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Find the average value of F(x, y, z) over the given region.F(x, y, z) = xyz over the rectangular solid in the first octant bounded by the coordinate planes and the planes x = 6, y = 4, z = 3. 

Find the average value of the function f over the given region.; R = {(x, y): 1 ≤ x ≤ 5, 1 ≤ y ≤ 5}

Find the average value of the function f over the given region.; R = {(x, y): 1 ≤ x ≤ 2, 1 ≤ y ≤ 2}

Find the volume by using polar coordinates.The region bounded by the paraboloid z = x2 + y2, the cylinder x2 + y2 = 25, and the xy-plane.

Sketch g(D) from the description of D and change of variables  (x, y) = g(u, v). x = 3u, y =v where D is the rectangle 0 ≤ u ≤ 2, 1 ≤ v ≤ 4

Which is NOT a main argument of the article?

According to Ojha, we should not let Barbie’s flaws deter us from finding her constructive lessons.

Find the value.If , find

Find the linearization of the function at the given point.

Solve the problem.Evaluate  at t = 3π for the function w(x, y) = x2 – y2 – 9x; x = cost, y = sin t.