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Unformatted text preview: MA 162 Final Exam 1 December 2008 1. We want to approximate the sum i W
2 .
k=1 k +1 The alternating series error estimate guarantees that the error is < 10‘4, provided we
add the ﬁrst n terms, where n = A. 9
B. 10
C. 49
D. 99 E. None of the above is correct. ‘2
2./:l:1n:1;da:=
»1 A. 111241 , 13 m—m
C. 21n2—3/2
D. 1n2—3/2
E. 21112—3/4 MA 162 Final Exam 1 December 2008 3. The length of the curve a: = 6‘ cos 2t, y = ct sin 2t, 0 g t g 1, is
A. 1
B. 3
C. x/g (e — 1)
D. \/§ 6
E. 66 — 2 2+i_
3—i‘
A.% B. 2 ——i C. 1 + 22' D. 1 — 2i E. None of the above. 4. MA 162 Final Exam 1 December 2008 5. The vector of length 6 that points in the opposite direction to 2'7 — + 2]; is
A. 433+ 33' — 613 _; 7.7.
B.——k
Z2+ C. —4?+23’~4E
D. —2¢§?+¢§i~2¢§E
E. —2\/62*+\/65'—2x/613. 6. The Maclaurin series of m is
A. 1+2x2—2x4+4x6+...
B. 1+2x243x4+6x6+..
C. 1+2x2—2x4+811:6+...
D. 1+2m2—3x4—5$6+...
E. 1+2m2—2x4—5x6+... MA 162 Do 2
7. f we‘”0 dz: =
1 A. 1/62
B. 1/(2e)
C. 1/6
D. 2/3 Final Exam 1 E. The integral diverges. 25 8. Evaluate 5 — —— + 6
A. 30/11 B. .6/11
C. 30/7
D. 15/11
E. 15/7 125 625 36 216 December 2008 MA 162 Final Exam 1 December 2008 9. Determine whether the following sequence and series converge: 2122—1 °° °° 2719—1
371,2 + 8n ’ 1 3112 + 8n' "=1 n: A. Both converge. B. Only the sequence converges.
C. Only the series converges. D. Neither converge. E. None of the above is correct. 10. Consider the series I.1—1+1—1+1—...,
1113 ln6 ln9 ln12 II ——— ———— 3 6 9 12
A. By the alternating series test both are convergent. . By the alternating series test both are divergent.
. The alternating series test is inconclusive for both. II. is convergent by the alternating series test, I. is divergent. spew I. is conditionally, II. is absolutely convergent. MA 162 Final Exam 1 December 2008 00 A _ 37;
11. If 2 §%§ is the Taylor series of a function g(x), then g(G)(1) = ——1
. 90
36
. —36
—32
24 wpowm 12. The area between the curves y = 1 — 2a: and 2 — 29: — 2:2 is
A. 7/3
B. 4/3
C. 5/6
D. 2
E. 3/2 MA 162 Final Exam 1 December 2008 13. Which statement(s) is true? I. The series 1:; k1]; k converges for q = 1.
°° 1 II. The series 1% klnq k converges for q = 2. A. Only I; B. Only 11; C. Both are true
D. Neither is true E. None of the above is correct. 0° 2k+4 .
14. k; W 1s A. convergent by the ratio test;
divergent by the ratio test;
convergent by the comparison test; divergent by the comparison test; 91.0.0?“ convergent by the root test. MA 162 Final Exam 1 December 2008 15. Which is / are absolutely convergent? 15°: (—ilr' i=1 H. i (‘2)? j=1 7 III. i (4)166,“ k
k=1 k All are. None is.
Only I and II. ‘
Only II and III.
Only II. 515.0??? 2d$
16. / Ten—1)— a: 2 A. In ——+C'
__:I:—2 a:
B.In$——1 +l+0
(I: (B
C. 21n "1 +E+0 (E .77
x 1
D. 2111 +—+C
_ 93—1 :1:
E.ln$_l>—3+C'
SL‘ MA 162 Final Exam 1 December 2008 17. Which integral arises when one uses a. trigonometric substitution to compute / (czdzz: ?
\/4+—$2 '
A. f 4 tan2 9 sec 0d9
B. 2tan20cosad9
C. / 8 tan2 (9 sec2 0030 D. / 4tan2 aces 0019 E. /4sec36d6 18. The radius of convergence of the series °° _32n
z L 2,} n=0 is spew?
wuss MA 162 Final Exam 1 December 2008 t 19. The tangent line to the curve :1: = cost + sint, y = 62 , corresponding to t = 0, has equation A. yzx B. y=ea¢+1—e C. y=$1n2+1~1n2 20. The polar coordinates of a point are r = 2V5, (9 = 17/3. What are its Cartesian
coordinates? A. (3, x/i) B. (1,3) 0. (V313) D. (2\/§,\/§/2) E. None of the above. 10 21. lim (n+2)1/3"= Tl‘—}OO A. 1/6 B. 1/3 C. 1 D. 0 E. The limit does not exist. 22. Which curve is represented by the parametric equations :1: = sec t, y = tan2 t,
—7r/2 < t < 7r/2? 11 MA 162 Final Exam 1 December 2008 23. The cosine of the angle between the vectors 2; ;+ I; and 3+ I; is 24. Let D be the region in the my plane bounded by y = 2x — x2 and the (It—axis. Find
the volume of the solid obtained by revolving D about the y axis. A. 117r/6
. 27r
81r/3
137r/4
371' wwcw 12 25. Which of the curves below corresponds to the polar equation r = 2 + cos 26? ‘2'
I 13 ...
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This note was uploaded on 09/27/2009 for the course MA 261 taught by Professor Stefanov during the Spring '08 term at Purdue.
 Spring '08
 Stefanov
 Calculus

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