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: 10

Answer

The limit is $$\lim_{(x,y)\to(0,0)}(x+4y+1)=1.$$ The function is continuous on its' domain.

Work Step by Step

This limit is calculated by a simple substitution $$\lim_{(x,y)\to(0,0)}(x+4y+1)=0+4\times0+1=1.$$ This function is continuous on its domain because for every ordered pair $(x,y)$ we have $$\lim_{(x,y)\to(x_0,y_0)}(x+4y+1)=x_0+4y_0+1.$$
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