Calculus 8th Edition

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

Chapter 14 - Partial Derivatives - 14.2 Limits and Continuity - 14.2 Exercises: 30

Answer

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

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 $\sqrt {1+x-y}\geq 0$ Since, $cos(x,y)$ is continuous at $R^{2}$ and square root of the function does not exist at $R$ when it contains non-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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