Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.2 - Limits and Continuity - 14.2 Exercise: 1

Answer

$f(3,1)=6$

Work Step by Step

As we are given that $\lim\limits_{(x,y) \to(a,b)}f(3,1)=6$ In general, we use the notation $\lim\limits_{(x,y) \to(a,b)}f(x,y)=L$ to indicate the values of $f(x,y)$ approach the number L as the point $(x,y)$ approaches the point $(a,b)$ along any path that stays in the domain of $f$. A function of two variables is continuous at $(a,b)$ if $\lim\limits_{(x,y) \to(a,b)}f(x,y)=f(a,b)$ $\lim\limits_{(x,y) \to(3,1)}f(x,y)=f(3,1)$ Hence, $f(3,1)=6$
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