MAC 2313 Midterm: MAC 2313 FIU Exam f15fk
15 Feb 2019
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Then nd the work done moving a particle on an arbitrary smooth curve c from p (1, 1) to q(0, 0). 4a) [5 points] find the mass of the lamina in the rst quadrant of the xy-plane, bounded by the axes and x2 + y2 = a2, with density = xy. 4b) [6 points] find the center of gravity of . 5a) [6 points] compute the jacobian (x,y) coordinates. Use the de nition from ch. 14. 7, and show all your work. (r, ) for the transformation from polar to rectangular. (x,y) for the transformation from rectangular to polar coordinates. You can answer in terms of x, y or in terms of r, , whichever is easier. If d is an closed set in r2 then every point of d is an interior point of d. If f is an inverse-square eld on r, not containing the origin, then divf = 0 on r.
