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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 = —I+ 1:}. Find a: so that (1' is perpendicular to Ei— Ii. “M -' , "“1" 73, —-\o :2: Zi 4'31“) a Quit—"IO m“=9 Q+CLHXZO ”'3 7(3—* .2 WEI .._’y (10) 2. If P = (1,2,3), Q = (—1,0, 1) and R = (1,1,0), find prfiéPR. PG 2.— - “2."? ~-“2§ -— ”-5 FR .- ~i—[email protected] ~ a P" - . {51% 2 Po. -’ FEW. Po.- __._ P G ' " MA 166 Exam 1 Spring 2000 Name _— Page 2/5 (5) 3. Let (I : 3;- 23 and 3: (s — t);+ t}. Find 3 and t so that Ei+3m 5+ 3. b 1(3+e,_t)|_ +0923 (1+ 3+!“ '1‘“ _. , g+%-t:4.) f-t'Z‘: (4) 4. Let 5 and Ebe unit vectors and let 0 be the angle between (i and 3. For what value of 9 in [0, 7r] is (1' - b maximum? in”. uni—"P aio :Cpse W <3; mgei‘ri “9:0 NFC -EB (10) 5. Let a: 3— 35+ 2% and (3': —2i'+3'— 512. (a) Find a vector perpendicular to both (1' and b. T T T; cieT+i—5L< :3 ’2— ‘1 C534 1-5 __’ --4 axb (b) Find a unit vector perpendicular to both E and 3 and having positive 1; component. H13 T-i-rifig-‘zll '17 W Oh (/ cons/51cm! Mun Wm“: Chitin-W IV? (a) . (10) (14) MA 166 Exam 1 Spring 2000 Name _ Page 3/5 6. The points Q = (1, 0,0) and R = (—1, 0,0) lie on the unit sphere 9:2 + y2 + 22 = 1. —> —> If P = (:r, y, z) is any other point on this sphere, prove that the vectors QP and RP are perpendicular. QP: {x m +jd+3E @ RP:(X4’1)L+UJA +2Lfi- @ ' Q P .L R P 7. Find the following limits: H /"””flm TM;‘\ J I... H @W , . - 1 L . -— ’5 :1 h 4 X r” (a) lim M1“ m ___ {1m ...‘?me.3x z—rD x O 2 X _._ 2- o x " x40 ‘5' Q. 0 - MJ 1°“ XH‘” _' [”7" "‘""@M# LH “L ’l .1.2 Qm *“(1'%)=Lf; finals): Mm E.) x—JOO 0041} x ~ .4;— x-'*°° '1‘?” _ mm M; M (PW: 6’1 @ -m‘gt {—«av mt'esr'wb Aux 0*" in 33 MA 166 Exam 1 Spring 2000 Name _________ Page 4/5 (24) 8. Evaluate the integrals: F‘Qfl: -.\ Ffi[email protected] M w. (a) fxsin(3x)dm "—”'“""' ———gxc,os(37) ‘1‘"‘3 [MSBZ)A%‘ :2. LAT—=7 dVUZ‘SIHGXF-lw "" mini ‘ .,__,~_._ "—- —-w-—-—w—"”‘"""H 'F ® #Jéwma©x)+{§ Sinfiflq—C E] r; \ MQWWW b)/mlnmdx :1 9%...an “fozidfx '2 7r LL‘JMX druz‘ni'r qufl‘ i \ ~— -— , "7r dA:%—tix @235; "’7 u 25x0 2 2 2 war:- + c LWm_W______WW _ 0 J @3 Z. fifl/nw —~— 34- + C E3 fi[email protected]—“ ""\ 3 -2 ' - ‘ (c) fcos msm 3:111: :12 (1—Sln2x) SHnQX wst'R’ 1 O,( 6) /”’ W — K‘Nm: {Kiwjfl dazcnsfird’x / M. "—3 [(43-43) ”1% '3 “WM; : 3H7 )f__ SW) >r +_C "is S % T!— (d)/ coszmda: —_: "If" m . f1, 0 d)”: 3—- ‘x + istxy4~ "} Z .4.»- _,_—-+-—-va‘aI-T 1£+$~ " '8 Ar ’2 a [email protected] MA 166 Exam 1 Spring 2000 Name —._._._._ Page 5/5 (18) 9. Evaluate the integrals. PARTIAL CREDIT will not be given unless steps are clearly shown. 1 3 d3: ZS — 9' 3 (Lu ._ <9 ‘2’?) (\1'9’37 x ”7; “film; fix x333inm elk: BmsudJ-A @ 9.1“ 9.47" :BmSLL @ / \ — a gw’ilau = Lta/nu +C _. 0/ 4 ’1. W 7: ——~ + C 9.77. @ SHL— Ci)! 2: —J-—- mozuw 1: (launch. I 4— 7-1 \ie f; .flwmflx ,1 .4 : blacu-I—tmflul‘VC CD :Qh‘JH-x‘ +Xl “PC ®F S" :frcix -_: Lanr+xZ +rfl¥lilfi ‘ IE r “5 1 d C b d Y d :1 t 0/, () 1 \/1+—332 :1: [oumaynee :l/fsemtm nsecm+ an$|+ ]. gfi Jfi ’1 30¢ a sac ?&.L3.J~L: 1 W gfi/a‘ seen (a, mztcuw» CL'X'; sacuAA a: a X “-qu _: 942C“ 4 IE E 2 [24‘3ch mam? ———Qm)326,‘—f +1W§l TQMIQ-l-Gl‘imlfi +1‘l Rm 2+5; @Z—f \F ..._. '3 “ «2+1 0%: (El ...
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