   Chapter 14.2, Problem 43E

Chapter
Section
Textbook Problem

Graph and discuss the continuity of the function f ( x , y ) = { sin x y x y if  x y ≠ 0 1 if  x y = 0

To determine

To find: The given function f(x,y)=sinxyxy is continuous or discontinuous and then sketch the graph.

Explanation

The given function is, f(x,y)=sinxyxy .

Since every polynomial function is continuous on 2 expression xy is continuous when xy0 .

Also it is known that the sine function is continuous everywhere.

Thus, the given function f(x,y)=sinxyxy is continuous on 2 when xy0

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