Sol-166E1-S2000 - MA 166 EXAM 1 I Spring 2000 Page 1/5 NAME...

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Unformatted text preview: MA 166 EXAM 1 I Spring 2000 Page 1/5 NAME Gene we. KEV STUDENT ID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. 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, 4 and 5. . The test has five (5) pages, including this one. . Write your answers in the boxes provided. 4. You must show sufficient work to justify all answers. 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. No books, notes or calculators may be used on this test. 0310 —a —o (5) 1. Let (I = ;+ ' and b = —;+ Find a: so that (1' is perpendicular to Ei— w" -' , "‘1" 73, —-\o :2 Zi 4'31“) a mu; Q+€LHXZO "'3 7(3—* .2 V531 .._’y (10) 2. If P = (1,2,3), Q = (—1,0, 1) and R = (1,1,0), find prfiéPR. Po 2.— a “231-23-— “my FR * ~i—$L@.. ~ a P? u 5 {SR 2 Po. -’ l” Po, __._ P G ' " MA 166 Exam 1 Spring 2000 Name Page 2/5 (5) 3. Let 6:35— 23amd3:(s—t)§+t}l Findsandtso thatd+3m5+i b 1(3+e,_t)|_ +0923 (1+ a+m "r" _. , g+%-t:4.) f-t'Z‘: (4) 4. Let E and Ebe unit vectors and let 0 be the angle between (i and For what value of 9 in [0, 7r] is (i - b maximum? in”. uni—"P :Cpse W <3” mgeti “9:0 NFC 93 (10) 5. Let a: 3— 35+ 2% and (3': —2i'+3’— 513. (a) Find a vector perpendicular to both (1' and b. —»-* T :K:iet+i—5L Qxb: (33" "'5 2 -2. fl “'5 (b) Find a unit vector perpendicular to both E and 3 and having positive 1; component. H13 T-l-fiv‘g-i“ '17 W 01A (/ cons/sfan Mun Wm“: China-W YT . (10) (14) MA 166 Exam 1 Name Spring 2000 Page 3/5 6. The points Q = (1, 0,0) and R = (—1, 0,0) lie on the unit sphere x2 + y2 + 22 = 1. —> —> If P = (m, y, z) is any other point on this sphere, prove that the vectors QP and RP are perpendicular. QP :{x-m +13 +21~ @ [EB —(x+1)i+v33 +2“ ..—--9 _. 7. q, QP.P-P :(x2«1)+‘3 +2 (9;) A W‘ emu x1+32+2f27¢@ QP'RP :0 ® ' QP .LRP C33 . 7. Find the following limits," /‘””’”M 3 H r ,_ ' 3 _1 L -' 31h“ J ’"W (73 (a) :2 m I {am fl?m¢ W ‘5' 9, 0 a (b) 2320 H)” -—= 95m 6‘ W" 9.. a 9:20" W 00 x “W —" l_w__u _ ,,,..‘,,-...__@—--—-w' ’1 L.” ,' ’l ,.1.2 QM" *W1*%)= Lm bafii’lé hm x—400 x30“ 3;... x-aoo l. 00'8 0 x ®" 1'2, ‘5 _ x HQ?! r it.) ’ ' >r . k ‘1 $300 ('~ i7) == e @ -m‘ot {—«av mt'esiwb Aux 0*" in 33 MA 166 Exam 1 Spring 2000 Name _________ Page 4/5 (24) 8. Evaluate the integrals: M fi%u@fl,._w 1. I \ G ‘ ‘ (a) fxsin(3x)dm "—”"'""' -—- XCflSE'z) ‘1“ "' [035870 A“ :2. but"): dflJ 1% [Infifld ‘X —" mini ‘ .,_.,...m .. —- —-w---—w-”"'"‘"H 'F ® fligwma©x)+—E; sifixh—C E] r; \ “@— .... “M (b)/mlnmda: fléfxzidq 7r LLifimvt dmz‘xArr qufl‘ i \ fir..de ’Ule :7 x—‘E‘Sxoq X 2 2 :- éw—a‘r + c gymmmczjmmm _ 0 J Z. 2539an —~— 34- + C Ea fi-—__.__.@————— —-——m_..\ p. % T!— (d)/ coszmda: —_: "If" m ' j, 0 any": —-*'X+ iLtWZX)/* 0 ")1 fin!- I r7” .. ‘11 j A ““ SIN—- — —-—+.._.. i MA 166 Exam 1 Spring 2000 Name —._._._._ Page 5/5 (18) 9. Evaluate the integrals. PARTIAL CREDIT will not be given unless steps are clearly shown. L )3 0L“): -— ___9-_———— 3cosuciwk : 9—12 (a) 1 d3: ’3— g (El—w?) (\f” "' 1 @3333: WWW; 5&7 ‘fi :ESI'WLL cl'x: 3co3u<ipx @ MIC: 9-x: 94*" 230°“ @ / ‘ —— .1; S fiecQLLcLLL :: -1—'--'ta/nbL *'(:L 0/ 4 t: 3; ‘X +-<:: <:::> 9 9-71 84,41 3; __L._.. 5.23am :(szcuclug H— 75“ m___,/) d 8}) : Mimicu-I—tMM-l‘VC CD :Qn‘m3+xl+c (2!: 3 Ar rm- f ~»-—--l~—~--~-'-ci?|t':. lleH-xz-FXfL '1;— rx I T_____ 3| “PX? -: RM M +fif’iwrlfé— 'H, @ 9 W2. + Cl -WMW J5 0/”: (b) / J1:_2 d3. [You may need: / Wnfl + C]. 1 :13 {3‘ “73$ 53 *1, mztcmus d15sacu‘ziux 6‘ x in l-t-Y :QQCLL 4 IE :. Miami; +tmg " Mimi +tm§l Q +(5\ flimwi +i| 1: ball a 2+“ @l" _. ’ -+\Fz " {an 3M3” [9! ...
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This note was uploaded on 09/14/2011 for the course MATH 166 taught by Professor Staff during the Spring '10 term at Purdue University-West Lafayette.

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Sol-166E1-S2000 - MA 166 EXAM 1 I Spring 2000 Page 1/5 NAME...

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