Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - 14.2 Exercises - Page 924: 30

Answer

continuous on ${(x,y)| {1+x-y}\geq 0}$

Work Step by Step

Given: $f(x,y)=cos\sqrt {1+x-y}$ The given function is defined for all values of x and y except at $\sqrt {1+x-y}\geq 0$ $cos(x,y)$ is continuous at $R^{2}$, and the square root of the function does not exist at $R$ when it contains a negative value. Square both sides to obtain inequality to represent the domain. $ {1+x-y}\geq 0$ Hence, the function $f(x,y)=cos\sqrt {1+x-y}$ is continuous on ${(x,y)| {1+x-y}\geq 0}$.
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