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Unformatted text preview: Exam 2, MA 162, Fall 2008 Name in capitals
Lectumr’s name in capitals Time of lecture Recitation Instructor’s name in capitals Time of recitation class 1. On the scantron, ﬁll in the requested information, most especially,
your name, section and division number and your student ID number. 2. On this cover sheet of your exam booklet, ﬁll in your name, your
lecturer’s name, the time of your lecture. Then ﬁll in your recitation
instructor’s name and the time of your recitation meeting. 3. There are 12 questions, each worth 8 points. The remaining 4 points
are free. 4. Show all your work. . No calculators are allowed. were 31> 41A 3% 6C3
7?) 6c QC lag MB DA 1. Compute ﬂ} A. 1113—an
B. 1115—an ‘ C. 21n3 —1n2
D. 1115—21112
E. 21112—1113 ' . . . . . —4
2. Find the partlal fractlon decompos1t10n of the funct10n A. 3—5114
B. 5+???
0. 3+fﬁ
D. ﬂiﬁ 2 13—1
E. x + T” +4 3. Which trigonometric integral arises when one computes f A. f2sec6tan6d6l
B. f2tan6ld6 C. f2sin6d6l, D. fsec0d6 E. f2sec2 0d€ 4. Use the rDrapezoidal Rule with n = 3 to compute the approximate value of 12% xzdx. ' F11 .U .0 P0 ?>
MID oolox glen coloa 5"] 5. Compute I12 6. Which statement about ffo 520115 is true? +
A. The integral diverges, by comparison with I100 %
B. The integral converges, by comparison with I100 d—f
C. The integral converges, by comparison with If” g
D. The integral diverges, by comparison with ffo g? E. None of the above statements is true. 7. Which integral represents the area of the surface obtained by revolving
the curve y = Zﬁ from (0,0) to (1, 2) about the :c—axis? A. f01 27n/a:+—4d:c
B. f0147r\/_$+—1d:c
C. f01 277mm:
D. f6? 477de
E. jg 2wmdm 1/3~
8. Compute the length of y = §(1 + $)3/2 from (0,2!) to (2, A. (8 — zﬁ)/3
B. 2 — «37 C. (16 — NW3
D. 3J3 — N?
E. 3¢§ — 3J5 9. Three objects of mass 3 grams, 2 grams and 1 gram are placed at (2, 2),
(l, l) and (2, 4) respectively. Where is the centroid of the system of three
objects? DON
VV $50.50?
8 MW cum cola" who tow:
N)
V wlm
v 10. Given that the plane region deﬁned by O < y < 1 + m2 and —l < a: < 1
has area equal to 8/3, its centroid is at n2—2n~12). 11. Evaluate limnqoo (n —— n A. 0
B. 2
C —4
D. 42 E. The limit does not exist 12. Evaluate limzHOG 13$).
A. 0
B. 1
C. 1n4
5
D. 1111 E. The limit does not exist. ...
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 Fall '08
 Gabriel
 Math, Limit, integral converges, integral diverges, trigonometric integral arises

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