   Chapter 14.2, Problem 14E

Chapter
Section
Textbook Problem

Find the limit if it exists, or show that the limit does not exist.14. lim ( x , y ) → ( 0 , 0 ) x 3 − y 3 x 2 + x y + y 2

To determine

To find: The limit of the function lim(x,y)(0,0)(x3y3x2+xy+y2) if exist; otherwise show that the limit does not exist.

Explanation

Notice that the given function is rational function where numerator and the denominator is a polynomial function.

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

As the given function is continuous, substitute x = 0 and y = 0 directly in the given function and obtain the required limit

lim(x,y)(0,0)(x3y3x2+xy+y2)=lim(x,y)(

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