Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.2 Limits and Continuity in Several Variables - Exercises - Page 772: 11


$ e^2$

Work Step by Step

We are given $ \lim\limits_{(x,y) \to (2,5)}f(x,y)=3$ and $ \lim\limits_{(x,y) \to (2,5)}g(x,y)=7$, then we have $$ \lim\limits_{(x,y) \to (2,5)}e^{f(x,y)^2-g(x,y)}=e^{\lim\limits_{(x,y) \to (2,5)}f(x,y)^2-\lim\limits_{(x,y) \to (2,5)}g(x,y)}\\=e^{3^2-7}=e^2.$$
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