The accompanying figure on the next page shows the solidthat is bounded above by the

Chapter 14, Problem 32

(choose chapter or problem)

The accompanying figure on the next page shows the solidthat is bounded above by the surface z = 1/(x2 + y2 + 1),below by the xy-plane, and laterally by the surface x2 +y2 = a2.(a) By symmetry, the centroid of the solid lies on the zaxis.Make a conjecture about the behavior of the zcoordinateof the centroid as a0+ and as a+.(b) Find the z-coordinate of the centroid, and check yourconjecture by calculating the appropriate limits.(c) Use a graphing utility to plot the z-coordinate of the centroidversus a, and use the graph to estimate the valueof a for which the centroid is (0, 0, 0.25).