   Chapter 14, Problem 9RE

Chapter
Section
Textbook Problem

Evaluate the limit or show that it does not exist.9. lim ( x , y ) → ( 1 , 1 ) 2 x y x 2 + 2 y 2

To determine

To find: The limit of the function lim(x,y)(1,1)(2xyx2+2y2) if exist; otherwise show that the limit does not exist.

Explanation

Notice that the given function is rational function.

Since every rational function is continuous, the given function is continuous.

As the given function is continuous, substitute x = 1 and y = 1 directly in the given function and obtain the required limit.

lim(x,y)(1,1)(2xyx2+2y2

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