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Chapter 13: Q 6 (page 1065)
For what values of in the spherical coordinate
system is the graph not a cone?
The required answer isnot a cone.
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Explain why it would be difficult to evaluate the double integrals in Exercises 18 and 19 as iterated integrals.
In Exercises 57鈥�60, let R be the rectangular solid defined by
R = {(x, y, z) | 0 鈮� x 鈮� 4, 0 鈮� y 鈮� 3, 0 鈮� z 鈮� 2}.
Assume that the density at each point in Ris proportional to the distance of the point from the xy-plane.
(a) Without using calculus, explain why the x- and y-coordinates of the center of mass are respectively.
(b) Use an appropriate integral expression to find the z-coordinate of the center of mass.
Evaluate the sums in Exercises .
Evaluate the sums in Exercises .
In Exercises 61鈥�64, let R be the rectangular solid defined by
Assume that the density of R is uniform throughout.
(a) Without using calculus, explain why the center of
mass is
(b) Verify that is the center of mass by using the appropriate integral expressions.
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