Explanation Given information: The given function f ( x , y ) is continuous at ( 0 , 0 ) where, f ( x , y ) = sin ( x 2 + y 2 ) x 2 + y 2 for ( x , y ) ≠ 0 Calculation: Since, the function f ( x , y ) is continuous at ( 0 , 0 ) which is given in statement. Therefore, evaluating limit of function at ( 0 , 0 ) by plugging polar co-ordinates x = r cos ( θ ) and y = r sin ( θ ) , so that x 2 + y 2 = r 2 and r → 0 . lim ( x , y ) → ( 0 , 0 ) ( sin ( x 2 + y 2 ) x 2 + y 2 ) = lim r → 0 ( sin ( r 2 cos 2 ( θ ) + r 2 sin 2 ( θ ) ) r 2 cos 2 ( θ ) + r 2 sin 2 ( θ ) ) = lim r → 0 ( sin [ r 2 ( cos 2 ( θ ) + sin 2 ( θ ) ) ] r 2 [ cos 2 ( θ ) + sin 2 ( θ ) ] ) = lim r → 0 ( sin [ r 2 ( 1 ) ] r 2 [ 1 ] ) = lim r → 0 ( sin ( r 2 ) r 2 ) .....

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 11.2, Problem 42PS

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Tofind:For what value of f(0,0) is the function f(x,y) continuous at (0,0) , where

f(x,y)=sin(x2+y2)x2+y2for (x,y)≠0

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Chapter 11.2, Problem 41PS

Chapter 11.2, Problem 43PS

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Chapter 11 Solutions

Student's Solution and Survival Manual for Calculus

Ch. 11.1 - Prob. 1PS Ch. 11.1 - Prob. 2PS Ch. 11.1 - Prob. 3PS Ch. 11.1 - Prob. 4PS Ch. 11.1 - Prob. 5PS Ch. 11.1 - Prob. 6PS Ch. 11.1 - Prob. 7PS Ch. 11.1 - Prob. 8PS Ch. 11.1 - Prob. 9PS Ch. 11.1 - Prob. 10PS

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Tofind: For what value of f ( 0 , 0 ) is the function f ( x , y ) continuous at ( 0 , 0 ) , where f ( x , y ) = sin ( x 2 + y 2 ) x 2 + y 2 for ( x , y ) ≠ 0

Solution Summary: The author explains that the function f(x,y) is continuous at 0,0 right, and evaluates its limit by plugging polar co-ordinates.

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Tofind:For what value of f(0,0) is the function f(x,y) continuous at (0,0) , where

f(x,y)=sin(x2+y2)x2+y2for (x,y)≠0

Want to see the full answer?

Chapter 11 Solutions

Tofind: For what value of f ( 0 , 0 ) is the function f ( x , y ) continuous at ( 0 , 0 ) , where f ( x , y ) = sin ( x 2 + y 2 ) x 2 + y 2 for ( x , y ) ≠ 0

Solution Summary: The author explains that the function f(x,y) is continuous at 0,0 right, and evaluates its limit by plugging polar co-ordinates.

Videos

Tofind:For what value of f(0,0) is the function f(x,y) continuous at (0,0) , where f(x,y)=sin(x2+y2)x2+y2for (x,y)≠0

Want to see the full answer?

Chapter 11 Solutions

Tofind:For what value of f(0,0) is the function f(x,y) continuous at (0,0) , where

f(x,y)=sin(x2+y2)x2+y2for (x,y)≠0