162FE-S2010

162FE-S2010 - MATH 162 - SPRING 2010 — FINAL EXAM — MAY...

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Unformatted text preview: MATH 162 - SPRING 2010 — FINAL EXAM — MAY 7, 2010 VERSION 01 MARK TEST NUMBER 01 ON YOUR SCANTRON \ STUDENT NAME‘fi~————-#———__—_—_——— STUDENT ID RECITATION INSTRUCTOR INSTRUCTOR RECITATION TIME—WW INSTRUCTIONS 1. Fill in all the information requested above and the version number of the test on your scantron sheet. 2. This booklet contains 25 problems, each one is worth 8 points. The maximum score is 200 points. 3. For eaeh problem mark your answer on the scantron sheet and also circle it in this booklet. 4. Work only on the pages of this booklet. 5. Books, notes and calculators are not allowed. 6. At the end turn in your exam and scantron sheet to your recitation instructor. 2 1) The area of the triangle with vertices P(1, 2, 1), Q(—1, 3, 2) and R(3, 1, 1) is equal to A) 2 B) 445 a)? 2) Let PQ, 4), Q(3, —-l) and R(1, 3) be 3 points. The cosine of the angle between vectors PQ and QR is mag—3 13% C)—\;—% 13% 13);” 520 3) The area. of the region bounded by the curves (9 = 2 — m2 and y = x is 4—2 5 B)6 A) 37 C) 2- 4) The region bounded by y = 2:22, 3; = 0 and a: = 2 is rotated about the y—axis. The volume of the resulting solid of revolution '(using the disk / washer method) is A) f: 7' (4‘. (92) d9 B) f «(2—92 dy 0) f0 «(22:)2da: D) [)2 21m) dz: E) [)2 27r((2:1:)2—2)da: 4 5) The region of the first quadrant bounded by the curves y = a: and y = fl is rotated about the axis 93 == 1. The volume of the resulting solid of revolution (using the cylindrical shells method) is equal to A) 2w/01x(fi—x)dw B) 27r/01(1—m)(\/_—33) do: 1 C)27r[)(1—2x)(«/E—a:)dx D) 27r/(j(1— xxx — x/a?) (13: E) 27r/01x(x —- d1: 6) If the work required to stretch a spring 1/2 it beyond its natural length is 8 ft— lbs, how much work is needed to stretch it 1/3 ft beyond its natural length? A) g ftwlbs B) 32 ft-lbs 9 C) 24 ft—lbs D) ~3- ft~lbs E) :— ft—lbs mm 7) f we“ dm = 2 A) 1n109 —— e2 B) 90 + e2 C) 90 — 62 D) mm” + 3e2 E) In 1010 — 10 — e2 7r/6 8)/ ‘sinxcos3a: dx = o 6 9) Which integral arises when one uses a trigonometric substitution to evaluate 2 f 50 d2: 11:2 —4 A) /4sin29 d6 B) /4sec30 d6 0) /4tan208e09 d0 f4tan6sec26 d0 D) E) /4seczg d9 10)] Egg/fiche: A) "Tsln|m|—%1n|x—2|+$+C B)Zmix|+gmlm—2|+i-+o C) ¥mlx4+§1nlxm2[—%+o '- m w D) iln|x|~§ln|x~2]—%+C’ -—5 3 1 13732 A) the integral diverges B) 7ran C) 7rln D) 7r E) 27r 12) The curve y = :02, 2 S a: g 3 is rotated about the line (I; = —1. The resulting surface has area given by A) /: 2W(x2—1)mdx B) /: 27r(a:+1)\/1—W do: 0) /: 27r(ac)\/1-|_—4x3 do: D) /: 27r(m2+1)m dx E) f: mag—1)de 8 13) The area of the region of the first; quadrant bounded by y = 2 — :32, y = a: and the 7 y-axis is equal to 6. Find the x—coordinate of the centroid of the region. A) 7/12 . B)3/8 C) 5/8 13)4/9 E) 5/14 14) The limit of the sequence can = nsin is equal to 00 15) Which of the following statements are true about the series 2 an? n=0 I) If lim nan = 1, the series converges. n—mo . a 1 . II) If 11m M = 1, the serles converges. n—ioo an i III) If 131m lanII/n = 1, the series diverges. —+oo A) All three are correct B) All three are incorrect C) I and II are correct, III is false D) II and III are correct, I is false E) 1 and III are correct, II is false 16) What can be said about the convergence of the following series °° l °° Inn °° 1 :91 = Znsin , 82 = :7, S3 : Z(—1)n-\7_7;? n=1 n=1 n=1 A) 5’1 and 5'2 converge, 5'3 diverges B) .91 and 6'3 diverge, $2 converges C) 81, 82 and 33 converge D) 3;, 32 and S3 diverge E) .91 and .93 diverge, 6'2 converges 10 17) Which of the following series diverge? 00 2 00 2 00 n +1 n +71 1 = = "171' z ’91 g n3 ’ 32 ;( ) n3+n2+n’ 5"" ; nzlnn A) 51 only. B) 5'2 only. C) S; and 5‘2 only. D) 52 and 5'3 only. E)All of them. 18) Which statement is true about the following series S “(—1)ns_°°(—m °° n_n7r? 1:; 771%: 2—; n4 1 S3=Z(—l) 3111("2’ ' A) All are conditionally convergent. B) All are divergent. C) 81 is conditionally convergent, 82 is absolutely convergent and 5'3 is divergent D) 51 is absolutely convergent, 82 is conditionally convergent and S3 diverges E) 81 and 6‘2 are conditionally convergent; S3 is absolutely convergent. 11 r m<4re—m 19) The radius and interval of convergence of the power series 2 11:1 satisfy A) The radius is equal to 1 and the interval is (0, 1). B) The radius is equal to 2 and the interval is (0, 2). C) The radius is equal to 1 and the interval is (1, 3). D) The radius is equal to 1 and the interval is (1, 3]. E) The radius is equal to 1 and the interval is [0,2]. 00 2n 20) Let f (as) = 2 £501: — 1)”. We can say that the third derivative of f at the point 1 n=1 is equal to A) f<3>(1) = 10. mflWn=%. eflWn~%. mflWn—§. mflWu=§ 12 21) Which of the following is a power series representation of the function 22) The foci of the ellips A) (~3, 0) and (3,0) B) (—5, 0) and (5, 0) 0) (OM/i) and (0: W) D) (—W, 0) and («10) E) (0, *3) and (o, 3) x2 2 e—+y—=1are 9 16 13 23) The graph of the curve given by the equation r = 1 — 2 cos (9 looks mostly like A) B) C) 1 2 3 D) E) ‘ 2 3 24) Which of the following are polar coordinates of the point whose Cartesian coordinates are (—1,—x/3)? 7T A)7‘—1,9—§. 271“ l4 1+3i. 25) The complex number 3 + 4%, 13 equal to A) 7+§¢ ...
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162FE-S2010 - MATH 162 - SPRING 2010 — FINAL EXAM — MAY...

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