# A2w - f R 2 → R such that f x(0 0 and f y(0 0 both exist...

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Math 237 Assignment 2 Due: Friday, Jan 23rd 1. Determine if f ( x, y ) = ± x 4 - y 4 x 2 + y 2 if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) . is continuous at (0 , 0). 2. Determine where the function f ( x, y ) = p x 2 - y 2 is continuous. Justify your answer. 3. Find the partial derivatives of: a) f ( x, y ) = arcsin( x 2 ) + x 3 y 2 - 1 y . b) g ( x, y, z ) = z tan( xyz ) - 3 xy + xz 3 . 4. Let f ( x, y ) = ± x 3 - y 3 x 2 + y 2 , 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 where f is continuous. 5. Find a function
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Unformatted text preview: 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). Justify your answer. 6. Find the equation of the tangent plane to z = p x 2-y 2 +1 at the point (2 ,-1 , √ 3+1). 7. Use the linear approximation to approximate arctan ( . 95 · (1 . 01) 2 )-π 4 ....
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