   Chapter 14, Problem 3RCC

Chapter
Section
Textbook Problem

What does lim ( x , y ) → ( a , b ) f ( x , y ) = L mean? How can you show that such a limit does not exist?

To determine

To describe: The meaning of lim(x,y)(a,b)f(x,y)=L . How it can be shown if the limit does not exist.

Explanation

Consider the function , f(x,y) .

Let the domain of the function f(x,y) be D .

Consider the arbitrary point (a,b) .

Now xandy approaches the point (a,b)

That is, x approaches a along the path C1 , y approaches b along the path C2 .

If f(x,y) approaches the certain point L as (x,y) approaches (a,b) then, f(x,y) has the limit L .

That is, lim(x,y)(a,b)f(x,y)=L

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