MATH 251 Midterm: MATH 251 TAMU 251-Spring 11 Exam 2 ans
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Sample exam 2 answers: d, b, a, d, e, c, c, you need to solve fx = y x2 = 0 and fy = x 2y = 0, and then you nd that (0, 0) 4 ) are the critical points of f . Use the second derivative test to nd that (0, 0) 2 , 1 and ( 1 is a saddle point and ( 1. 4 ) is a local maximum: (a) you intersect the two surfaces and nd that they are sitting above the disk x2+y2 (8 2x2 2y2) dy dx. Setting up the integral yields v = z 2. 2z (b) v = z 2 (8 2r2)r dr d . Changing the order of integration we nd that. This integral can be evaluated easily, and the answer is 17 p1 + y2. 2 : after looking at these two surfaces for a moment, you realize that the cone is above the paraboloid.
