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: 16


The domain is $$\mathcal{D}=\left\{(x,y)|x^2+y^2\geq2^2\right\}$$ and it is sketched on th figure below

Work Step by Step

The argument of the square root has to be nonnegative so we need that $x^2+y^2-4\ge0$ which gives $x^2+y^2\ge4$, and this can be rewritten as $$x^2+y^2\geq2^2.$$ This means that the domain is geometrically the exterior of the circle with the center at the origin and with the radius of $2$ (the circle is included in this region). So we will write for the domain $$\mathcal{D}=\left\{(x,y)|x^2+y^2\geq2^2\right\}$$ and it is sketched on the figure below
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