7. Find the average value of the function f(x, y, z) = x2z + y2z over the region enclosed by the surface z = x2 + y2 and the plane z = 1. __(g)__

2. (10 分) Let C be a positively oriented, piecewise-smooth, simple closed curve in the plane and let D be the region bounded by C. If f(x, y) is a scalar function with continuous first and second partial derivatives in D, derive the following formula: ∬D ( fxx + fyy )dxdy =where = ∇f⋅N is the normal derivative, N is an outer unit normal, s is the arc-length.

7. Find the average value of the function f(x, y, z) = x²z + y²z over the region enclosed by the surface z = x² + y² and the plane z = 1. (g)

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