Calculus (3rd Edition)

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

Chapter 15 - Differentiation in Several Variables - 15.1 Functions of Two or More Variables - Exercises - Page 766: 56

Answer

Please see the figure attached for sketches (a) and (b).

Work Step by Step

(a) The vertical traces at times $t = 1,2,3$ These vertical traces tell us that at larger time $t$ the heat diffuses slowly through the bar than at earlier time. (b) The vertical traces $x=c$ for $c = \pm 0.2, \pm 0.4$ The vertical traces tell us that as time goes by the temperature cools off more rapidly near the center than points farther from the center.
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