Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.1 - Functions of Several Variables - Exercises 14.1 - Page 788: 40

Answer

See image. .
1578505094

Work Step by Step

$ a.\quad$ To sketch the surface $z=f(x,y)=\sqrt{x^{2}+y^{2}}$: * note that z can not be negative, so the surface is on or above the xy plane * in a plane $z=k$, the trace is a circle of radius $k$ * in the plane $x=0$, the trace is the graph of $z=|y|$ * in the plane $y=0$, the trace is the graph of $z=|x|$ This is the upper part of a (circular) cone. $ b.\quad$ In the xy plane, we equate $f(x,y)$ with several values of c, $z=\sqrt{x^{2}+y^{2}}=c\qquad $(so only nonnnegative c apply) These are circles with radii $c.$ Take $c=0,1,2,3$....
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