Docsity
Docsity

Prepare-se para as provas
Prepare-se para as provas

Estude fácil! Tem muito documento disponível na Docsity


Ganhe pontos para baixar
Ganhe pontos para baixar

Ganhe pontos ajudando outros esrudantes ou compre um plano Premium


Guias e Dicas
Guias e Dicas


logaritmos elon, Notas de estudo de Física

Logaritmos, Elon Lages Lima

Tipologia: Notas de estudo

Antes de 2010

Compartilhado em 27/11/2010

lucas-barros-10
lucas-barros-10 🇧🇷

2 documentos

1 / 64

Toggle sidebar

Esta página não é visível na pré-visualização

Não perca as partes importantes!

bg1
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18
pf19
pf1a
pf1b
pf1c
pf1d
pf1e
pf1f
pf20
pf21
pf22
pf23
pf24
pf25
pf26
pf27
pf28
pf29
pf2a
pf2b
pf2c
pf2d
pf2e
pf2f
pf30
pf31
pf32
pf33
pf34
pf35
pf36
pf37
pf38
pf39
pf3a
pf3b
pf3c
pf3d
pf3e
pf3f
pf40

Pré-visualização parcial do texto

Baixe logaritmos elon e outras Notas de estudo em PDF para Física, somente na Docsity!

OIRLSEACACAM AENADA UNA ANA DAO ADA Epa a PRJRAGGSMANARARERARARAA, COLEÇÃO DO PROFESSOR DE MATEMÁTICA SOCIEDADE BRASILEIRA DE MATEMÁTICA A, mr PIIIPIIITIAN ) — AV ETE Em “REP PPRRIN O ELOT1 (VT ce Terror A [4 ES ES a A VA PIDIVUVOCSU BSS Logaritmos Elon Lages Lima Segunda edição v bstololedadoda 009559 SULA VU | eu] soger uoTa “T66T 9P Ola 1049] OXOUPP Op ONT “opóIpa aguasead ep “ossaroqui 9 BLUgrrd uroo Mnopino anb 9 sosino soLIZA WO [euláLIo 09X99 0 nosn onb “sato BpuBi 9p Seuop E EprAIp equi vpute ogsajtuem “OjuaAo Op BAIRIoTUI Bjad “TYILIA 2 sojuompoprige Snour IvuIojxo virá opisedO v ogoAoidy “T66T 9p oxtouel uia “oapouep op or ou oprrtur “nei opungas op vonpuIajeW Op Saxossajoid ap oquoweutox op ojaford tm op oqed ouro? “IVILIA SPepawos vd eperueury 107 ogôipo aquasord y “BIBLIA op earagiscag opepepog ejod 'sogórpo setipa uia “aquowjeuisio oprogqnd toy onb o sodimay PY I4oxosa enb “sougLieão| oigos ouigytsodxa 09x0) ouanbed “wn op vpeonipow opsIdA eum 9 EIS OPEP. eia eres sa. eee ce rd Rc 2 RÃ A An A CRTÁ A CA AA DA A ARO RD ÊS Es 3 o) PS ls Es > > 15 > 15 Es 15 | Lo [a Ló 15 '> ALLA EDP DVVOAO--0-O OO0ONTCTOOTD “(AJT 2 (2) sounirso] sop emos vos 349p ONpold op fz) ountvõo] o “A a x soanisod sorotunu sIOp sotreaydnnu q 1 Hesoj ' nu st Eu! s (g “eNoutp x (7) sountrdo| snas wos 1911000 PAP OUISAU O “ajuaosaro tuapio ta sorsodstp tosaAnso epranbsa g euntos ep 2 SOIunU so ag (y :S90STpuoo senp Jozeysnvs SAP ejaqri essa “(euaisis ajonbeu) 7 ap ounuvão; O opeweyo (x) [vor OIStUpU WIN *eJronp v jostu ousou ou “apuodsaroo vpranbsa v vunjos eu x 04! ISOd Jeo1 Olotunu vpro y “seunjoo Senp tOD vjaqui eum quauisajduns 2 sougpunão; ap DuloJsis wm *L | oops Op opjui ou “ratdeN p107 “1optigoosap nas 10d oprutõem ouuojuoy “7 “Queuouw opep unu ajunsIxa pzapuris ejanbep spepnuenb y Teuojorodord à (ouawrosaroap no) QUIS AP EXP) vÍno ezopuriZ vum op ogônjosa p ou wronpuajeu T9ADIOSAP 9S SP EXSUVIL PITUN E tuampsuoo “fejouauodxa ogóuny e 'estoaur ens v 9 vorunuedo, ogôuny e onbiod quauvutrad 9 opôIsod vssg “sogsporde SUNS UIQ 9 BIOÚPIO PISaU UEdnoO anb jentoo OEÍISOd Y OpIAdp “ronpuaje 2p ousua ou anbeisap op opáisod pum J99RIOUI P “SOSIDAIP W2Q SOAnOI 10d *urenunuos sounirão| so “ossp Jesody seorugnapo seyurummbem sy -9d Qxa apurif woo opednoo afoy “JOpejnojeo auaroya ap xe3n] asso oduo) wnB]e py weIoprad “orpuoror1y quaodxa woo opôgrouaod rum no “sous teB|p SOJNtU UIOO SOXUNU SIOp op opseardnnw v owos seprongd -wdo sogópiado “opstoaid 9 zaprder woo “uWassemajo os onb opugrunad “Oonpuntre ojnojpo O reoyiduwis ered Oludtunnsur Osoygarrew op jaded o tvIequadiasap waq op) otaw 9 sojnogs som aurinp end 'sounureso; so “Ez :suoBesuouI sojuinõos se initusurm v PIO] SP Ojunsse O opumuasaide “SOU vão] SIGOS IRjUdUIa|a OpSIsodxa pn Ugo OI ouanbad asg ovinpo.guy my ENA: TETE + 9oDACCDDPNNTAA À um Em um um - N00C0D00TATTT: 5 E) [a I E a 13 5 La 13 lá 15 E) ls Ls E) E 15 É 1: | | DDD UU ] ) BUINT Sae uoja 9661 ºP IQL “oxoueç op org “Setup xa vIed sagisonb sestaatp sejsodoid ops a 'soresua ap opSezIjvol o opssnastp exrd SSJurssaIajur seuro) SOLPA SopHaBns orgs apuo 'c7 ojmidro o toquaosozor OSSIp WAV "sopiõuoo U2IOJ JOHOjUE Opórpa eu squajsixa soro SOLPA OvIpa ppundos ejsoN OBMPA «Z BP OPEpId ap Seunjoo senp ap ajuatujeouasso astsuoo sountreo] ap egg un “SOLBISIDATUM solossagoId UIOI QUIWIRUOTIL [DI nos 2 sagópaand sens v optaop “Sing op e onb op Joreuw ont 107 sountIvão] SOp QUIWIAjOAUISap OU Jade N 2p PrUgngur Y “OZ9T wo ng ap se 2 pI97 ta seprorqnd turioy 1ordeN op sengr sy “sountvr3o] op sengr sextotLid se erva qnd *omno O ajuaurenauy opusoayuoosap sajap wm vpro “oompuaeiu 2 030/99) “s990989 a1gou um “(LT91-0SSI) JatdeN UYOr 9 “IOUIAUI 9 OMMPlajeUI *sOdILIQUONSE SQuawnnsur op aqurouiquy “odjns (TE9T-TSST) IBINg 18Of 'sountvõo so ud noomuoor unssy “opurdnoo twyuia os son jenb op “quejodur ewajgord um op opônjos % 9puodsarioo euaQoIsap [tl ivrdugpruiod sajdwis op vem as OBN “ajuour -auopuadopu! opuryjeqen seossod sreur no senp 10d quaweaue nus vitoy 9? vOYNUd viagodsap opueis run onb vrougnbar uoo coauooy “sejdwIs seu ojueod 9 Jotajur atogdsa op eum » ajopdsa sg no «Tt Pp Ogdviado epro Jznpoi ossptuiad anb ossadord wn opjuo as-varino -O1d “ajopdsa sg op sagãpado se wommsuoo opSearpei a opsviouajod onb ojuenbua *ajopdso s7 9p OBS OBSIAP 9 Opóvaidujniu tajopdso sI op sogóp4do se weuos opóenqns 9 opópr :sodmuS g wa sepeoyissepo 128 Wopod seonguntre sagóeiado se “opepjnoyip op neiã o opungos “Peruomepuny eurojgoid wm “O09T 9p souwrxpId soue sou “pro Sozjei ap sogópixo 9 sogópiuaod “saostAtp *saoSeardnnu pzaisard woo remoyo assntuttad onb opojyau tum Ieyar “UISSE OUIS9W “epipungip auawajuoroyns OgU vpUre PIOQUIS “SIeUIIOop SO95I SEP OLÍU9AUY a]U9901 E TOO OpNgO PIOJ BÍ OsojooId orpxne wWn 'soMmPunLe sojnajpo sosotoqr 2 soguo] vigixa OpSpBaAPN EP 9 PILIOUONSY UP OJUIUILAJOAUOSAP O TAX Ojos Op uy ON BLIOJStH “TF VTC EN DO PAT PBONHCECNNP DUDE UDDIDIVUOO VUSVULUDDDÍVUVUVULULVULUCUDDU “Do189] Diugjvamba ap ojoquis e» HDL E Br oduoxo od vodu Y,, SSL E V Opssaldxa y "vo/39] opôpojdiur ap ojoquis *<= fooz)=,u soauIsod sipau sosaunu sop ojunfuoo *,.H SID24 SOJaWNU SOP Ojunfuoo *H fra Bt Ss FRIA » WND2TZO 8-8 SIDUOJIDA SOJUNU SOp Ojunfuoo *& ut eectete tio get) =7 SOJtau] SOLWMU SOp Ojunfuoo “7 ut te T=N “SIDANIDU SOLONU SOp Ojunfuoo *N] :SogópIOU Sajunãos se SOuaresn OIAI] NSSN S9032J0N setuos v 1anbstenb sozotunu stop ap ompold O xznpar Sotuapõa pp pie 10d “pero ens vp opexpenb o “oxunu epeo op Pisa pata epqu eun op os-erag “s(2/2) = fi ogóuny vp soiopa so pre Frode ! 2 “somposd ap ojnojpo ou 'sountre$o] Sop Jejuaturpns omnsqns onng *Z | “SazIe1 9 SEIoUgIOd 9p Ojnojpo vid apepinnur “ns BU IP[vJ WAS ONS] "SO1ONLJ SN Qp steu op sonpord está Ea ba APepjnatp P 9 ONINAuOUOBEN Opolu Dsap suafrurasap sep eu) :v)JoN “zo8to x eL8'o (9 “e(TLLSS'O) (q "seL'0 x Te6'o (é :OxIeqe sompoJd so ajnojro “oporptu asa opuesn “(A — z)soo + (A + x)soo vuos ep apro » quatusojduns pros oprinooud À - x ompoid O “(A — z)soa a (A +x)soo oi sou ara v QUDPAON “À — E RôUOIagIp vo À + x vuios v sowepnopo À = sos a X = =so2 nb ste À 'z soxotunu soureyr (nowojog op odio) o apsap eistxa enb) seoLnotuouoBIm sagSuny op enqra eum aprotour J0d “19 io soprpuaardmos ogisa X 9 X onb 10dns sotuapod “senda sep ogáiso 2 a steuis snas opuepnu “reordnjnu exrd x o x sOwUNU SIOp Sopra z : “(A — m)so> E + (A + x)soo p= fisoo. 7509 T :PLROUIQUOZIN OP PjNULIOZ vproaquoo vu opraseq “onpoid op ojnojpo O rIed ossooord wn wrariopr “sotmueSoy SO vpuIv Opuadayuod opu “Bing 2 JatdeN op Saiossasajur so “T SO JOXA “jeUOjoeINdtuo ajuaurejinso vzomeu ug ogu enb seuojgord wo sounuvão] op saosearde ap sormuatara Soldado sunsje souarp “py ojmydeo ON “ooosuLnur iojea jaspiodide 19) eme ns “sengyi sep esneo 10d seuade sajueodu ureia ordyuud ou an! pa -v8o] SO “opuas twIssy "sounHvSo] SO OS SOpruoror|oar quaueanso op: soduQUOI 9 soaIBojorq *sootumb “sOoIsty SOuatuQuay soLipa 9 seonpua) ru stay SPSIDAIP OND JENSOL OI [LIS WO Serougro sep 2 ponpuory vdeg VANCE di Dm Dim Jim Di deem ii ai DADD-DDLDU-U-U-D DCD DU Feto — — OPVONCCCNONPPPTTNANCCCNATONNTTITTN PP OJU9UITAJOALOSOP O “spongunpe soospiado JUNE pIvd ouOssod owod SOpEIUSAUI OPIS lu soja vsoqua “oraja WoD eluguodwr penuoo SP 198 é prenunuos a q rpuje sountresop Sop opmso O seyj -seompura “BU SEJ9QUI SENNO LOS Opuadauoar owsaw o “omajpo ap oquownnsur OUOS 9SSNUY nas Op Oy wezoprod Sounivõo| op senqpy se “seIoprI “DOJ29 Sep epesjnarp sreur zoa ppeo ovseziynn v wo “Nuatajuadoy “SouiuDBo] SOP D4894 DSOYpAD4DU DP OpÍuosap nun vompuBis anb “onduosap suouDo UntOUnILDÃO] 1oNiutjy On O Sengya sens se nop “eragoosap ens ap JOjra O OpuMdayuodar “juawesapow oque; um “otdeN oudord O *OUIOUONSP OP [euoroeindiuos 1opod o ajuamesva PARUSuNE,, ajo opunãas onb euoq -0989p 2AOU Pjad Ojuawdoyuosar nas BALISNE “OZ9T 2p ejoa 10d “Iajdoy Pr eigojouoay ru o BRUZIO EU PAISIoop as-nojasar ºpepuun ens 'sountr -BoI sop BIGOISAp € urrIopoons onb Sojnoas 4 asenb so queing Teutoop opórraunu ap euosis un souresn 9P 123 Op ojtorord ur onb “SOupUIpLO souDBo] no “SIDUJIp sous -v8o| sopro so opusjuoy “opSpzmnn qropy sem 2P “enqei paou pm “otdeN woo Nusurmunf *nosoqro “PJOJXO 2p stodop a “SSIPUOT 9P apepis “I9AJUN) vp J0ssajord “(TE9T-T9ÇT) SSSUg AIuoH sajõur Oompuajrur o “rard “EN ?P sountrego] ap enqu PISWLd ep Quowiarede Op stodap o3o7 “URISPA sagórpe :sogápordnynu Tenjajo “sowrdip “sreur estoozd wonsuju “oprindaxa app stodaq “os un 2 “efas anb oanesuro q oguo ste 10d “sountv$o] op engpa run TeJoqeja op Oureqen O :ogSeszasgo sjumãas PP QueLOd eynsor sounprrSoy sop peutêuo SPEPION Y "eonpuaeIA eu ovsuny op ONS9U09 OP Opónponur 7 JOprajur 107 SounLrão[ sop ogôudaur e onb “Wg10d “rejou wgauos “opSunf ep vuryo as onb o q sountvõo|- op engyy um 2P Olou 10d eproojaquisa essa ouiod BrUapuodsarios rum “sfoy 9P vonpuIajeur vrgojouruna vN “ZIRI Pp dorpur ojad oxownu op OUNHLBO O TPIATP eIsq “OJUWPU UM Sp pLISg-U Zre1 É Jrenxo erpd “Quatpeur “qquaodxa Ojad olotwnu op ounireõo| o eondopnu “IS2Q PIoUgIOd en p OIUNU um IPAdjo vreq “sounte$o] so xrenqns eISeq SOIStUNU SIOp NprAIp ered “QuSumuryjawos “ountr3or ajonbe wo onb Olaunu o jenb “epronbso e pred BISIIP BP “engpa eu Joy eiseq “ompoid o Teye ereq "onpoid op ounteão] O 9 opripnsar o “sountre3o] snas xewos PISLQ “SOIOtNU stop reordnynur BIRd "OUIIADEO] nos O opeureyo “eJrarTp ens E OJUmU UM apuodsanoo vpronbso R EUNIO9 SP OIatumu vpro y “SoIotunu pés BHoISIH Z “4 = 60: 4 apepauidosd e epure apra (OLA 0 0< b) soupuorri n/n = sa b/d = 4 ed owsou onb sowasrsdo o “4 JRUOROLI OIWINU OPO) RIPd “OpIUyop pisa D “ums Wa “OLPUOIOLI] NO OANEBOU *Ojnu OAIISOd OIUI eles 4 19nb ê D RIUQIOd E JIUYAp sOUIAQES “O < D jeor Ounu wn Opep “voSy oo Vl = bp? “equouvd vg “DA = bj? onb Ieuuye voyIugIs ojst “Zter op OpSIuyap 10g “qo Tent 9 vrougiod eurtsa-b eíno oanIsod [ear oIatunu O 198 o40p ba? 0807 “4? = p(ojay? = b(bja?) :opuuidiuno OANISOd [ear orotwnu wn sou v opou op bjao vrougiod e auyop SOlUSA9P “OPUSS WISSY "SEpIA QjuauLoLque sopepaudoId sp no -sop OpU ? OPOU 9P OBÍIUYAP ESSO Ivp sowarnT) “O < bo soxour ops apuo bjd = + BULOJ vp 'SOLIPUOIOPI] SQjuaodxa IInjour v opow ap “O < D Teo ortuinu tum ap vrougiod ap ogdou v Jopuasa v108e sowamaorg É *D OANISOd OIounu Op puiso-b ziD4 v Opeureyo 'D/A jeor orowpu op opSuifop e wamnsuoo =»(00) 2 0<2h sagóBuye se “Quenod “O =D — bT opôenbo ka vanIsod ztr pojun v 'efos no *D e Jenãy 9 prougiod vunsa-b vino Ono peor orunt O pyttosardos Dj) ojoquiis o O < b oxour oxunu úm o q tetis o Jesn SOUZA “D 9SDQ DU X 2p OUBUDBO] O 9 À os-ga 7 PB0j = A as-asorsg “E = pD nb opouw pe op v Iago 249p as onb e £ quoodxo o q p asvq BUQ< T ortunu um op OUDÃO] O “O < D [ear oroumu um opra :Opou ajuinãos op ountrr3oy o uwouyap SIBUOIMPEI SO] SO “O < D Jear OJtINU UN OP [euojorr ajusodxa ap Seugiod sep pejuourvpuny apepauidosd vp o ovsuyap ep essod sq “equd = SP = so souto) ouoy 090 nNDONNA “abf(bntad)? = 9 :onb 1eztp 1onb OST “barad? SIA PIUgIOd puntso-nb pfno ORUNU O 9 D+ 0 onb sounA “bntadO = baD “ado = absD “abs? = abls2) - ab(40) = ab(50 40) :o807 no =a(60) à qo=s(,0) anb sotuages “orrayo wo vdey oesjpHy QB —— DON anvoan “Soluauafip SOWIADÕO] wp1 Sajuosafip sonmsod sosawpu “p oisy “Dagafut ouduos p | — 1] DIuujuDão] opSuny pum “I apepaidosq “sepetounuo vuuror (g 2 (y 2p setougnbasuos ogs anb sapepouidosd “q oIst “seotuntIvõo| sagóuny sep sopepaudoid ap eisy pum pioge SOLOTE;] (1 souatuvBo] ap vwais;s ou no “7 opunãas x ap oumurõo] O 9 (2) enb sowonp “T ap woe seoruntrão| soodung senno opuriduauoo soutoanso 28) "Z ap outuvõo) O as-eweo (z)7 own o *,y 3 x opor ereg “+H 2 tz sonbsynd vavd (A)q + (z)7 = (Az) (g (MT>(z)T+eA> pos 'auaoso opSunf vun 2 7 (v :Sopepaudosd sajutngos sp wa opuenb sowzun8o] ap DIBISIS UN NO DOjujuDBO] OpJun] vun os-eweyo 'sonnIsod star sozownu sop + H ojunfuoo o q otumuop ofno *y — Mim quar ogôuny vu “UOppoujoo seojuntredo| sogóuny 1onbsyenb senp “queisuoo 10727 um ap sous e *onb souarensow o seoispq sapepoudosd sens SOuIarada] -SQuisa *eojunLIvõo| OgôUNy ap Ogófuyop 2 somarep “ojnydro ajsoN “BUIONSIS QSS9P SOUNLIVSO] SO SOpO) Quejsuos visa pun 10d Ivondonu :SOUNHV3O] 9P PLIOISIS UM JEIMJP OP PIJoUeu eum asixo 9s 'sopepoudosd senp sejonbe types onb z94 pu “eroUgIajoId op orsonb rum seuode 2 sop-puasade op ossooo1d op vujooso e onb opow op “strimeu 2 sajduns MuoWeuwanNXa sopepatidoid senp 10d Ivzjoerro urextop os sountreão] so nb sotuareaoId OoinauooS opraso assa soturerotur ap “tupiod “squy "QUOLIPOLMOUIOOB SOPrIRI OpIAS SOUNIrSO SO OA] ojsou onb Opurpounum 9 SEpeuo/og|21 vja OO SIemSdu0o Sapepynomp setunSpe opurm -sou “ountr8o] ap [euolNpen Opótuyap e Jojajue ojnydeo ou SOUIAdY SeoTUNLICTO] sogduny *€ 4 eo 02» SS UVUVU DE Ce Co Cetera | I | I I I D aros SDS VUOLV OS 4 SD a má mi “oursguor ru um onb op 1ouauw elos , (666'0) onb pl O < U ajusodxa um rquaigo “repnonred ug “opexyold O < 3 1onbjenb e saxoLIajur 28-IeuIO) WISpod 9 w90s0109p Essag É net) qt ug tugçdo aja Em tgo'T seAISsoons setougiod se onb onso T>Z>o0 ras 'L (no y (z)7onb sr fa x sonnisod SOItUNU Teo Jasjssod oidwos 9 *g 9% Sfeo1 sor tunU auswrireniqre sopep “anb poyrufis vuroe opôpuuye y “auouuouafur a 19H HT DOnUjuvão OpSuny Dun“ apepotsdoq “SOPIUY9P 198 U WVQUIA SOwIIvão] so OtOo rejnotued tvItou Bu ep opu a (g (y sapepaudosd sep seuode uminsar “o oist 'sporuntres -O| Sogôuny se sepoy red wapea “ojnydo> ajsou SDplojaquisa wosas SIDUP SD OO? W0Q *G é | sopepotidoxg se anb reznejua ugAuOS “Teto poem! OIotunu um 9 2 opuenhb ,2 Iuyop op provem JOyjau v 90u107 sountzõo| Sop e110a) ? “opepioa BN “TeuopeI qusodxo woa sejougod Tuyap seuade souuages op ojry op wgaoId Teuojori efos + quoodxo O anb op opáinsor y “9 epepetidog vp opensuomop v PUIULIO) OJsf (z)T:4= (,2)7 onb tefos no (=) (b/d) = (42)7 onb eynsor (z)7.d = (uz) - opeppengt vg “opraoid 103 Bl onb op opmuta wo “(z)7-d = (ax) = [5(42)]7 = (uz) -b 0807 “ae = blbjat) = p(42) SOWa 1H DZ Opo rItq 'N252975d opuo b/d = + onb wo “Te198 Oseo O “quawyeui (o)tu- = (ue)T-= (u-2)7 de rpo '0=(DI=(u-2)t+ (uz)t 0807 T=4-Z-yT SOU O < Topo emd “OBM "OAnvãou oxtajur tum ? + opuo “a os 'N 3 utu— ='1 onb wo ospo 0 vide SOUWIpIsUO)) (=)7-:0=0=(D)T= (02)1 0807 1 = ot onb os-ay “+H 2 Z orunu opo eird “sjod Q = + Opuenb apra waquey vg “Temmeu Oxounu un 9 4 = 4 Opuenb apra 9 opepondosg e “oueod ()t-u= (+++ (rs (e. ecz-a)r= (a) CBI N 3 U 98 “rejnonred ug SL sesjunucõo, soosuny edeo CCVA 618: 814018 q Jh plo am A A O A A A O Fiz prvrlrielr tatoo matei aba PIVVULULDL (tara ros (Eo)r+ (atos (ureeer ta) :QueIp 10d wisse q (e)r+ (D+ (er =(2)1+(A-v)r= (2-(fo))r=(2-A-2)7 *ojdtuaxa Jg "So1oyey ap 1onbyenh OIoupu um ap omposd o exvd apuaiso as (A) + (2)t = (fa) apepoudosd e onb as-varasgo “en| oxownd wa “sedeja 10d zey 28 9 oprpauidorg ep ogdpnsuouiap y (ot 2 = (,2)7 as-mor b/d = + jDUOjDI OJoWNU OPOJ 9 ,H 3 E opos vid] "9 apepaidolg (Or=-(o1=(A/DI+(s)= ((R/1)-z)1= (A/2)1 “Ojtajo woS “(RI ET (er (M/ma ava *,H 2 fz sonbsmnd cava *s apepatidoJg (s)T> = (2/1)7 opuop o=(DI=(z/1)1+(2)7onb ps = (z/1)-z op “otaja mo) (=)1—= (2/1)T asus o0> (2)79 as (A)7 > (17 >(z)TensrA>T>T>o op Quo T Opuas “ojajo wos “SOAUDBaU SOUNLDBO] UL9I T anh op sasouaw soanisod Sosotunu so a soauisod souguvBo] wi T anb op sasojpu SoJunu so *€ apepatidosg (DI+(Di=(roT= (na soto) (g 10d “ojtajo woS “OJoZ 9 T ap ouyuDão] O *7 opepatudosg (TA (aa onb as-Injouoo A 7 x op “osmodiy 1nbpenb wa “(z)T > (AT os-mo Oseo opungos oN “(A)T > (x) onb (y op ejnsor “osvo oxawnd oN “Z> fino f>az noopua'sauargp ogs +H9 Atz os “oxojo woy o=(1)T oSo gaia Seojusedo) sogóun4 | “o >z wpnsirg'z—-o > “o —» oBol a-0> Usup-» Ê ogug uOT T—0> — 1 onb 9) OpI U SOWILIOT “OANISOA por oJouwnu tun 9 7 —» onb vogugis » > x “onoja wo) “Lo > x enb py O < U um INSIXO 949p OtiUa “o onb op Jus 9 x [eos oawnu wn og o“0-vo»S Up asma BOL qi sriE OE ug “pr TpTotOp = UM “um do) R£) SOLIIIDADIOSO “O < U opoi reg '6º **:*g*T'Q soxojea so nunsse wopod T Zu “p sreuop sowstegje so 2 1onbyenb oxtojuy orounu um q Op exojuy ourd v opuo ot z0T , OT eceipe pp Tan teto pt = um DID'0v =p Teutoop opSpuasardar run oyupe o 1221 Oratunu Opo) anb sowa:quiay “7 ew2102] O rensuouap op sauy “> (2)7 > n sowa “upul = 2 opuod (an) = 7 ojeazour op Joumuy ou ro (as pue) = o"ui sojdujnul sassap à einBis " - 5 o 4 + + 7 o e dy BS » = me wn souou ojad “ouenog “(a*n) = 7 opeaiqur op n — a ouawudmos o onb op Jouau ? 2 ouuotuiduoo ofno *sorsodeisnl sojearauy wo jear vjar v uogdmooop u zou Cu put) =(e- mu soxtojur sojdnjnu -d 61 sesjunebo; soodun4 edey uam DDD DDD DDS al Dk Dia Dome PD, esa um A A O O O E E O E va um mi so u/(2)T = 2 sowraasg en —a > u/(a)1 os (oJT/(n — a) onb op Joreu u jesmeu oxownu un SOU9XE] eu op OgSvu)suouiad “T OgSUny ep sozojea 10d opruos 9 Ou 7 OjeAINUr O onb pmãasse 7 BUIDIOAL O stod 1eurturpord opensor tum 9P 9S-BIRM “MuSwajuaprag “7 ogdung ep (x) Jojea wmu souaw or uguos (atn) = 7 OU9QE OjeaIajur opor anb vOyIuBIs pwoj sy a>(zT>noanbmo M sjDa4 SO4Dunu sjop PIQULDUDUNQUO SOPDÇ “DIuytuDÃo| opjunfoun y — HT Dog “eu auInãas op osn zey vjg (CoLproIod or quawranp Opuzssed “ep-nimo “rosmb as “9pod JON] O ) “eSuoj que) un 2 “TejuouI -2/9 BIOquIa “eruaI0a) auejrodiyr ajsop opSensuouap y :0BSEISUOuIad o = (2) onh IPI = oAuISOd jDos oxoumu (ootun) un ouduos DISIXO “O |D94 Ouounu sonh -9nh OS PT DORuijuvõo; Nj VpU E GULISAVO,| “nuinãos vwas0a) ojod Oplarposa 2 quod aisg “eanaforgos 2H «HT vorunueso Ogun e onb Jemngassy souapnd as eiajduioo Peso Os vuogoid op ogónos 7 “selapped sennon jo = (9) 1 onb pr +H 3 q Ienuosua aidwos sowopod “o Te oxwnu o opep “onb quer -23 sou wont) “ogisonb rum 281Ns eta? ogôngos 2 Opururtuexo-oy “OPIAJOSOL PUSIgOIg “D/S = q onb soumjouo (A)T = (g)1 op “1 oprpoudorg voz > — (g)x onb rm q oamisod OIswnu wn sowenuogua (ostaaur opnuss ou 94 ISP) engra e opuesn SUSLPAON “Opiosyuoo oxawnu um 9 = (DA) sowago a u 10d soup “IAIP O Quowjtory “(DM sopra O somenuosua “I SP Soiofea op enqyy eum Opumjnsuoo “u/(D) = (2/A ) sowa 9 apepeLidorg ejod “| porunireão OPSUn run eprosyuos sowodas “OSS! exe “fermeu oxtunu um u q oanIs -Od [eo1 oroumu wn 2 D 9puo 'D/) Iejnojeo afosop as anb souryuodns “OPONL O IeNSNTt ap uny e ojdwoxo um sourfoA “ooo op Qusumnsur ouoo ogórzynn ens ered Ojuawep -UNJ Pp tusAros seproataquisa Bo sountvão| Sop sapepodosd sy “TENSUOUIap sourerionh ou? '9 < z opo ered (n)7-2 = T)W nb “elos no 9 < 2 opoy erdeg SeSjunseBo) sogSuny gy “(2)/ sopa ousa o trepuodsanos x ap SSJOJEA SQjuaragip e onb 19110090 apod */ vupniqre opóuny vun exrg “(2)/ op smuopuodsanos SSIOJeA SO “NIop E “eUNTOS EINOU 9 E [aApEVA PP SoJOjeA SO as-t100d “epuonbsa x “BUN]OD BUNN “SoJOTrA 2p engra pum e woBLo vp / opóuny 1onbjend “H2 4H aaa (opdalig) vooajuma DIUapuodsoato? pum q | — +: DIjuijaDõo] opdunf Dpoj “otig|0109 7 “SOL OP Opôrnsuouap e Injouoo ojsj (2) > q dozeysnes v Opou op opnqo 103 7 anb ap ox o opurizenuos “q > (“o)T > (z)7ogug “u wungp exd to > x onb “ojumanua “errromdur Osj “O > 2 onb sowemnpuoo (w)7 > (z)t ap “quaosor q 7 ouos ()T>(sr>a enb Te O < x sowrango rua o quatraou opuesn “onajo wo) "q < (p)T 1a apod os opu “quowedopeuy “q > (2) onb opow ap opngo 103 2 OJotunu o stod “opinsqe tun T “q< EE +“) < (2)1 erreinsar ,0T/T + “o < 2 op auooso 9? 1 owos a> sos ML up 080] 'z > 40T/T +» somejio uOT/T < 0 — onb opueif og u opuvuio) “Org “> 7 eIRordur ojst “QUSosar 9 TT OtuOD "G > (Z)T>(D)Tbmo (0) a8s0y 28 “ojry aq “q = (0) onb soweunyy , '0 as (to) sas-uo) “4 --- Zn To tOp = “y opuod “nb [2] Ep DE += tp torpop = um D Teo oxatunu um PP IEP opSeuasozdar p sowentoda “Quawe3opeur opurngassorg |Z sesjunueBo; sagsung edeo DDODDSDDDDDDDDO em a e O O RA Db = pm pm ND SDS gi) qi am pt ulatas SEM E o) ] E Sid OS-u19) «OT, OL = too , zo toto= vIvtOp = To opuod “onb pe 6 3 &o 5 q cp sIXo onb souia Cro rp. 8 rp 20 ro ay T 6 (A T SOINU SO Opuriapisuoo “quaurõopeuy - (O/t+ No) >q 5 (ro)T as-119 O og titiga fo Ip opuod “nb jr 653 Ip 3 O “oltouy To imsixo 9A9P “9 OJsT (otT/1 + To)T > 45 (Fo) onb sm “etougnbas pssou OT/T+ To 9 To SOANTIaSUOD SOjuauaja stop INSIXO UdAop “(T+ )T>qS5 (90) ouoS T+0% DE cops «DE 2 dp Oo “om 6 z T SOIsunU so sowarapisuos “epinõos wg (T+ Co)T >9q5 (9%) soma OWUZ "q < (T+ OD) onb pm OUT JOUSUI O T + Op vas “q < (y)T onb sm * SOXSNUY INSIXO OA ap 080] “epeuIT ajuaosoro opôuny vun 9 7 onb SOWRIQUIO, “CD Prroqu ajed v TeUJULISIop ereg “Q=(0)T or op wo os onb Sowarensour 'eprngas wg Cv up-toTntop =» TES OJUNU OP [eunoop ogómuasadar » ugduioo anb rtp Cep ctp top soIraqur So “um 2 un “ruturagop wo PISISUOO Opogu assg - Tensojoo ojuauajo OP Opou, o urarueyo soSnue Sesouryo so onb 'sogsenba ap votgumu ogônjosas pred TeUO] tu Ossa001d Um ap ruzopow OBSIGA PIUN sOuIaresn “o Tee reg q = (0)7onbpo OAnISOd [ear oxaunu un Iago SOuIDAdp, “Q Teo oxounu um MUSUPIENIQ Opeg :7 euo10oaj op opSensuomad edeg sesjunneBo] sogsung OZ “EM extey é 2 epeingoeu ogiõos y — € esnbj4 x q D -|e ps A “qH Ojoquis ojad opiõo1 essa sowareotpuy “H º10qrdry ejad a 'sesstosqe sep oxta ojad Q=2'D = sonia sejor senp sejad eprytuy ouejd op opiõor v sowruo à “q > D uoo 'q*» soamis -Od syvar soxatumu stop sowexy opurnb BPIGO 9 ajoquadiy op vxim/ run z esnbia x I 1 | T=fzoo< zo ouomos a “os H S2 aloquadiy op extey own ap sosy pdeg PIVOSLLLLUSSSSSDSGULUOSLUS SUE “> E A DL | een VATONNTVE e quem qua DD 4 S. 7 Ouunfuoo or aoua1ad ouejd op (fz) ouod un “2 oNst “aueipenb oxtatupnd Ou opnuoo pisa onb T = fiz ajoquadiy vp owes o q H “Nuswromawosr Em (7=8 0 2 apuo) “ogátsodwosap vp [p '2] sojearaur Sop wm vpro tua aseq wos “soisodeisnf sojearajur op oxuy oxaunu wnu [9*D] ojesiaur o sowodwovop “SOLPIPOtLIQUI SOjuOd op otau 104 “qH exrey UN 9P voIp v Iejnopeo op uy v-19pooord ouros 108? soworensoja a +18 >h50 95250 i(A'z))= mg souro 'sojunfuoo sop vtoo ep ogórou EN 'Z/ISÃSoo 9575» sogópuos se quouroumnus woiduno sepeuap1iooo selno (A 'z) sojuod sojad vpruoy 9 qH BxIRJ 2 “Queuog pdeg aloguadiy 2p extey eun op say og