   Chapter 14.2, Problem 7E

Chapter
Section
Textbook Problem

Find the limit if it exists, or show that the limit does not exist.7. lim ( x , y ) → ( π , π / 2 ) y sin ( x − y )

To determine

To find: The limit of the function lim(x,y)(π,π2)ysin(xy) if exist; otherwise show that the limit does not exist.

Explanation

Notice that the function (xy) is polynomial function.

Since every polynomial function is continuous, the function (xy) is continuous.

It is known that sine function is continuous and hence the given composition function ysin(xy) is also continuous.

As the given function is continuous, substitute x=π and y=π2 directly in the given function and obtain the required limit

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