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: 13


The domain is $$\mathcal{D}=\{(x,y)|x\ge2,y\ge1\}.$$ It is presented in the figure below:

Work Step by Step

Arguments of both square roots have to be nonnegative so we get $$x-2\geq0,\quad y-1\geq0.$$ This gives $$x\geq2,\quad y\geq1,$$ so we can write for the domain $$\mathcal{D}=\{(x,y)|x\geq2,y\geq1\}.$$ Geometrically, it is an infinite region of $xy$ plane that is bounded by lines $x=2$ and $y=1$, including these boundaries (rays along these lines starting from the point $(2,1)$ where they meet.) It is illustrated in the figure below
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