Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.1 Vector Fields - 16.1 Exercises - Page 1114: 33

Answer

$(2.04, 1.03)$

Work Step by Step

$x = 2$ $y = 1$ $V(x,y) = (x^2, x + y^2)$ $= ((2)^2, 2 + (1)^2)$ $= (4, 3)$ $t = 3.01 - 3$ $ = 0.01$ $t \times V(2, 1) = 0.01(4, 3)$ $ = (0.04, 0.03)$ Location at time $t$ is calculated as follows: $V(x, y) = (x, y) + (t_x, t_y)$ $= (2, 1) + (0.04, 0.03)$ $= (2.04, 1.03)$
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