Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 2

Answer

Domain: x, y can be any real numbers in the x-y plane. Range: $f(x,y) \gt 0$ Level Curves: $x+y = \ln{c}$ (constant),

Work Step by Step

Function: $f(x,y) = e^{x+y}$ Domain: x, y can be any real numbers in the x-y plane. Range: $f(x,y) \gt 0$ Level Curves: $f(x,y) = c$ (constant), $e^{x+y}=c$ $\ln{e^{x+y}}=\ln{c}$ $x+y = \ln{c}$ (constant) Hence, the level curves are a series of straight lines. For example, when $c=e$, $x+y = 1$ which is shown in the figure.
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