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tut4 - ∂ 2 f ∂x∂y State any assumptions you needed to...

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Math 237 Tutorial 4 Problems 1: Determine all points where the function is differentiable. a) f ( x, y ) = | x | + | y | . b) h ( x, y ) = x 2 / 3 y 4 / 3 x 2 + y 2 if ( x, y ) = (0 , 0) 0 if ( x, y ) = (0 , 0) . 2: Let f ( x, y ) = x 2 sin( xy 2 ) and x = x ( s, t ) = e st and y = y ( s, t ) = ( s + 2 t ) 2 . Define g ( s, t ) = f ( x ( s, t ) , y ( s, t ). Find g s and g t in terms of x , y , s and t . 3: Let g : R R and let f ( x, y ) = g ( u 2 v ), where u = e x and v = x 2 + y 3 . Use the chain rule to find
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Unformatted text preview: ∂ 2 f ∂x∂y . State any assumptions you needed to make. 4: Let g : R 2 → R where g has continuous second partial derivatives. Calculate f xy where f : R 2 → R is defined by f ( x, y ) = g ± x 2 y, x cos y ² ....
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