Explanation Given information: f ( x , y ) = 2 x 2 + 3 y 2 x y Calculation: We will calculate limit of the function by setting y = m x as follows, Substituting y = m x in f ( x , y ) = 2 x 2 + 3 y 2 x y we get, f ( x , m x ) = 2 x 2 + 3 y 2 x y = 2 x 2 + 3 ( m x ) 2 x ( m x ) = 2 x 2 + 3 m 2 x 2 m x 2 = x 2 ( 2 + 3 m 2 ) m x 2 = 2 + 3 m 2 m Now we will find the limit o

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ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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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 16E

To determine

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the limit of f(x,y) depend on m, and therefore the limit lim(x,y)→(0,0)f(x,y) does not exist.

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Chapter 14.2, Problem 15E

Chapter 14.2, Problem 17E

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Toshow: the limit of f ( x , y ) depend on m , and therefore the limit lim ( x , y ) → ( 0 , 0 ) f ( x , y ) does not exist.

Solution Summary: The author explains that the limit of f(x,y) depend on m, and thus the function limit does not exist.

Concept explainers

Toshow:

the limit of f(x,y) depend on m, and therefore the limit lim(x,y)→(0,0)f(x,y) does not exist.

Want to see the full answer?

Chapter 14 Solutions

Toshow: the limit of f ( x , y ) depend on m , and therefore the limit lim ( x , y ) → ( 0 , 0 ) f ( x , y ) does not exist.

Solution Summary: The author explains that the limit of f(x,y) depend on m, and thus the function limit does not exist.

Concept explainers

Toshow: the limit of f(x,y) depend on m, and therefore the limit lim(x,y)→(0,0)f(x,y) does not exist.

Want to see the full answer?

Chapter 14 Solutions

Toshow:

the limit of f(x,y) depend on m, and therefore the limit lim(x,y)→(0,0)f(x,y) does not exist.