Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 13 - Functions of Several Variables - 13.2 Exercises - Page 887: 7

Answer

The limit is $$\lim_{(x,y)\to(a,b)}(f(x,y)g(x,y))=12.$$

Work Step by Step

It is given that $$\lim_{(x,y)\to(a,b)}f(x,y)=4,\quad \lim_{(x,y)\to(a,b)}g(x,y)=3.$$ To find the required limit we will use that the limit of the product is a product of limits: $$\lim_{(x,y)\to(a,b)}(f(x,y)g(x,y)) = \lim_{(x,y)\to(a,b)}f(x,y)\lim_{(x,y)\to(a,b)}g(x,y)=4\cdot3=12.$$
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