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Sol-166E1-S2010 - MA 166 Exam 1 Spring 2010 Page 1/4...

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Unformatted text preview: MA 166 Exam 1 Spring 2010 Page 1/4 GRR—DWQ 22E?” NAME Page 1 /14 10‘DIGIT PUID Page 2 /32 RECITATION INSTRUCTOR Page 3 /24 Page 4 / 30 RECITATION TIME TOTAL /100 DIRECTIONS 1. Write your name, 10~digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3, and 4. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. You must show sufiicient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. N 0 books, notes, calculators, or any electronic devices may be used on this test. (10) 1. Find the center and radius of the sphere with equation: 2$2+2y2+222=8$-242+1 20222.22 )22, 2, 2 2(2 212,2 22.1 2V?“ +4“) “’th +2{2 $212 2232) :1+2 2272, 252 2222921226) 21 (x 2) +2; 22(226) 2222-2 “i center (2 0,1,5) Q radius (4) 2. If 2: <5, —12> and 5 = (—3, —6), find the following: 222+»? t: ”W m m ”\x, an m , (x b h <2 3,122c2/<2, :28) 222222 :2 2;; 2 222 2222212921 2222 MA 166 Exam 1 Spring 2010 Name Page 2/4 (8) 3. Find all values of t for which the angle between the vectors 5i : tg+ E + I? and b:$+t}+kis§. it 222: : 5 “Er” :«2 a: v E: 2:: lg: lggmflg “a; t+t2iili$ f1+2{t +22 Cfléga Q) {‘32 425C222 :: i322 1.: :2 4:242:292 r 2:: Q 5’2 W (8) 4. Let 5: (1,2,1) and (3’: (3,—4,2>. (i) Find all unit vectors 1? that are perpendicular to both ("i and E, 222; 2:? 2259 M. w: . 2722 <2 22,: 5 am: ” ‘ fififélrsrmi‘flg‘é; ($1 1 :24 ' W ' 2,. ( j, M 725 '1' 22> 3 2-22 2 f 5%? (a: :3‘1‘3‘2) M #2222222 2-252" ,2» —. , w “fr 1:: l 5‘1 V632: 22 132595 531%”; u : 21 2:2 M V: ' 1., , I 4 , m ”:11, ’ ' 22 T}: {I} E 30b 4/) Wrwwrg I 91rd; W regf a; UL: $222122": m V755 (a 2 3:555 31’ E } ~ .1 "M _ 22 p 2 “3‘“ 3 WW5"? 55‘3“"“513 MEL $1.3de C aj‘riSwE‘f C9 (ii) The area A of the parallelogram determined by EL’ and l; is (8) 5. Let 5: (6,3,1), 3': (0,1,2), 5': <4,—2,5). :11, ,7.“ G 3 1 (i) The scalar triple product 6 - (b x c) is OK: “”6113:le x (2} ’7: i O 1 ‘12. / 222 < 2: 55W 5‘ Q 2} 52g 2 2:: 9,3622"; 22:32:}? as M. \ _ N222 2-: ,;> _’ barf-7L 3» 21:2;‘223’24i 4 ‘1 (ii) True or False: C3? The vectors (1’, 5, 5' are coplanar. (circle one) T Q) [89? (8) 6. Set up, but do not evaluate, an integral for the area A of the region bounded by the curvesyzlnm,:r=y2—2, y=—1,y:1. 0 {3,133 fflr pmhlrm N L71 mom, Uanm 1 113mg LE2 wwvéga Limit?) LDLMi/t ,_ 05‘“ “1.5 5111:12255195 C3 / [A = ,y ‘ MA 166 Exam 1 Spring 2010 Name Page 3/4 (8) 7. Let R be the region bounded by the curves y 2 $2 and y = ——2:1:. Use the method of washers to set up an integral for the volume V of the solid obtained by rotating R about the :13— axis. Do not evaluate the integral. X2a21>< WNW-1123:: C? 7'» fl: 3‘92 0 (“2/ 4) k3 \Omnfl of hrfcecmimw 1 Volum 20¢ tuapicmi afimymmigm( nghmr: A V: [TM—2X) .1111ij Ejflx ‘CNQMVX (23 WW 4\fl V: /0 (WAX; 222W>< 4)olm Ei 1’35: (8) 8. Let R be the region bounded by the curves y = 2:4 and y : x. Use the method of cylindrical shells to set up an integral for the volume V of the solid obtained by rotating R about the line y : —4. Do not evaluate the integral. fir [/Xz‘li' 1L1 : 1/ “a /2'~/ 2-” MW 2,; amt 41222111211221125222222221 in” _-11éj‘f:)€/i Nfiw :5 g 2 AV”2W:€-rili~l“">—sieg (“D \/M\ ,g 13% [E] ‘13. (8) 9. A force of 10 lb is required to hold a spring stretched 4 in. beyond its natural length. How much work is done in stretching it from its natural length to 6 in. beyond its natural length? {4:311 1:: 10”; X:%{f 102: 212 22211220 @ 1/ ,. \Nmak' W: Jaclfimrw QTSX Fill/21222215.!” 3;: ftwibfla i“ 5 "$1 ,1: 4/”: 3?" “3 F?) i [Z I V? Jaw; cam: 1W £7 {”242 :111 m 1242 i212 5 t/ ii je w .2: 1 1 “it“ “21 121112241111 w Wed U1 S l h ‘3 CLO if} S- 4‘ ngflvi (423 (11) (8) (11) MA 166 Exam 1 Spring 2010 Name Page 4/4 10 An aquarium 5 ft long, 4 ft wide and 2 ft deep is full of water. Find the work needed to pump half of the water out of the aquarium (Use the fact that water weighs 62. 5 0 Q5,” @3992“? ””Ehe mflee‘fibhafi, ) 9:2: fiiwece {in 2222 SP2”; W2 419 X5623 920 29232; ,22 2 , )9 {<22 2222224 WeWM we 92e9 View 91% Awe, Tween {7 gnaw @‘ WOH¢ @232, C52,? «,2 ‘ A W332. Ejaéfivé 33031113 Q 2 Sm ft-le 22 {Leyla yeah! @9235 222,222 .2 2 2 i221 ‘5 ® I???“ 2x 2 —:25 4- 2 2:2 22,2, 11. /Sin 1mdm2QD Ni) Q{% 2?}; < >3 (2:: WW f “max 3321,16 Vlé‘fEk, 253%?! EM \ 227’}, i .222 i) \ t: x 3m 2’: 222. j L32 “:13 33(3‘h3flh'22fihhl 2122 ": S2812: 3% [U idée‘ fix?“ e , 21 ‘ r” 3% $22922 ”h? :2: 22212] 29,, «em ,, g 2?: “h 22,222 We”? 2 g’fi; 5'" ”3:2 WT” 247-2 2“ 22-: (”79‘2" <” {i 2* ”:1 mifihflfhk’ 27* e @ e3 eh 12. First make a substitution 3: 2? and then use integration by parts to evaluate the integral / 93 008(62)d9. Your answer in the box must be in terms of 0. 3 a 13,, m ‘1 My ( 2,, 2 ‘ W 36 (:20le 2‘19 22 2,, 3 2223322092 :égxeine emeeej 222 C f 3 MEWS” 2 7% ‘3“??? -= heme}, Tr; SAW %m,£ 1281:}? rifle“ 005 K UE’X , ,, _, , _, ,22 2 m ‘ ' f, ,_ a; :7” K 2 , ,Fg? , ‘29" wzlfiw fl) v, Sink! “ 2:: i aygthéii 2‘2 2%: (73332133? +9 C: ’2“?ng if “hi (0 missimg in We, a?” 5:229:99 5‘5”“? 2,, e e 23 3327332 :2 , r “h?” @ 2929,26“? '22 a“ 543259;} 222 i: \N/ M22 (:13 ‘22,, , :53 l @322) 3) M/ ED ...
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