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Unformatted text preview: MA 166 Final Exam 01 Spring 2008 NAME 10—DIGIT PUID
REC. INSTR. _____.___—__ REC. TIME LECTURER INSTRUCTIONS: 1. There are 14 different test pages (including this cover page). Make sure you have a
complete test. 2. Fill in the above items in print. Also write your name at the top of pages 2—14. 3. Do any necessary work for each problem on the space provided or on the back of
the pages of this test booklet. Circle your answers in this test booklet. No partial
credit will be given, but if you show your work on the test booklet, it may be used in
borderline cases. 4. No books, notes, calculators or any electronic devices may be used on this exam. Each problem is worth 8 points. The maximum possible score is 200 points. 6. Using a £2 pencil, ﬁll in each of the following items on your answer sheet: (a) On the top left side, write your name (last name, ﬁrst name), and ﬁll in the little
circles. (b) On the bottom left side, under SECTION, write in your division and section
number and ﬁll in the little circles. (For example, for division 9 section 1, write
0901. For example, for division 38 section 1, write 3801). (c) On the bottom, under TEST/QUIZ NUMBER, write 01 and ﬁll in the little circles.
(d) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your 10—digit PUID, and ﬁll in the little circles. (e) Using a #2 pencil, put your answers to questions 1—25 on your answer sheet by
ﬁlling in the circle of the letter of your response. Double check that you have ﬁlled
in the circles you intended. If more than one circle is ﬁlled in for any question,
your response will be considered incorrect. Use a #2 pencil. 7. After you have ﬁnished the exam, hand in your answer sheet and your test booklet to
your recitation instructor. 9“ 3‘ 00 mm 00 (—1)” 2 +1
. __ — ' _ n
e —E n!,$l<oo Slnx—E ——(2n+1)!a§ ,m<oo
00 00
(__1)n 2n 1
cos : , < = n
”3 2:0 (2n)! “3 ""3‘ 00 1—a: we“: "93’ < 1 MA 166 Final Exam 01 Spring 2008 Name: Page 2/14 1. Find a vector that has the direction opposite of 2i — 4j + 5k but has length x/S. A. B. V5 \6 V5
£4__i_£* «5 «5" «s
2\/E_4\/5. 5_f§k
«1‘1 «If m
_2~/5+4_ﬁj_§ﬁk
m m m
2 4, 5 ‘3‘ $35k 2 For what values of b are the vectors < —2, b, l > and < 3, b, —b > orthogonal? A. =L3
B.b=—a2
C.b=—z3
D.b=L2 E. b=2,3 MA 166 Final Exam 01 Spring 2008 Name: ______ Page 3/14 3. Find the area of the parallelogram with vertices A(1, 1), B (3, 4), C(7, 5) and D(5, 2). A. 11
B. 13
C. 10
D. 12
E. 9
4. Find the area of the region bounded by y = m2 and y = 2m — $2.
11
A. —
3
10
B. —
3
16
C. —
3
l
D. —
3
4
E. —
3 MA 166 Final Exam 01 Spring 2008 Name: —_ Page 4/14 5. Find the volume of the solid obtained by rotating the region bounded by y : m2 and
y = 4a: — 1:2 about the (II—axis. A. 1—3171'
B. 13—07r
C. l3—6—7r
D. §7r
E. §7r 6. It took 2700 J of work to stretch a spring from its natural length of 2m to a length
of 5m. Find the spring’s force constant. 150
800
73—
400
1400
T
600 snow.» MA 166 Final Exam 01 Spring 2008 Name: —— Page 5/14 e
7. Evaluate / 1n_22: dx.
1 .73
1—63
A.
263
3—364
B. e4
C. 6—2
e
62—2
D. e2
4—3e3
E. e3
37r/4 3
8. Evaluate / (:98 6 d6.
7T/2 sm6
3 l
A. ———
4 2ln2
l 3
B. ~12——
2 n 4
C. —l
l l
D. ———
4 2ln2
l l
E. —1 ——
2 n2 4 MA 166 Final Exam 01 Spring 2008 Name: —_— Page 6/14 dt
x/t2 — 4t + 13 5
9. A trigonometric substitution can be used to convert the deﬁnite integral /
2 into which of the following deﬁnite integrals? 7r/4 A. / sec6d0
0
7r/4 B. / cos6d0
0
77/3 C. / sin6d0
0
7r/3 D. / cos6d6
0 7r/3
E. / sec0 d6
0 10. Compute /02 % dos.
A. —81n3
B. —5 ln3
C. —3 ln3
D. —2ln3 E. —ln3 MA 166 Final Exam 01 Spring 2008 Name: —_ Page 7/14 00 1 n
11. Find whether the series :3 (—5) converges or diverges, and ﬁnd its sum if it
converges. ”:1
A. Diverges.
B. Converges and sum 2 O
C. Converges and sum = 2
D. Converges and sum = —1
E. Converges and sum = —3
12. Which of these improper integrals converge?
3
I. / 1 dm.
0 1‘ “‘ 2
II /3 1 dm
‘ o m '
°° 1
III. / — dac.
3 \/E
A. All
B. Only (I)
C. Only (II)
D. Only (III)
E. (I) and (II) MA 166 Final Exam 01 Spring 2008 Name: —____ Page 8/14 13. The curve y = 2:2 + 1, O S a: S 2, is rotated about the x—axis. The area of the surface
is given by 2
A. / 27r(m2 + 1)\/1 +4232 den
0
2
B. / 27rccx/ 1 + 4202 dcc
o
2
C. / «(:02 + 1)2 dcc
o 2
D. / 27rcc(cc2 + 1) dcc
o 2
E. /(cc2+1)dcc
. 0 14. Consider the lamina bounded by the graph of y = ﬂ, the cc—axis and the line so = 4,
with density p = 1. The cc—coordinate if of the center of mass of the lamina is A. 1
B.
C.
D. 2 3 E 2
12
E. —
5 MA 166 Final Exam 01 Spring 2008 Name: —__ Page 9/14 n! 15. Let aznliﬂrrolo ne‘” and b=nlingo (2—75? Then
A. a=1andb=%
B. a=0andb=%
C. a=landb=0
D. a=0andb=O
E. a=e*1andb=0 tan“1 l+n2 n.
IS 16. The series Z(—l)”
n20 A. absolutely convergent B. conditionally convergent tan‘1 n
C. d've ent since lim —1 n
1 1‘3 n—roo ( ) 1+n2 7&0 —1 D. divergent even though lim (—1)”tan n nqoo 1+n2 :0 E. divergent by the ratio test MA 166 Final Exam 01 Spring 2008 Name: __—__ Page 10/14 17. Which of the following series converge? A. (III) only B. (III) and (IV) only C. All D. (I), (III) and (IV) only
E. (II), (III) and (IV) only 18. Use a Maclaurin series and the Estimation Theorem for alternating series to approxi mate sin <%) using the fewest number of terms necessary so that the error is less than
0.001.
1
A. 5
23
B. —
48
3
C. —
4
33
D. 40
E_ 4_1 MA 166 Final Exam 01 Spring 2008 Name: 00
271
19. Consider the power series 2 Was”. The radius of convergence R and the interval of 71:1
convergence of this series are 00 20. The interval of convergence for the series 2
71:1 10"
W Page 11/14 (15—1)” is
A. (0,2)
B. [0,2)
0. (9,11)
D. [9,11) E. (—00, oo) MA 166 Final Exam 01 Spring 2008 Name: —_—_ Page 12/14 21. In the Taylor series expansion for f(x) = : : ; about a = 1, the coefﬁcient of (a:—1)10
1s
A. —2
B. —l
C. 0
D. 1
E. 2 4
cos($2) — 1 + $— 22. Evaluate lim —8——2.
:r——>O IL‘ A. .1.
2
1 B. —
8
1 C. —
6 D. —1
120 E. i 24 MA 166 Final Exam 01 Spring 2008 Name: Page 13/14 23. Find the slope of the tangent line to the curve described by a: = In t, y = 1 + t2 at 1521. mucwe
‘coo
H wll—‘N 24. A point P has Cartesian coordinates (13,11) 2 (3, —3\/§). Which of the following gives
polar coordinates of P? MA 166 Final Exam 01 Spring 2008 Name: —— Page 14/14 25. Identify the curve r2 = 'rtan(0) sec(0) by ﬁnding the Cartesian equation for it. A. ellipse B. line C. circle D. parabola E. hyperbola ...
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