Sol-162FE-S2010

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

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Unformatted text preview: MATH 162 — SPRING 2010 — FINAL EXAM - MAY 7, 2010 VERSION 01 MARK TEST NUMBER 01 ON YOUR SCAN’I‘RON STUDENT NAMHEUWW STUDENT ID RECITATION INSTRUCTOR INSTRUCTOR '. RECITATION TIME—MW INSTRUCTIONS 1. Fill in all the information requested above and the version number of the test on your scantron sheet. 1 2. This booklet contains 25 problems, each one is worth 8 points. The maximum score is 200 points. ' 3. For each 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 M w “a ~> ‘3 A B)4\/§ W) M39 f ’ k W \ V3 PQ X :7 'ZJI l :<l/ 2") 9/ C)— 2 Z Wl C) I)”; M ' W 6:1 M :: w» X E)2\/§ W01; ?& L 43 v mm - l W 2 '” 31/17 +0) H) 3., [E Z 22 Let P (2, 4), Q(3, —-1) and R(1, 3) be 3 points. The cosine of the angle between vectors PQandQ‘Ris W") (’1; "—3 3 HS? 0M Qll‘: «72% Mm i > < 1 > 2 “In? M B)-——-— A a {Z126 COS 3 '3 ‘ M mm?» mm We \ \le 3 mm :: v—Z P20 E) "22 Wu 4.,” 520 J19 J20 «a “22” 3) The area. of the region bounded by the curves (9 = 2 — (1:2 and y = a; is 4) The region bounded by y = 293, y = 0 and a: = 2 is rotated about the y—axis. The volume of the resulting solid of revolution (using the disk/ washer method) is of «(4+ <92) iv (2” B) [)4 «(z—g); dy 0) [0 «(2:5)? dx D) f: 27423;) doc 2 E) [0 27r((2:c)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 :0 == 1. The volume of the resulting solid of revolution (using the cylindrical shells method) is equal to A) 2&/()1m(¢5—x)dx 2vr1<1 — $)(\/5~ as) due 0) 21r1<1 ~ 2mm?— 2) duo D) 27r/01(1— 2:)(3: - «93) da: E) 27r/1x(x— dz: 6) If the work required to stretch a spring 1/2 ft beyond its natural length is 8 ft— lbs, how much work is needed to stretch it 1/3 ft beyond its natural length? 4 w l/L Alt“le 3 he gm 5; 2 1M: 3”;- ft~1bs 0 7/ 7L {L him «*5 xx ( r; g _/>» Ti, 1% M C) 24 ft—lbs 7/ 0 ‘\ 8 /—;> 1:04) 3“ 6va D) ~3- ftwlbs Va V; 3 L . l 5% in =’~ 32/74 3 J“ fir“): E) g ft~lbs « o 0 cl A)ln109—e2 AAA: (LN Wat v.2. e)“ B 2 )90+e AD X YV all”) émfi C)90—e2 37/ K6 Ck; =~ fig ‘1 fijle 4% £40 D 10 2 ,, )Inlo +3e ' gagexntg @1111010 — 10 — 62 ;’»’@w{mw (O) 6’ (7.61 '6?) : [OQMOW lo we, :fikQ‘O-VUD “"6, "Z. 64 B): u(o}:to>0 :— l (4%)" 505%? 5437; 7 Mg M, W?“ D)? ‘ m I «apt \ ~7 JED—6? : l a} v\B “f W9 : i. J— “ w + tr » a \b n, 3» 6 9) Which integral arises when one uses a trigonometric substitution to evaluate 2 a: dm / 932—4 3‘; ‘fi A) /4sin26d6 /4sec30 d0 C) /4tan26?sec9 d6 .7, D) /4tan686026d0 *1? j w ZCmem&&Ef E) /4sec20d0 2. m9 A) ?mlml—EMJx~2I+%+C X (KW‘Z) )K X92, 5 3 1 B) Zlnlzvl+ZInIm—2I+E+O __..L @islnlxl+-§—1nlxu~A2l—%+O X: 0 "l1‘3 5/3? “9 ZBm’l'OC’W? 7” =- E Xi; M3 : -O W ({C "7) C” Lf, 3 5 1 D)——1n|x|—-—1n[a;-2]-—+C’ I 3 x ~ 45 43 m1 X?‘;B;ilc;§:’5 ‘fing’EH‘wa A33“; E)—Z—1n|m|+ZinIa;-—2f—;+C ‘ 3 :wflinxl- 3: ">2 + “a; «Qua?! oo \ “it 71' j—\ , F 19/1 was": $61? 3 “134% r, 19% J A) the integral diverges 1“ (saga “ I B) 7ran C) 7r1n @)r E) 27r :fie/%+fl:mwav 12) The curve 3/ = :02, 2 S a: S 3 is rotated about the line y = —1. The resulting surface has area. given by A) /3 21r(ac2 —— 1)V1 +x4 da: 2 B) [3 27z‘(:z:+1)\/1+4=x2 dm 2 C) /3 27r(:z;)\/1 +4x2 d2: 2 3 / 27r(a:2 + 1)\/1 + 4:1:2 dm 2 3 E) / 27r(:c2 — 1)\/1 +4152 d2: 2 8 13) The area of the region of the first quadrant bounded by y = 2 — :32, y = a: and the y-axis is equal to Find the w—coordinate of the centroid of the region. Z L o 2 2a W -l B 8 )3/ 3(X+1KK”W C) 5/8 D 4 9 ) / ’9‘; my @5/14 X :jé : 2 E) ‘7 \i/ 3 I - 7: X a f "a IL} : E I; 14) The limit of the sequence an = nsin is equal to A 0 » .L ) 2% m shf-L five 91:) :: I @1 “@369 n “@539 :5; m2 Chg“ m3 00 15) Which of the following statements are true about the series 2 an? gm:- n=0 go . _ . a u_ I) If nan — 1, the ser1es converges. W . “mm? is» w. I M Z t dim?!” II) If lim 0M1 = 1 the series convenes ‘\\ :3 23’ lfio AW nHQo an ) g \\ ’ 2 an 0/ 2 r N r \ \\ III) If lim mull/n = 1, the series diverges. l) ' 71—900 {Mlle} {24%;}? Qa‘b‘o (fwd A) All three are correct RM Tear [KA- MLOMf/(AJIW . All three are incorrect 2: ‘, L “:3 (lives/gm f, M 2 dim CMvekgieg . C) I and II are correct, III is false D) II and III are correct, I is false N y EVIL ’lg We, Mom; Mme i E) I and III are correct, II is false \ m m M (2M Tate 16) What can be said about the convergence of the following series °° , 1 °° 1 °° n 1 $1 = E nsrn SQ = E £9, 83 = E (—1) n=1 A) 81 and 32 converge, S3 diverges g. mmfiflfl : y l s) ; B) 51 and 5'3 diverge, 82 converges l A . \ sn‘m l h $1)“ :1 (“a ‘ WML>(L£‘ “L C) 1, S2 and 5'3 converge [70 V\ m . .L M i “7/ mix/mam. D 3,5 andS' diverge ) 1 2 3 Si ewes) a’bgélwldfl‘ E) .31 and 83 diverge, 82 converges V29 Ga ‘ [ E V\ , _, “L w :4- “? ) W996” in it Tc ‘I; Lari. g3 mm?» gen; 55“ W o Walm m) :7" l 4 l (IAN @ W l l “ h 7 M m M §3 CHM/Law “Ram M Z W l (£- \ g” l 10 if T‘ Wrens a 50 kg he}? \A in wt; Vt 9M 17) Which of the following series diverge? 0° n2+1 W n n2+n 0° 1 81“; n3 ’ 32—;("D n3+n2+n’ 33“; nzlnn , vfitL we \ A 3 “ML \ 1 g. ctan 1 1w an CW n K B) 32 only _..:> g! dmfig’w % Cfimgw’fim 13:65“); L CSandSonl.S CMW lam lath—@410, ) 1 2 Y a. 3M” Vfwxp WW5?“ A D) 82 andSs only. M $0“ .; xlr‘lax ’ M0716: #2640, WHEN Xltxl‘l E)” °f"‘hem‘ (9M 2 (‘Wz‘i7E_:,‘_l;;l?fi‘l{7’>3,,_ill : ~— [ flex [ 0 Q‘l‘fl‘i’UL [)5le 2' I MM QL Commyg by fatemmfirwfi Set/lg 72.5% 18) Which statement is true about the following series (*1)" n4’ SI :3 i (—397: S2 = :0: n=1 “'3 n=1 A) All are conditionally convergent. 00 83 = Z (—1)" sin(n-§7:) ? 71.21 B) All are divergent. @1 is conditionally convergent, 82 is absolutely convergent and 33 is divergent D) 51 is absolutely convergent, 82 is conditionally convergent and 33 diverges E) .31 and 5'2 are conditionally convergent; S3 is absolutely conver ent. l’\ S, m. CW. H) WCMJL gefll‘ltfil ’) Z 71V;— clhr‘ (4p~£m‘e§ ) m"3 o” | \ gm aloy CW. Z :31 05W\ (F‘Ww' MEQV‘QN(%B¢O Natl Qufll:il “mace é. 3 divongea 11 .(—1)n(zz: -— 1)” 00 19) The radius and interval of convergence of the power series 2 (n + D3 n=1 satisfy A) The radius is equal to 1 and the interval is (0, 1). h H : m CH) , @H)? . . . . yr) 00 3 B) The radius IS equal to 2 and the interval is (0, 2). 0,4 422,) QM ) i x 3 C) The radius is equal to 1 and the interval is (1,3). : zQ/w I X4 1 M 1 1 X4] _ W90" 0n +2); D) The radius is equal to 1 and the interval is (1,3]. M I km” 41 W}, _“ 4 X4 4' ’3 O c, X L 2 \ @The radius is equal to 1 and the interval is [0,2]. ‘ “'5 Well FM 53!» Weafi-ma is {1. , C W ca at“ M : m: cm “KEN—n“ “0° 4,. CW (MW \ W W Wm X’Dfiézwi (mi ‘ ‘Ciwti lgm 5‘: , Vi h 4 R \ e» h XLZ Egg 2. {L249 CW, by M. games left 20) L913 “93) = i 2;!” — 1)". We can say that the third derivative of f at the point 1 n=1 is equal to I (k) W A) f(3)(1) = 10. {Mg—L :: 3,2. n I. V] B) We) = 1‘3. 3 153. :> fl .2: $2.5m C) f(3)(1) = 3! 16 ‘ f(3)(1)= g. :> *(Z)[\) 3 g. ,4) 3: 1% 1 mflWn=g 12 21) Which of the following is a power series representation of the function x — 1 flflzfl—%+m7 °° m_ n+1 ’4 A; 1: W‘l 3,) A) QED“ 9,31 Qf—zx fl) +0) Cf +660 00 n($ _ 1)2n+l \ — Wm B — 1 _ , “ <fi><TTYE>V 00 a: __ n+1 C) Z<~1)n( 37:31 9! 3 ' ":30 m _ 2n+2 A VD L V‘ mD—nn‘ :3 2 5" :7 fl 1%)) n;0 (a; _ 1)” 0’ m 5;: E) Z(—1)n 3n+1 M 3 3’: m I 2m 4-! Z. 6‘) mm ( W' W g? 22) The foci of the ellipse £93 + 311—; = 1 are A) (—3,0>and(3,0) (f: ((0 -q : -.7 A (,2; if? B) (—5,0) and (5, 0) @(0, 47) and (0, W) 1»(—vio)mm(¢io) E) (0, ——3) and (0,3) 13 23) The graph of the curve given by the equation 7‘ = 1 — 2 cos 6 looks mostly like A) 1 2 3 @VTT 24) Which of the following are polar coordinates of the point whose Cartesian coordinates are (—1,—\/§ ? C) 34%9 LB A)'r=1,6=%. B)7'=2,9=2?W )r=2,a=16"5 a, E)r=2,6=Z—7: 14 25) The complex number A)7+—:-z' B)§+%i a): D); E); 1+3z'. 3+4z, 1s equal to Hg; \. 3i; 2 +q" 350%" : 3 f5" f1??? 0)’ 7‘ (14(6): ; 3 +9 fl}: q we M - . 2§ : LE g 2 2f 25 : 23 T g; ...
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Sol-162FE-S2010 - MATH 162 — SPRING 2010 — FINAL EXAM -...

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