(a) Assume that f(x, y, z) and F(x, y, z) are arbitrary differentiable functions such that f(x, y, z)= 0 and F(x, y, z) = 0. Prove that dy af OF дх' дz af a OF Of дх' дz OF Of dx əy Əz ду' дz (b) Let D be a circular domain of radius R with center at the origin. Show that !! sin(x² + y²), (x² + y²)³ dr dy is convergent. D (c) Consider the following integral I = [[(x + xy - x² - y²) dA, D where D is a rectangle with sides 0≤x≤ 1 and 0 ≤ y ≤ 2. Prove that -8

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