a2 - g ( x,y ) such that g ( x,y ) is continuous at (0 ,...

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Math 237 Assignment 2 Due: Friday, Oct 1st 1. Let f ( x,y ) = ( x 4 - y 4 x 2 + y 2 if ( x,y ) 6 = (0 , 0) 0 if ( x,y ) = (0 , 0) . Determine all points where f is continuous. 2. Let f ( x,y ) = ( x 3 x 2 + y 2 if ( x,y ) 6 = (0 , 0) 0 if ( x,y ) = (0 , 0) . a) Determine all points where f ( x,y ) is continuous. b) Find f x (0 , 0) and f y (0 , 0). 3. Let f ( x,y ) = ( sin( xy ) ln( x 2 + y 2 +1) , if ( x,y ) 6 = (0 , 0) 0 if ( x,y ) = (0 , 0) . . a) Find f x (0 , 0) and f y (0 , 0). b) Determine if f is continuous at (0 , 0). c) Find a function
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Unformatted text preview: g ( x,y ) such that g ( x,y ) is continuous at (0 , 0), but g x (0 , 0) and g y (0 , 0) both do not exist. Justify your answer. 4. Find f x (0 , 0) and f y (0 , 0) for f ( x,y ) = ( x 3-y 3 x 2 + y 2 + 1 if ( x,y ) 6 = (0 , 0) 1 if ( x,y ) = (0 , 0) ....
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