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 pointon 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 thank24. For what k: is the volume of R equal to 100? ...
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 Fall '06
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