calculas - Unlvereite d’Ottawa University of Ottawa...

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Unformatted text preview: Unlvereite d’Ottawa - University of Ottawa Facet-:3 ties srlenees FJC'JIlf of 5:5E"EE Matl'lernafieues EL de statistique Mathematics and Star'stics FINAL EXA :xl-MM‘H 1300—2002 A/ 3 :1 December: 2092 . .L NmelZPrint LE-GTELY} C" L: l \Ufih 1D. Numb er_ Instructions-This final examination eonelelle of 15 mulniple ehoiee oueenione worth 4 [homes eeeh. Your answers to [he 1:1ultiple ehoiee queeLions moot he clearly marked in the fiqueree below. There are also 3 long answer o‘oeetiene worth a iota} of rill pointe. For the long answer questions, you meet ehow your work on the exam itself and elem-15.r display your oneweze. Do not. unsteple lhese pages. NO CALCULATORS. ND NOTES OR BOOKS. Reel: sentient will reeeive one booklet for eeroteh work only. Scratch work will not he gradefi. Do ILoE unetople the booklet or remove pages. Your name! eludth number enrl see-L number meet appear on the booklet, end you mueL turn the booklet i1". ml: the end of the exam. E‘v’lultlple Choice Answers: 9 2.» e o o L: e e E. o l Questinn 1- CalcuIaLu f “([1], when I [I] is given by Lhe Following function: _ 4r. |-|_1 _ 352—5 ir U“ I. .I’ I 'l IMF" W , 6%?” J¢wm~> Lat-ax“ 1 @331 €33 QIKQU "- K‘Qbfl-flma) H rq/ K331 h 3 Question 2 ClaJnulflte: fin?) 'IH . ’1. “Ta 1r k-E ‘ I go in“ 1 T X43 Tag-1 \fi_ 1-) x a; 1*1 Question 3- 5'1an thn interval on which the finmtiflll fIZJS] = :54 — 3.175 + 1832 -— 113'. -| 21 is mnuava down. BH—Dcul} Eli-00,3} D) {-2.3} E) {I311}. “’- Ll'€3#1quifl 133E er W») : \aquwg-fi Hi: i: at; 7" WA 553‘} '2 Va. \fi."3\ Lisa ‘ITNME: 1!; new m'wa ‘Qraw 'jxrr '3} 3 Question 4- Find uhe t'LlLIaLi-fll'l nf thr— tangent Line tn the graph off 3; — $4 — 53:3 + ‘3 when a: — 2. A]y=—28$+2fi EJ-y——32I4212 (3 y: 323+23 ij— Hflnr+5fl y = —331'-i- 3&1 gift t5 J 1: '" Q1 \‘h. Qgfifi Him: 411 Questinn E- Suppuau a, denmnd functiun for a pffidutt it; givnn h}? pix} = 1H?- — 23:2. WhH-‘L is [11% dammit}? uf :ieman r] when I : 10'.’ L“: rlmmmd elaarztir: at this poinL'? A) —%, infllaatin B} —§Er mamzin I . —i, iamlmtic F3] elastic a h n- 1 ' ' W ,3: . “Linn Question 5- Width of fine fallow-mg statemenns is correct for the function fix} = {r- — 316.2: + If A) m —- [II is. a local max. B} 3: = fl is a local min. D] a: = '2 is a [med min. 9.: z 3 is a local mien (“x m t w? mama Ev-W'TW *W‘éfl F'L — . ' Gm [Um—“LL 3—: km 13, q (jg) £57 h -3 a“; J 1:; QUE-‘3 M-‘rfiq‘xfihb 5|€5T I a ‘ 3:: may EEG?) =~ <3 H 0 *‘r ‘5 (I \W‘ wk M \m “at f Question TL Suppose y '1': defined ivnlulit‘jtljifr as a l'unctinn 0‘5 3: by the: equ atizf-n: 'J’? + VIII} = #2 Find at film paint {23]. m— B}; c}; D}§.E)~" 5"! ' ' . r - .4, J; 1 _ i’ 1 - ‘_ . 1 1m L, i p11 1“ ,m M mg.) 1%Ll :1.t1".,ra_--a x . l L\L ‘3 “Oh-1 —> 1 "'1 xi + awigkkkia T> 1* 1 ‘7 I f 3 "‘ ‘1 :‘> ' *2 m 1 ‘1 ,7 Question 8- H' flat} a function and: Lhat fTI} = 1% and Hi] :1; filld H3]- w 3}?)01” D}% a}? I ‘1‘“); '5'; g‘fi Exit '3‘ 7“ Birfltfba} _ ‘2‘ ' E 5";3 5'1 Uff— :: :1. <3 3 0'33; J0 EL?sz a}: if; . 3 - '1 cr- (5; a -':-_ a E 3 LT! Question 9- Calculate: S 5 1 V1 1 0‘ Earl 57; fut) 13-?- ‘F; wrigk )JVJ‘ '_' ‘iLK‘LJ m = “ill -—E> EH *2- 9wth 1 Q L. _ W1 4‘? a 1 "ED \ 1’ l. u ': J 3 ’3’ 3 Question 1i}- Q nest ion 1 1—Ca1cu1am-1: r'Z‘C- { 25"4L'rf:r A) H) '3} g D) The imam-3,1 fliwrges. u A“. .p-.___ a. a 41k, Question 12- Suppuat Lhat frn' H. certain pruduct: Lhe dmnnnd function is given by Diff} -— 21 — 3.1: and the filippl]; funntinn is given by Slim} — 2:2 I- 3:. Calculate the producer surplus. Questiun 13— Cultulam I] mitt: B124 0] 25: "5 IE FR (“"1 Ma 3. 3 (11-15\ = Queatiun 14— Fin waL 1.2. 511' rlnw the curve fir} = E! — :52 and alum-w.- LhL—E x—afls. :33'} 35 E) 40 171 for fE-T. ? I] — 4r.“ — 3.12333 + 22f + 11. All-5 13116 61-15 D)1[} E) -1! - 1 Q E 1‘1 -- “JR _ _ 1 {3 W)“; #H 1“1 {:0 Questinn 15— Consider the function g] = FIE Eirhinfll flf the [blluwiflfi stammfints is correct? A) fflfirgyj ham: :3. lnmJ minimum at. [[Lfl]. B “fr—{Ly} has a local maxinmm at {0,0}. ‘ fix-1y} 1135 a satédle point at [_fl,}.-fif‘—‘ D] fix: 3;} has. a saddle point at {-LJ}. E] fins: 3;] has a sadfila paint :L’r {1,—1]. .1 M -M -- it 1“L “Em "Wadi £5 0H1 0? k0?) {2‘1 : mafia. Long Answer Question 1 (15 points] A pig farmer Joust construct. suitable fenced—in regions to contain his pigs. He must constrizct a roclengolar area Twith two additional fences across its width, as shown in the following picture. Find the dimensions which maximise the area. he can enclose with some f5“ 0f fsncins- Be sure to explain why your answer 1'.= no absolute max. You may assume all thrno Teciengles have the same dimensions, hut this will not affect the answer. r“®*\ l III Leittticomismnctumhfi length] w ‘mvc QM'ulws’sidoo tr arm,ng \oie cm taxis} he wath twin-N1 e.Qtoor3\\1lL{ Sc Nip: Woo \1—21 x11 Mw-mmtggmflwwckwwsl “1E Wane} no. sews. Tim: C? u. ll] {Queatiun 2 [1:3 puiuL-S} Consider the iwu ILLIIUliUfl'zl Jim] 2 1' and y = 3:” — 21' {3 901.115] Find L111: inLeraeclion points 0f thra. graphs of the two functiuus. {MW palms} On the ne-xL page, graph 131135-52 Fun minus-1., and shade the regiuu hounded by 9":1], a: = II] and 1' = =1. {cl-{Li points] Find the area. 0F the Rhnflm'l ruginn. Cg Nit-Mm; X'Tf‘g‘fi “3'1” Xfirfllxuflh 32 M fix-flm 1L0 “Ax Q‘f-L hall-.3;- Sflfi} Hum $m~r§TSL . 3 C4} 9.. fat-a “I . [x '“ (33- flxfikh + nga-AA + "7:8 ex“); fr“ it}: .1.- W 32/ 93"" I?" -r w “I?” Ju Laid-r” 9/ )6” H' I U4 y ll Questinn 3 {m Pmnm} Cnmiflnr the fimmfinn of two variables fix: 3;] = 2333 +331: _ 142ml; _ 1L Find a” Critical points and idamfifi:r thfih. JEFF“; {D F?“- ® E13: [5‘1'\3~3t if) 1% “fax, Sugm‘m ® éi—aang Emtxr‘h—AQ 6?:- K‘; O or '11q_ gt) Alli-{2:1 ‘1‘“ {1,215 {5f k0 IE3} HQM 50 EELF&{£@.&§<019}fiuuw$mwwr Far LL)J‘%) J pj’b c911 Emfioj '51::- [kqflh t5 ‘1» \ai~\ W'Hva _ 13 ...
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This note was uploaded on 02/24/2009 for the course COMPUTER S MAT1301 taught by Professor ? during the Fall '05 term at University of Ottawa.

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calculas - Unlvereite d’Ottawa University of Ottawa...

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