MATH 0240 Midterm: MATH 240 Midterm 2-67
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All work must be shown in order to get credit. Please write legibly and explain your logic by words whenever appropriate. If more space is needed, write on the back of the pages and/or ask for more paper. Find the center of mass of the lamina in the shape of the circle x2 + y2 4 and the density (x, y) = y + 2. Evaluate the triple integral of f (x, y, z) = z3 + 1 over the solid bounded by the surfaces y = 2x2 + 2z2 and y = x2 + z2 + 1. Find and classify all critical points of the function f (x, y) = ex y ey. Evaluate the integral of the function f (x, y, z) = z 1 over the ball x2 + y2 + z2 4. Use the transformation x = v u, y = v to change the variables in the integral f (x, y) da,
