MAC 2313 Midterm: MAC 2313 FIU Exam f15k
15 Feb 2019
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Prof. s. hudson: find the centroid of the tetrahedron in the rst octant bounded by the coordinate planes and the plane x + y + z = 1, evaluate the surface integral. Zzs z2ds, where s is the portion of the cone z2 = x2 + y2 between the planes z = 1 and z = 2: [12 points] answer true or false for each part. The mass of a two-dimensional lamina is the product of its area and its density at its centroid. The ux of an inverse-square eld across the surface of any cube in r3 is zero. F(x, y) = hxy2, x2yi is conservative on r2. Lagrange multipliers are used to solve optimization problems. If f is a vector eld and f = , then is a potential function for f. 4a) find a unit vector in the direction in which f (x, y) = y3e2x decreases most rapidly at.
