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

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Math 237 Tutorial 2 Problems 1: Let f ( x, y ) = e xy 2 + x 2 + y 2 + | x | . Determine the first and second partial derivatives of f . 2: Let f : R 2 R be defined by f ( x, y ) = xy 2 x 2 + y 2 ( x, y ) = (0 , 0) 0 ( x, y ) = (0 , 0) . a) Determine ∂f ∂x at ( x, y ) = (0 , 0). b) Determine ∂f ∂x (0 , 0) and ∂f ∂y (0 , 0). c) Determine if ∂f ∂x is continuous at (0 , 0). 3: Let f ( x, y ) = | y ( x - 1) | . Determine whether
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