MA 227 Final: 3-11s-Final exam
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~f (x, y) = (ey y sin x)~i + (xey + cos x)~j is a conservative vector eld, and if yes, nd a potential function f for it. 2: use green"s theorem to evaluate rc. Compute its mass and the center of mass. 4: the solid b lies inside the cylinder x2+y2 = 1 and inside the sphere x2+y2+z2 , calculate its volume, evaluate the integral by reversing the order of integration. )dydx: find the minimum and maximum values of the function f (x, y, z) = 5y(x + z) subject to the constraints xy = 1 and y2 + z2 = 3. 8: we know that x, y, and z are positive numbers the sum of which is equal to 1. Maximize the value of xyz4: find the points on the ellipsoid 4x2 +y2 +z2 = 1 where the normal line is parallel to the line connecting the points (2, 1, 2) and (3, 0, 1).
