MATH 230 Final: Math 230 Final_SampleC
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Instructions: there are 12 problems on this exam for a total of 150 points. Some problems have multiple parts: please, show your work. December 13, 2004: (9 points) suppose the equation a) or b) or c) below holds for two vectors u and. December 13, 2004: (10 points) find parametric equations of the sphere centered at the point (1, 1, 0) with radius 1. 4. (a) (6 points) find all critical points of the function f (x, y) = x2 3y + y3. (b) (7 points) determine if they are points of local maximum, local minimum, or saddle points. December 13, 2004: (14 points) convert the triple integral. E x dv, where e is the solid region in space inside the cone z = x2 + y2 below the plane z = 4, into: (a) (7 points) a triple integral in cylindrical coordinates (do not evaluate. The integral); (b) (7 points) a triple integral in spherical coordinates (do not evaluate.
