tut2 - Math 237 1: Let f (x, y ) = exy + of f . 2 Tutorial...

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Unformatted text preview: Math 237 1: Let f (x, y ) = exy + of f . 2 Tutorial 2 Problems x2 + y 2 + |x|. Determine the first and second partial derivatives 2: Let f : R → R be defined by f (x, y ) = a) Determine b) Determine ∂f ∂x 2 xy 2 x2 + y 2 0 (x, y ) = (0, 0) (x, y ) = (0, 0). at (x, y ) = (0, 0). and ∂f (0, 0). ∂y ∂f (0, 0) ∂x ∂f ∂x c) Determine if is continuous at (0, 0). ∂f (0, 0) ∂y ∂f (1, 0) ∂y 3: Let f (x, y ) = |y (x − 1)|. Determine whether and exist. 4: Let g : R → R be defined by g (x, y ) = (x, y ) = (0, 0) 0 (x, y ) = (0, 0). Prove that gx (0, 0) and gy (0, 0) exist, but g is not continuous at (0, 0). 2 x2 y , x4 + y 2 ...
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This note was uploaded on 01/27/2011 for the course MATH 237 taught by Professor Wolczuk during the Fall '08 term at Waterloo.

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