Question

1. Let f (x, y) = xy((x^2-y^2)/(x^2+y^2)) if, (x, y) 6= (0, 0), 0, if (x,...

1. Let f (x, y) =

xy((x^2-y^2)/(x^2+y^2)) if, (x, y) 6= (0, 0),

0, if (x, y) = (0, 0) (it's written as a piecewise function)

(a) Compute ∂f/∂y (0, 0) and ∂f/∂x (0, 0).

(b) Compute ∂f/∂y (x, 0) for all x, and ∂f/∂x (0, y) for all y

(c) Use part (a) and (b) to compute ∂^2f/∂y∂x (0, 0) and ∂^2f/ ∂x∂y (0, 0), then verify that:

∂^2f/∂y∂x (0, 0) does not equal ∂^f/ ∂x∂y (0, 0)

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