162E1-F2008

162E1-F2008 - MA 162 Exam 1 September 2008 1. The distance...

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Unformatted text preview: MA 162 Exam 1 September 2008 1. The distance between the points (2, 1, 4) and (1,2,2) is A. 2 B. 4 C. «‘5 D. «2—1 — 3 E. 12 2. The radius of the sphere m2 + y2 + 22 + 2x —— y = 1 is A. 1/2 B. 1 C. 3/2 D. 2 E. 5/2 MA 162 Exam 1 September 2008 3. A bug is doing 2 meters / min along the diagonal of a terrarium, indicated in the figure in overview. The terrarium is mounted on a cart going at 6 meters/min, again as indicated below. The speed of the bug relative to the ground is, in meter/ min A.\/2—8 13- 5. Cart C. «3—7 ‘ v—é D' m 600 E. 4 4. (i’+3+12')-(f— 23’— 212) = A. 2 B. 1 C. 0 D. —1 E. —3 MA 162 Exam 1 5. Which is true? For vectors 5, I; I 5 x I; is a vector; II 5 X I; is a real number; III 5 x IV 5x _; = (I if 5 and I; are perpendicular; = (I if 3 and l; are parallel. Only I Only II Only I and III Only I and IV Only II and III HPQF’? 6. The f—component of (13+?) x (I+§— is A. —1 ' B. 0 C. 1 D. 2 E.-——3 September 2008 MA 162 Exam 1 September 2008 7. The curves 3/ = $3 ——2:c and y = x2 intersect at three points: («1,1), (0, 0), and (2, 4). Find the area of the region in the 2nd quadrant that is enclosed by the curves. A. 5/12 7/4 . 4/7 5/2 2/3 recaps 8. The base of a solid is the region in the xy plane bounded by the curve 3; = a: — m2 and the m—axis. If cross sections perpendicular to the arc—axis are squares, the volume of the solid is 2 \ A. / (ac—1:2)2dzc o 1 B. / (cc—11:2)xdx o 1 C. / (w—x2)2xd:c o 1 D. / (x—x2)2dw o 11 —(x—x2)2d$ 0 2 MA 162 Exam 1 September 2008 9. Let D be the region in the xy plane given by the inequalities 0 g y, y S :1: — 1 and :1; g 2. The volume of the solid obtained by revolving D about the y axis is 2 A. / 7r(a:——1)2dar: 1 2 B. / 27r-(ar——1)2d:z: 1 2 C. / (213:2 —27rx)d:c 1 2 D. / (7ra:2—7r$)da: . 1 2 E. / (27rx2—27rzc)d$ 0 10. A 5—lb cable is 10 feet long and hangs vertically from the top of a 30 ft tall wall. How much work is required to lift the cable to the top of the wall? A. 25 ft-lb B. 50 ft-lb C. 25/2 ft-lb D. 40 ft-lb E. 20 ft—lb MA 162 Exam 1 September 2008 11. If f satisfies 0 S f g a: for 1 _<_ :1: g 3, what is the maximum possible value of the average of f on [1,3]? A.2 B3 0.4 D.6 E.8 1r/2 12. / 23: cos mdw = o A. 27r~1 B. 7r—1 C. 7r—2 D. 7r+1 E. 21r+1 MA 162 Exam 1 September 2008 1r/2 13. / sin3 a: 0033 xdzz: = 0 A. 5/12 B. 1/12 0. 2/15 D. 4/15 E. 1/24 14. Which of the following integrals arises after making a trigonometric substitutioh to 2 9; d2: V4 —— 1:2 A. /4tan29sec0d0 -2 1i/Zsm Ode ? compute cos 0 2 C. /4ta,n Ode sec 0 D. f 4st 0cost9d6 E. f 4st 9d0 ...
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162E1-F2008 - MA 162 Exam 1 September 2008 1. The distance...

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