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Math 226 SI Midterm 2 Review

# Math 226 SI Midterm 2 Review - Math 226 SI Professor...

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Math 226 SI Professor Mancera SI Leader: Lauren Haas Math 226 SI Midterm #2 Review 11.8-13.2 1. Find the maximum and minimum value of the equation ( ) subject to the constraint 2. Evaluate the following double integral by reversing the order of integration: ∫ ∫ 3. Given the following region: the region above the half circle with and below the surface a. Set up a double integral in xy-coordinates to find the volume of this region, but do not evaluate. b. Evaluate the volume of this region using polar coordinates.

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4. Convert the following integral to cylindrical coordinates and then evaluate: ∫ ∫ 5. Calculate the volume below the spherical surface ( ) and above the conical surface . 6. Consider the tetrahedron with corners at (0; 0; 0), (a; a; 0), (0; a; 0), and (0; 0; a), with density: ( ) ( ) where is a constant. Calculate the total mass m . 7. Compute the Jacobian for the following change of variables :
8. a. Evaluate the line integral where C is the counterclockwise oriented triangle

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