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PracExam1 - Math 32b Practice rst hour exam 1 Sketch the...

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Math 32b Practice first hour exam. 1. Sketch the region of integration, and then reverse the order of integra- tion. 1 0 x x 2 f ( x, y ) dydx 2. Suppose that E is the ball of radius R and center at the origin and f ( x, y, z ) is a function defined on E. Write the following as a multiple integral: E f ( x, y, z ) dV. 3. A thin plate covers the region bunded by the X axis and the lines x = 1 and y = 2 x . The density at ( x, y ) is given by μ ( x, y ) = 6 x + 6 u + 6 . Find the mass and center of gravity of the plate. 4. Calculate 1 - 1 1 - x 2 0 ( x 2 + y 2 ) 3 / 2 dydx. 5. Use the formula
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