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 771: 3



Work Step by Step

Given $$\lim _{(x, y) \rightarrow(2,-1)}\left(x y-3 x^{2} y^{3}\right)$$ Since $ \left(x y-3 x^{2} y^{3}\right)$ is a continuous polynomial function, then by substitution, we get \begin{align*} \lim _{(x, y) \rightarrow(2,-1)}\left(x y-3 x^{2} y^{3}\right)&=\lim _{(x, y) \rightarrow(2,-1)}\left((2) (-1)-3 (2)^{2} (-1)^{3}\right)\\ &=-2+12=10 \end{align*}
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