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A2 - 5 Find a function f R 2 → R such that f x(0 0 and f...

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Math 237 Assignment 2 Due: Friday, Sept 26th 1. Determine if f is continuous at (0 , 0) where f ( x, y ) = sin( xy ) ln( x 2 + y 2 +1) if ( x, y ) = (0 , 0) 0 if ( x, y ) = (0 , 0) . 2. Determine where the function f ( x, y ) = x 2 - y 2 is continuous. Justify your answer. 3. Find the partial derivatives of: a) f ( x, y ) = x 2 + 3 xy 2 - y - 2 . b) g ( x, y, z ) = ze xy sin y - 3 x . 4. Let f ( x, y ) = x 3 - y 3 x 2 + y 2 , if ( x, y ) = (0 , 0) 0 if ( x, y ) = (0 , 0) . . a) Find f x (0 , 0) and f y (0 , 0). b) Determine where
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Unformatted text preview: 5. Find a function f : R 2 → R such that f x (0 , 0) and f y (0 , 0) both exist but f is not continuous at (0 , 0). 6. Find the equation of the tangent plane to z = p x 2 + y 2 at the point (1 , 2 , √ 5). 7. Use the linear approximation to approximate ln ( 1 . 05 · (0 . 9) 2 ) ....
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