University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Section 13.2 - Limits and Continuity in Higher Dimensions - Exercises - Page 691: 16



Work Step by Step

Solve the limit $\lim\limits_{(x,y) \to (2,-4)} \dfrac{(y+4)}{x^2y-xy+4x^2-4x}$ $\lim\limits_{(x,y) \to (2,-4)} \dfrac{(y+4)}{x(xy-y+4x-4)}=\lim\limits_{(x,y) \to (2,-4)} \dfrac{(y+4)}{x(x-1)(y+4)}$ Thus, $\dfrac{1}{2(2-1)}=\dfrac{1}{2}$
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