{1}{3}x$ (including this line). It is shown on the graph below
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