(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 OF af dy af OF дх' дz ?х ' дz dx af aF OF Of ду' дz əy Əz (b) Let D be a circular domain of radius R with center at the origin. Show that ]] sin(x² + y²) + y²)³ dx dy is convergent. D (c) Consider the following integral I = ff (x- (x + xy - x² - y²) dA, where D is a rectangle with sides 0≤x≤ 1 and 0 ≤ y ≤ 2. Prove that -8 <1 < ²/3

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