Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 14 - Section 14.1 - Functions of Several Variables - 14.1 Exercise - Page 946: 2

Answer

a) $g(\pi,0)=0$ b) $g(\frac{\pi}{2},\frac{\pi}{4})=\frac{\pi\sqrt{2}+\pi}{4}$ c) $g(0,y)=0$ d) $g(x,y+h)=x\sin (y+h)+(y+h)\sin x$

Work Step by Step

$g(x,y)=x\sin y+y\sin x$ a) $g(\pi,0)=\pi \sin 0+0\sin \pi=0$ b) $g(\frac{\pi}{2},\frac{\pi}{4})=\frac{\pi}{2}\sin \frac{\pi}{4}+\frac{\pi}{4}\sin \frac{\pi}{2}=\frac{\pi\sqrt{2}+\pi}{4}$ c) $g(0,y)=0\sin y+y\sin 0=0$ d) $g(x,y+h)=x\sin (y+h)+(y+h)\sin x$
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