Math 242, Fall 2013, Assignment 10

Mathematical proofs, like diamonds, are hard as well as clear, and will be touched with nothing but strict reasoning.

- John Locke, Second Reply to the Bishop of Worcester

Carefully state the following theorems (you need not prove them):

1. Properties of double integrals (equations (6)-(11) on pp. 849-850).
2. Evaluation of double integrals in polar coordinates ((2) on p. 854).
3. Formula for center of mass of a planar lamina ((5) on p. 860).

Solve the following problems:

1. Section 12.3, problems 1, 7, 15, 21, 41, 45, and 47.
2. Section 12.4, problems 5, 7, 11, and 27.
3. Section 12.5, problems 3 and 7.

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