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 914: 36

Answer

I: paraboloid II: cone

Work Step by Step

Contour map I: as we move away from the origin in equal increments, (say along x in the positive direction), the level curves get closer together, indicating that z-values increase with an increasing rate as (x,y) moves away from the origin, indicating a paraboloid. Contour map I: the level curves are evenly spaced, meaning that the rate of increase of z is constant, indicating a cone.
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