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 = 2 and y = −1 directly in the given function and obtain the required limit. lim ( x , y ) → ( 2 , − 1 ) ( x 2 y + x y 2 x 2 − y 2 ) = ( 2 ) 2 ( − 1 ) + ( 2 ) ( − 1 )

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ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0…

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Chapter 14.2, Problem 6E

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To find: The limit of the function lim(x,y)→(2,−1)(x2y+xy2x2−y2) if exist; otherwise show that the limit does not exist.

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Chapter 14.2, Problem 5E

Chapter 14.2, Problem 7E

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Chapter 14 Solutions

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The limit of the function lim ( x , y ) → ( 2 , − 1 ) ( x 2 y + x y 2 x 2 − y 2 ) if exist; otherwise show that the limit does not exist.

Solution Summary: The author explains that the given function is a rational function, and that it is continuous. Substitute x = 2 and y = 1 to obtain the required limit.

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To find: The limit of the function lim(x,y)→(2,−1)(x2y+xy2x2−y2) if exist; otherwise show that the limit does not exist.

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Chapter 14 Solutions