Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - Chapter Review Exercises - Page 835: 8

Answer

(a) $f\left( {x,y} \right) = xy$ matches contour graph (ii). (b) $f\left( {x,y} \right) = {{\rm{e}}^{xy}}$ matches contour graph (i). (c) $f\left( {x,y} \right) = \sin \left( {xy} \right)$ matches contour graph (iii).

Work Step by Step

We sketch the contour graphs of the functions (a)-(c) (please see the figure attached) and compare them with those in Figure 3. Thus, we obtain the following matches: (a) $f\left( {x,y} \right) = xy$ matches contour graph (ii). (b) $f\left( {x,y} \right) = {{\rm{e}}^{xy}}$ matches contour graph (i). (c) $f\left( {x,y} \right) = \sin \left( {xy} \right)$ matches contour graph (iii).
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