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Unformatted text preview: MA 162 FINAL EXAM Fall 2002 Name Student ID Number
Lecturer Recitation Instructor
Instructions: 1. This package contains 24 problems for a. total of 200 points.
2. Please supply all information requested above and on the mark—sense sheet. 3. Work only in the space provided, or on the backside of the pages. Mark your answers
clearly on the scantron. Also circle your choice for each problem in this booklet. 4. No books, notes or calculator, please. 5. Some trigonometric formulas: 2 1+cosZm ,2 1—cos2a:
cos x:— srnx=# 2 2 MA 162 FINAL EXAM FALL 2002 (8 pts) 1. Find the area. of the triangle whose vertices are (0,0, 0), (1, 2,3), (4, 5,6). A.6 3J6
2 0.3 D. 3%
E. 4 B. (8 pts) 2. Suppose the vectors 11' = E— 5+ I: and? 2 E— a} + a}: are perpendicular, then a = A.0 MA 162 FINAL EXAM FALL 2002 i
(8 pts) 3. Compute / :3ir12.1.'cos2 Lads:
0 =1 ml: rhI'A cola 3: Ma (8 pts) 4. Compute / tanxsec“ 3:033. A
0 . ml“ '‘ IPl" NIH ﬁlo: 1
:c
(8 pts) 5. Catlrnputef0 (3+1? :13. A. 1:12 MA 162 FINAL EXAM (8 pts) 6. The substitution best suited for integrating / 2
(8 pts) 7. Compute the improper integral /
1 1
(arm I); dz. 4mz+4m—3 1 A. 9:13.093?» FALL 2002 (13:13 :5— lsinu
‘2 rs—sinu—l
_ 2 .‘BESBC‘U 1
x: —secu 2 x=secu—— 2
—2
integrai is divergent 1 ~—1 MA 162 FINAL EXAM FALL 2002 (8 pts) 8. If it takes 4 ftlbs of work to stretch a spring from neutral position to a distance 2 feet
beyond, how much work is required to stretch the spring from 2 feet to 3 feet beyond
neutral position? 2 ftIbs A.
B. 3 “~le
C. 4 ftlbs
D. 5 ftlbs
E. 6 ft—lbs (10 pts) 9; Let R be the region bounded by y = 111.1: 3; = 0, :1: = 1, a: = e. What is the volume of
the solid obtained by rotating R around the y axis? A. £032 — 1)
3‘: 2 B. 2 (e + 1) C. £032 — 3) D. 11'(82 + 1) E. «(32 — 1) MA 162 FINAL EXAM FALL 2002 (10 pts) 10. Find the area of the surface of revolution obtained by rotating the curve 3; = :33,
0 S .7; 5 1 about the m—axis. 51' §
2—70.03 H1) '54'01)“ — I)
300% — 1)
1 27 E 9 (X)
. . —1 n . . . .
(3 pts) 11. We wish to estlmate E ( ) to mthln 10“. Then the alternatmg genes test says I:
we must. take 2
“=2 (10 pts) 12. If we write tan“1(:c) = Z 0,,(9: — 1)", then 02 = UNIO’2 11:2
(—1)" (111702 with k at least 100? 1120 EPQWF’ True False 1/2
1/6
1/4 —1/4 MA 162 FINAL EXAM FALL 2002 °° 2 3 n .
(7 pts) 13. The interval of convergence of the power series :1 % 13 A. 3 < m < 5
B. 3 S a: g 5
C. a: : 4 only
D. 2 < :c < 6
E 25z<5
. 9"(n + 1)
(8 pts) 14' “1330 10 +1(n+ 2)
9
A. m
9
B. E
C. 0
9
D E E. the limit does not. exist (8 pts) 15. i 32:1 :
n=l
. 2 MA 162 FINAL EXAM FALL 2002 1
name)2 .. EX)
(10 pts) 16. Which of the following statements is true for the series 2 n=2 A. The series converges by the integral test B. The series diverges by the integral test . . . 1
C. The senes converges SInCB hm n—roo Minn)2 2 0 D. The series converges by the ratio test E. The series diverges by the ratio test (10 pts) 17. The series : ﬁn“? converges if and only if A. p > _1
B. p > 0
C. p > 1
D. p > 2
E. p > 3 MA 162 FINAL EXAM (10 pts) 18. Which of the following is the Maclaurin series of 00 'n
(5 Pts) 19. The series 2 (2: +:) is n=1 FALL 2002
2 ?
(1 + :c)3 A. Z (*1)“ ——("+”2(”+2) 1."
n=0 B. i (—1)“(n+ 1)(n+2) :5“
°° n_ (n+ 1)(n+2) n
0. “225—1) 1 —2——————:z: D. in: (—1)“1 (n+1)(n+2) 2:“
=0 E. f: (n+1)2(n+2) :3"
n=0 A. absolutely convergent
B. conditionally convergent C. divergent MA 162 FINAL EXAM FALL 2002 (8 pts) 20. Find the slope of the tangent line to a: = £3“, 3; = —, at t = 2. E"
 .59?”
1
.5;
N N (10 pts) 21. The area inside the curve 7' 2 3sim9 and outside the curve r = 1 + sine is given by A. 2.1L
1 3
E f (831112 6—1w23in9) d9 3 g;
1 a
5 / (4aiu29—4sin6+1)ds
1:?
in.
1 a
5/ (4sin26—4sin6+1)d6 i1; 1 e 5/ (8sin26w1ﬂ2sin6)dﬂ
€ 1 £1 5/ ° (4sin26+4sin6+1)d6 MA 162 FINAL EXAM (10 pts) 22. The length of the curve 7' = 51:13 9, 0 g 9 5 ﬂ" is: FALL 2002 A. / sin 6Vsiu3 + 3cosﬂ d6
0 B. fainGVsinG + 953n2ﬂcos2 6d9
0 'II‘ C. [sinﬂVsin46+3cosﬂd6
0 D. fsin23\/1+8c0536d6
0 11'
E. f sinz ﬁx/sinzﬁ — 9cos2 9 d6
0 (8 pts) 23. Find a. vertex of the conic section whose equation is :52 + 43:: — 43; + 8 = 0. 10 A. (2,1) B. (2,4)
0. (2,:)
D. (—2,—1) E. (—1,2) MA 162 FINAL EXAM FALL 2002 5 . Th t' = ____
(8 pts) 24 e polar equa 1011 r 2 _ 33111 9 describes a conic section. The type of conic section
and the directrix are: A. ellipse, y = g B. ellipse y = —g C. hyperbola, y = g D. hyperbola. y = #3— E. parabola, y = g 11 ...
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 Spring '08
 Stefanov
 Calculus

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