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# FinRev - Math 32B Calculus of Several Variables Final Exam...

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Math 32B - Calculus of Several Variables Final Exam - Practice Problems Disclaimer :- The choice of problems was entirely my own. I have no knowledge of what will appear on the midterm, nor how the exam will be structured. These questions are designed to cover what I think are some of the important parts of the course so far, but I do not claim that they cover everything you may be asked in the midterm. Finally, any mistakes are my own entirely. Problem 1 Evaluate the double integral 20 0 10 1 2 y e - x 2 dx dy . Problem 2 A solid sphere of radius 10 has an ellipsoid cut out of its middle. The ellipsoid has radii (distance from the origin) of 2, 3, and 6 in the x , y and z directions respectively. If the density at the point ( x, y, z ) is z 2 , find the mass of the resulting solid. Problem 3 A homogeneous solid of density 1 is bounded by the surfaces x = 1, y = x 2 , y + z = 1 and z - y = 1. Represent the mass of the solid as a triple integral, and write down the iterated integrals for all six possible orders of integration. Then choose one and compute the mass.

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FinRev - Math 32B Calculus of Several Variables Final Exam...

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