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Scan0006 - Math 192 Second Prelim Thursday October28 7:30...

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Unformatted text preview: Math 192. Second Prelim, Thursday. October28. 7:30 — 9:00 PM Fall 2004 _ No calculators. An 8.5 x 11 inches sheet with information on both sides is allowed. Recommendations: Write your name and section number on the exam booka let. Carefully read every problem. If you don’t know how to solve a problem. _ move on. Draw accurate pictures and explain clearly each of your steps. Write neatly. .L- (a)(8 points) Find the point(s) of intersection of the following pair of curves in polar coordinates: ' r r _ (b)(8 points) Find the point(s) of intersection of the following pair of curves in polar coordinates:- 1 — c0309) cos (9) .- 5 sin(26). ﬁle | { r2 — 5cos(29) 2; (14 points) Find the critical points of f (3:. y) = 3:3 -——- 3m + 23:2 — y‘4 and classify them as local maxima, local minima or saddle points. i (20 points) The ellipsoid 3:2 ye 32 _ _ _ = 1 4 + 9 + 25 _ does not intersect the plane 153: — 1031+ 32: = 90. Find the point-on the ellipsoid closest to the plane and ﬁnd the point on the ellipsoid farthest from the plane. g (15 points) Find the mass of" the thin plate covering the region R between the curves y = V2 — 332, .y = x/l —— \$2 and y = 0 if the density is 6(zr,y) = em2+92._ Q: (15 points) Compute the volume of the region bounded by the following inequalities: ' 03 :1: £2 03 y swat—\$2 \$2+y2§ z 54 :14 _ gk—y, such thank-24. For what k: is the volume of R equal to 100? ...
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