Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - 14.1 Exercises - Page 913: 31

Answer

Top half of an ellipsoid.

Work Step by Step

Trace in x=0: top half of an ellipse Trace in y=0: top half of an ellipse Traces when $z$ is below $0$: none (square roots are nonnegative). Traces for z between 0 and 2: ellipses, $4x^{2}+y^{2}=k^{2}.$ Graph: top half of an ellipsoid.
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