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MAC2313_Test3_Spring2010

# MAC2313_Test3_Spring2010 - Page 1 of 4 MAC 2313 Test 3 Name...

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Page 1 of 4 MAC 2313 Name_________________________________ Test 3 Date: March 18, 2010 For full credit, clearly show all work that justifies your answer. 1. (8 points) Set up, but do not evaluate , a double integral that represents the volume of the solid in R 3 bounded by the cylinder 1 2 2 = + y x and the planes z = 8 and x + y + z = 2. Express your answer as an iterated integral. 2. (8 points) Set up, but do not evaluate , an expression that would give the x -coordinate of the center of mass of the lamina that occupies the region bounded by the graphs of x y = , y = 0, and x = 1, where the density function xy y x = ) , ( ρ . Express double integrals as iterated integral. 3. (8 points) Find the directional derivative of ) ln( ) , ( 3 2 y x y x f + = at P (2,1) in the direction of Q (-1,5).

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Page 2 of 4 4. (8 points) Determine the number of saddle points of 4 2 3 2 3 ) , ( y y x x y x f + = . 5.
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MAC2313_Test3_Spring2010 - Page 1 of 4 MAC 2313 Test 3 Name...

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