   Chapter 14, Problem 11RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f(x, y) = sin x + sin y, then − 2 ≤ D u f ( x , y ) ≤ 2 .

To determine

Whether the statement, “If f(x,y)=sinx+siny , then 2Duf(x,y)2 ” is true or false.

Explanation

Compute the value of f(x,y) is as follows.

f(x,y)=fx,fy=fx(sinx+siny),fy(sinx+siny)=(cosx+0),(0+cosy)=cosx,cosy

Thus, the value of f(x,y) is cosx,cosy .

Obtain |Duf(x,y,z)| as follows

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