Explanation Given information: f ( x , y ) = x y ( x 2 + y 2 ) Calculation: We will calculate limit of the function along x axis as follows, lim y → 0 f ( x , 0 ) = lim y → 0 x y ( x 2 + y 2 ) = x ( 0 ) ( x 2 + 0 2 ) = 0 ( x 2 ) = 0 Now limit along y axis, lim x → 0 f ( 0 , y ) = lim x → 0 x y ( x 2 + y 2 ) = ( 0 ) y ( 0 2 + y 2 ) = 0 ( y 2 ) = 0 Hence form the above it is clear that the function approaches zero along x and y axis

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ISBN: 9781319308858

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 14E

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f(x,y) approaches zero along x and y axis and prove that lim(x,y)→(0,0)f(x,y) does not exist by showing that the limit along the line y=x is non zero.

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Chapter 14.2, Problem 13E

Chapter 14.2, Problem 15E

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Chapter 14 Solutions

CALCULUS:EARLY TRANS.(LL)-W/ACCESS

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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Toshow: f ( x , y ) approaches zero along x and y axis and prove that lim ( x , y ) → ( 0 , 0 ) f ( x , y ) does not exist by showing that the limit along the line y = x is non zero.

Solution Summary: The author explains that f(x,y) approaches zero along x and y axis, and proves that the limit of the functions is non zero.

Concept explainers

Toshow:

f(x,y) approaches zero along x and y axis and prove that lim(x,y)→(0,0)f(x,y) does not exist by showing that the limit along the line y=x is non zero.

Want to see the full answer?

Chapter 14 Solutions

Toshow: f ( x , y ) approaches zero along x and y axis and prove that lim ( x , y ) → ( 0 , 0 ) f ( x , y ) does not exist by showing that the limit along the line y = x is non zero.

Solution Summary: The author explains that f(x,y) approaches zero along x and y axis, and proves that the limit of the functions is non zero.

Concept explainers

Toshow: f(x,y) approaches zero along x and y axis and prove that lim(x,y)→(0,0)f(x,y) does not exist by showing that the limit along the line y=x is non zero.

Want to see the full answer?

Chapter 14 Solutions

Toshow:

f(x,y) approaches zero along x and y axis and prove that lim(x,y)→(0,0)f(x,y) does not exist by showing that the limit along the line y=x is non zero.