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: 9

Answer

The limit is $$\lim_{(x,y)\to(2,1)}(2x^2+y)=9.$$ The function is continuous on the whole doman.

Work Step by Step

The limit can be found by the simple substitution: $$\lim_{(x,y)\to(2,1)}(2x^2+y)=2\cdot2^2+1=9.$$ The function is continuous on the whole domain because for every ordered pair $(x_0,y_0)$ $$\lim_{(x,y)\to(x_0,y_0)}(2x^2+y) = 2x_0^2+y_0.$$
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