Sol-166E1-S2001

Sol-166E1-S2001 - MA 166 NAME R ' “’6 LEA. STUDENT ID...

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Unformatted text preview: MA 166 NAME R ' “’6 LEA. STUDENT ID RECITATION INSTRUCTOR RECITATION TIME EXAM 1 Spring 2001 DIRECTIONS 1. (.0 01 Write your name, student ID number, 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 . The test has four (4) pages, including this one. . Write your answers in the boxes provided. . You must show sufficient work to justify all answers. Correct answers with inconsistent work may not be given credit. . Credit for each problem is given in parentheses in the left hand margin. . No books, notes or calculators may be used on this test. (10) 1. (7) 2. Let 6, 5, E be three-dimensional vectors. For each statement below, circle T if the statement is always true, or F if it is not always true. (nax6=3xa (ii) 5- B = B - 5 (iii) (6 x X E is a real number (iv) (6 x 3) - E is a vector _. Find a unit vector that is perpendicular to both and j- k. (l; —T+—3+h 1 “l MA 166 Exam 1 Spring 2001 Name Page 2/4 (10) 3. .Find the area of the triangle PQR with vertices at P(1, 0, -—1), Q(1, 2, 1), and R(0, 1,1). FE; —_-_ 21121? 3R = If +T+ 2i? 7; x “R - T "3* “a : (4—2)? [02 —2(-'Hi {0" ‘Z“'7]“ ~ 0 7' (2’ 1" '7 ~9 —1 L % = W @3 .4 —-9 \ Am 0; PQR : é- ) PQ x PR1 GD ~2r-t" l0“ “mam/I- = WEE E 0‘? _. _ a”; _, onjdb _ \al'z. 0' @ \ 2+3 1(2213532) 4+9+_ (_ __, é 27,157+? \43 ‘ :T%(2i—33+k)@ I4+(L J > :3. (5) 5. Find the value of :1: 96 0 such that the vectors (—353, 2:17) and (4, m) are orthogonal. <—3x, .2><>.<+,>‘<> =0 ® 42x + 2x1=0 i MA 166 Exam 1 Spring 2001 Name ' (10) 7. Find the value of the positive number c such that the area of the re ion enclosed by ' the curves as Otvédit Par Froglt‘“ 1/- mot—j " = 4——4 =4— 4 l ' 'tem' wvo y :1: c and y c :1: Mn 1. t m . “a an jitem gum ' 1t —. . ‘ iseQua o 5 Arm ¥ alpha?“ 16 (“MI-g w'pd (8) Page 3/4 Nu) ' or #4734!de ) /. 0 t +1¢m gymwe V’ 8. Set up an integral for the volume of the solid obtained by rotating the region bounded by the curves y = 11:2 and y = 4 about the line y = 4. Do not evaluate the integral. AV :. 'IT(4-——2(Z)Ax Volnm 0/, affrox;"milwoé Add”: (8) 9. The base of the solid 5' is the region bounded by the curves y = 2:2 and y = 1, and cross-sections perpendicular to the y—axis are squares. Find the volume of S. *AV : 4% \loiwml. 0/ alrrvexiwmiimb $0,121. '. ~l MA 166 Exam 1 Spring 2001 Name Page 4/4 2 _ (10) 10. The region bounded by the curves y = e 1, a: 2 1, :1: = 2, and y = 0 is rotated about the y-axis. Find the volume of the solid thus obtained. Vomme o} olrfmx “ AV = in Sim (“‘2”) mama» m (8) ll. If the work required to stretch a spring 1 ft beyond its natural length is 12 ‘ft-lb, how much work is needed to stretch it 9 in beyOnd its natural length? ' - ‘ m 9 Mn \N 3 [gaSA—Xclx : 2‘35 12-81:??? 0 _.. 7.3/4— ‘1; ‘2; ’ 19” lo '12 '6 2+" @ 22,1 lug; 5‘3 ,5 ,3 ’L —— )5. __ (31.5-— -x \J 7— Jx 0/“de ——-—- ‘X 3 XA)‘ __,.Qmu__3_ tit-:me d'VIchlx . a 7 -- ,_. _ X dAL:.=l—d)( (Vi—x: ’ ‘I x 3 ' (4D @ ...
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Sol-166E1-S2001 - MA 166 NAME R ' “’6 LEA. STUDENT ID...

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