finalf06sol - Hague; — Lab Hectinn: MATH 2 lfi — Fall...

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Unformatted text preview: Hague; — Lab Hectinn: MATH 2 lfi — Fall EUUE Final E}: am in at iCITI REA]? THIS This |.!I'=C.lJ.IZ|| cannhm rI'IrIrg Jrrnulnfreri-H-j: ‘:.'L11Tll a total Uf lfJfJ fmiutfi. TIE,- fir‘m: fix-v I2|LH"H|.":I1_'ITI'_-i are run Itiphe. r."IIrJ'Lr.'e. "fqu film-H5 tic-1' those five (“mild-5115: an“: L6; 3w. {mum-car. in Line: I.” hire hehw. Problem zero has hem:- dnrm as, m: nmltmln. Nu Emrlinl c:r1::rJiE wili Em given fur the firs-.11; five firm-items. rm dinllblu frluxrli :r'ullr' wcll'k. l’k-‘un'e dc:- rmt. fllfiflt. The use t-fhc-nks. talcum.an m1] :t-lmmn-a. {:rfiuputersl “Mam c'IIHHL Shears: and .111 aids is 3:11-3:13» hmhlhjlmi. ("haul Junk. EHDW 'r’flLJli. ‘L-‘L-"UHIf. Indicate 530111“ answer Hwi nth»;- a 'Eul | “HTML i 100” | ‘1 Plflblmn II]. {If} — H -' H puim‘a‘j [3,] [I3I min-Lu} Whit-IL crl' Lln: full-wing hl-HJ-Hlfifr'fll'ti might! in Stephen D-JEMk-nr‘s; c:-pir:ic:-r:. be uaeful Fur this mnan _-"'L. flux-inf: IIIZIij:.'JI: — | .ur5r_| nag-film] = mag-:3] — air-Pfiz- _ ._ . _ 5 _ _ . . 1 c-::-'~I;2:':~I F]. anti-1:; _ EHITIEIL'IIL:IJ:'~IT:'.!'_I tin-LI, 3313(1) = . r. 1 | (11:42:51 i L. nun-rim: —- I). 'l'hrs l'rJTnIulfl-e ’r'iar therit'al coordinates: arr .“L' = .'J (:05 [5'] 3; {J Hill firs} Hir: ('1?) ,3: = pens-:5] @111 nl‘ 1hr ullm’it. [it-II [fl minty] ‘r‘r'lu'cl'. 0f the t'u::-llmw.-i:1::-h bLEl‘I-HULEIEH might. in Tmmr 'u'lr‘mlny'a erin'zuu. be “awful lb: 1.2Ii5 exam. in. firm-1m?) = 1,32 and Hincfirrl.-'. I: _ 1.53;; U. CUE-Ifrls'iljfl = film and Hirl “is: '3- Cflilzm'fi-F ' xii-"E and Him-{filr’fijl LEE. D. :IUHIHJ — | and sinfL‘I] = l]. @A II nf the Elbe-m. ah:- I’mblmu L. I}??? — W + If! pm'wisj- [PL] W priiwbs} [I' fl" — {2, -'.: '1';- Hud 1" = {—2.3! 1}! than III-1? equals; ."lll. 3 IE. -—I C. 1 3 {E E. Hm“: ul‘ :th “hm-ct. (In) I: H? paints] If 11': {2: 1.4}- mni 5— {—1.3 1}: than 3-: fl equals ..-L {I I.—LIJ.—3} B. {11,11'., 3;} @g 11. 41.13} [:I. {—I.1.'1D,3} E. None nf Elm alum-c: PT‘fl-hlfilrl 2. {it}: 5 + Emilltflj I:ij {:3 winks} Curmiuler the tune I“: paranml.ri.5¢-ru'l by 113.} -- {F.ta:1~(.§}— 5mm. flfi'fltslnfli} | cmffl} rm 3 '51 i '-'-'. r]. The length of {3‘ 1:: A. 1-13,”? (.1. 34,-"? I). H‘I‘fiffl |".- Hume (if the above. F'H-y = 4.[saw-flatuwcmihifi-t, aha in Ir Lmsfu *flriifb : «it smifijlfig, twatfl§ A: ‘1‘?“ {HF {:31ka H} A Lh-H’ 4 {EL-£14.} =$t “I w ‘4 hwy; «1-: S Wrmése = E'E-EEU 2 11 E- I IT'S-2' {5 minis} CHEJHMHT the curve Ii} pm'auml.:-iacc~.li by r-[.'.‘_I = {1} mam —fij11:;.'.:|1,lf3_ .I, Hing] +EDE.:tJ} rm 3 E '1 E 'l- 5m aquatic-:1 ffll‘ ihf: IHIIHHHL line 12-3- the BMW If?" m. I.|H: pmjril‘ li—i-Tfil'fl! —1‘.- 1'3 @fifi) {mainfrfl |- 3531?: —1 — a} 13. Figs) —{ my" _ 33fi___1_,;_~, its} — .: Mr“ + 33:, —1 —- 3} 13- fIlI-‘fi' ' {u-Tr, 1'“ — 331':! —I — 22$} E. - J: 72 — 33E, — III-W - ._1. ‘ "F‘Tt‘l '-' <1 Eihlfijfiilj 4. Legit-f) _"|..|' a run = '11” sin-.hr-J—‘p fl“: M9; : <—F~“.W"'i Ff) Jr'E (p, ism—m Pl‘flblfltn 3. [FIC' _ 5 .'- 5 pumice} [a] [:5 minis] 'Fln: IIiIZ'E:r!|.iI:HI. {min-err;in uh d. unit vet'trJIfI 0f Steep-E's: ascen‘. fur the funniinn fig, 3:: 3] = MIL?” + [migrng —' 111mg? at the paint (2,1.1] is {lf3r2f3.2f3} E. :4; wflm 3,! 3;”; E1. :1! EH : 3;“ £13. 3,-"w’13l- Iii-3!:I‘flilithillJ'JH. JEFF? L- < 1%.1 3 1/; ? if? Liam: : {,1‘1‘1‘? xmmfifiatfi [1'1] [:5 prelim-His} 'I'I'm. uritital priIzt [3:33. 4.1.33} fur Elm fun-nun” f-iragyj — may +yflfi;+$“ 11-: _":'L. EL Jmm] Inininllnrl frjr' H. :-I Iii-Ha] Tnaadmum for CI Edit 1.10th firm _.I'". 1 .1'. . 315.] (if th‘: Hhm'ct. $13; E $3” $5 Jinn? -::-|' the above. ; . 3-6;: ‘-' lkj "'7 L 5? = + 1 “’“j ‘1 "‘ L1 [If—L} : (EL 4 31.32% m=?’ Effljflr En4'E-qfir 1&23; 5; Kb: LHLI} _L 2_ —% - 5‘” ““W‘ '“H its. Problem 4. [:5 115-121-2133} T.f:L f? In: an}: curve fmm "111-3 pic-int {2: 1-3] m 1.2m pninl. {—L, E]. Tim inwarul .n. j [‘21];- + Inf —' L:| d3." .— {112 -|- 2313' | 1 rIy IL. 15. equal tn :1. 14 _ 4 .. _ _ I3. :4 = EU?~c1u~ .- 5; [4.95] -- [2.1) .54 C. é 5-H .5 ,Lfi_g—:_3’Lf |-‘.- The waver depends m: (3'. Lu'r‘m—a ELRLL‘) .— KLLJ +11% 4 x. 4% J: 23.1, END my MULTIPLE CHDIE'E Bet-DIE,- mtulll.'||||:ir~.3': {1} Media- slu'l: :r'nu have transfm-md yum' Hum-H3 fc-I muhlmrm | “112-:- the dun-I. cm nag-e tun-n. ~1..~.... . . . - ' LA, I'rlrukli. :-.n.4.a. j.-r.111 like-VIE mrrmily |TEJLjfElIDI.1_‘f.-'I.'J:.JI' rL-IIH'r'r'HTH m1- pmhl-L-zme. ] -1 m the dun-I. cm H513“ I'II'IHj. Problem 5. Hf:I mint?) Suppmm E 15 I110: L'flg'u'm in spam Ellfwirlil LEI-H th-c-aw. ul' I'r-i.n;l':11$ cmtorm'l cal. :th urigiu HIH‘J ralhcwcr |.]I+: ylurav z — 3. Suppuau that the denaitfir of E is given by th-n I'm-mum cc-sfimlfpfl lcgg'm‘. The mass (if E is Hz-I lag. F'im'] Lhfi minim nl" male-:3 if P}. I’mblcm [L [M minis] LE1. T Elan-Mr: Lhu Isrulgmu. plant: :-|'. Lhc~ [HilillL {13: _1_~.fi] hr; the gmamntflc airman-,- .51' air-tun by - | w I rm U] — m2 — w'. ringer-2 : 12:2; -r.- WILan l] E 1': in." 51 and -.' i 1': [1. Eémw Hum. thcr fuigir: Livia IZIII 'J' . 'I'h.-'.|. i':i_~ bI'HJI'i.’ that the 11-5-1111. [£113.03 i=5 u mind-inn m an Equal-lam which flea-31'in 1T . Fate: We will 3,11er lavish WELL-id Ltl'uclil. 1-D: mathnmzstjmlly MILE-311E Wfil'k: and wt: will IIIZI'IL! cmL ILL:,L_>;1I.'I'-.-:: EHJilllJ-i Fur rer-IIHHIHJ" lfyuu submit uniting: yin] will rt-xneiw: 5 EHZIiIIIJ-i I'flr |.':Ii1~[J1'rJh:-|ETI1. [ED ||_.l.1—"-.I"1'5‘151r : 1“Ill-4:: Ll. mu :-_ —E_1 my. LLmIL'LME-E ‘1- 1': 1 LA ‘1'“ I? “If ="I. hag—1 VP:— -|L:{~.-c—E-} +|Eah1~ {~33} .- :o[2_5} :5: 1:43 "'33"- JIEIk-j +131 :CTJ ._ I‘m eru ?‘-“"l"—' film—u; @fimkflfi (5.010} W; W‘ W I P $51.31 4 EH} "I gin") 7'3 i-‘mhlmrl 7'. [-‘5 3103.115} Suppose {315 the curve hflz‘flr:I-::‘..ri-.-1L:c[ h3- rfsj. = {<1cus{t_jl:5111|:£_‘.-:E} Fur CI 1‘ *‘4 2?. PM the I'm-9 inmng ul' l-‘I::.-::-a 1 .1} — {3:22: 2:531! L'Crsfi'yj} alum: le nun-w (if. (Hint: Sin-km? T'Emnnnr: may be. LJHE'fuL} Fififi) 1‘ {Ll'firtflhfgj J fihfi'lel-‘h 2:} Der-El; fléeél‘fi ‘.' {flung}; 5:935:73) “ r‘ffi‘fg"; (:flJDI-q'f") DUI: gwkfl [#11 fl r _ I. T '1'. Egg 1L?) -L|'r' dE'Lr—Egflfi LII a I Pl'flhllflrn 3. {EH — 5 1' E fire-Mb.) J.L:I. H he Lhn regifin LI] Helix: helludmi helm? h}: Ler [J]3.IU.-' with equetéen 1' = —2. en the eiefi by the eeeet'zen as” — y! = '1 end "eheve’: by; the pel'eheleir] ef at: - 1:3- I'c>'.'u|t1|.'mr| z — -'| [PI-J {.5 firm-his} Shel-ell H. ‘ILL- reel: be is? em“. :1":- e'a-cK-iw-‘el ‘1 LEV-‘k‘r'fl'a‘ 5'1!- {e.e.—fl. leHJHH-hhe if} £31,:- Ifb'J [1'5 mime] Let. 3' be the beunelery ef E and 1e: 5 he the eerie-3e (Ht-mime] h},- Ternuvjug :hr-g hettem feee ILL-RH the (URL: in the _|_II.|.-i.|||! z — -—?:l i'relrn .5”. We euppmee That .311 “mluvmd” c:-I"Ie:I|:-Il.ien. ll‘imj the He}: eereee S ef the veeter field Heme] = {El-AN. —21‘?;:?. [3-22 I EH3 -|- Iii}. (Hint: the divergence theerem 11w; he useful.) 3.43 = if E-fi"§§ Eris: 35"“ .r 5 CI} @ .35" i” $93 Lame} ex! = fl? “Jefq‘fi HRH?“ 5w ee 11; *5“ E e e ewe “f e— e r we 11: 1 41"?“ a a :L “: l 7E g E 1‘3 dwell-3r = g gfiqTE—rgfi'EU-hj efl-fifll -1 tut-H Th e e - =§L T’: :weeu: 11 f_'.r_1T|t.1'r|11e_-: }'r_11|r' wnr'k Eur [Huh-Inn“: H hum. @ EASE 5' ._~. *3 Twin—3: {TL-[eajvatE-hl-E‘) ‘E‘IE [flfl'ffl 1 re £51.21] -‘ {my}: mama}? a} w; E “— ai-meh ardflh, a“? Er 154i : L0,,U1T"? «ii— ammth-LJM 13$? HUI-FF) m .J 1 1‘11 21———_ F 43' —— ENE E" 18‘ <leirlfi—fi‘? (full; {nu—“7 Agar c: .n. '1 .h H ETII' S TF5 .—_'l'-...- _— {.1 END DF EKANI ELEI'L'M: Inn-wing; Lhcrc>:—::-I1||i||:-Il.in1l mum: [l] MEG-{I2 511m y'rr-u him-6: :ErLILFlIflFI'Ulil yunr .-:.II:-c'-.'.'I:I':-i Fm ljrifijlfll'llfi .l *1 m the chart (1:1 page Grant“: [2] .‘Ir'hIl-u: Hum gm: have plantfii wur IiflJllE and aectinn number 012 page amt. L3} .‘v'hIkH Hure 31H: t-‘JTTI in your exam 1::- thc pl'nJE‘ZC-l'. 12 ...
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This note was uploaded on 04/16/2008 for the course MATH 215 taught by Professor Fish during the Fall '08 term at University of Michigan.

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finalf06sol - Hague; — Lab Hectinn: MATH 2 lfi — Fall...

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