Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 14 - Section 14.2 - Limits and Continuity - 14.2 Exercise - Page 960: 6

Answer

$14$

Work Step by Step

$$\eqalign{ & \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {5, - 2} \right)} \left( {{x^2}y + 3x{y^2} + 4} \right) \cr & {\text{The function }}f\left( {x,y} \right) = {x^2}y + 3x{y^2} + 4{\text{ is a polynomial}}{\text{, so we}} \cr & {\text{can find the limit by direct substitution}}{\text{.}} \cr & {\text{Substitute 5 for }}x{\text{ and }} - 2{\text{ for }}y \cr & \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {5, - 2} \right)} \left( {{x^2}y + 3x{y^2} + 4} \right) = {\left( 5 \right)^2}\left( { - 2} \right) + 3\left( 5 \right){\left( { - 2} \right)^2} + 4 \cr & = 25\left( { - 2} \right) + 3\left( 5 \right)\left( 4 \right) + 4 \cr & = - 50 + 60 + 4 \cr & = 14 \cr} $$
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