Circuitos y Sistemas Lineales

7/30/2019 Circuitos y Sistemas Lineales

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Omufrm Bortrfk FhbortJfbreoh Ncktcrc Hpoz

Gerguetcs y sestonfs hekofhos

Gursc mo hfbcrftcrec


2/229

Trenorf omegek< jokor mo 2444

Mesoc mo hf gubeortf< Omegecks _TG

ohs futcrs 2444 Omegecks _TG 2444

Omegecks mo hf _kevorsetft Tchetgkegf mo Gftfhukyf WHLcrme Jerckf Wfhjfmc 76 4047= Bfrgohckf]oh+ 57= 469 007 Ifx+ 57= 46? 00?Omegecks Yertufhs< www+omegecksupg+oso.nfeh< omupgDsj+upg+os

Trcmuggek< GTMF (Goktro mo Tubhegfgecks mFbfst%Fv+ Mefjckfh 9=: O]WOEB 40420 Bfrgohckf

Mopsetc hojfh< B.?4:6.2444EWBK< 0=.0746.7:2.P


3/229

Trhcjc :

Trhcjc

_kf fsejkfturf mo hfbcrftcrec setufmf f prekgepecs mo ukf gfrrorf mo ekjokeorf teoko cblotevcs tfktcfgtetumekfhos gcnc fptetumekfhos+ Hcs prenorcs mobok creoktfrso fgef hf icrnfgek mo betcsoxporenoktfhos gcrrogtcs ifgehetfkmc oh mosfrrchhc porsckfh mo hcs ostumefktos fgef ukcs ntcmcs yprcgomeneoktcs mo trfbflc tfktc f kevoh mo phfkeiegfgek mo sto gcnc mo nomemfs y ohfbcrfgek mo

ekicrnos+ Hf oxporeokgef kcs mego quo oh xetc c irfgfsc ok ostf iukgek icrnftevf teoko ukf jrfkekgemokgef ok hf iuturf promespcsegek moh ostumefkto (os moger moh iuturc ekjokeorc% fgef hcs trfbflcsoxporenoktfhos+ Kc pcmoncs chvemfr quo oh cblotevc mo gufhqueor ekjokeorf os oh mesoc y ncktflo mooquepcs y prcmugtcs seokmc hcs prcgoscs mo ncmohezfgek nftontegf mo senuhfgek c mo fkheses pfscsprovecs f osto cblotevc iekfh+ Hfs onprosfs kc suohok busgfr prcioseckfhos quo shc sopfk lusteiegfr pcr quuk motornekfmc gerguetc c sestonf so gcnpcrtf mo ukf motornekfmf icrnf (iukgek ns prcpef mo hfGeokgef quo mo hf ]gkegf% sekc quo fmons pemok gfpfgemfm pfrf fgor nomemfs (gfrfgtorezfgeckos% mooquepcs y pfrf fgor mesocs rofhestfs quo rospckmfk f hfs ospogeiegfgeckos usfkmc pfrf ohhc hcsgcnpckoktos y subsestonfs ns emkocs+ Fh trftfrso mo uk hfbcrftcrec ekegefh teoko ukf fgusfmf ekgemokgefok hf icrnfgek moh gfrgtor mo hcs iuturcs ekjokeorcs yf quo tcmfvf kc so fk somenoktfmc betcs motrfbflc quo ok fhjukcs gfscs sorfk meigehos mo gcrrojer+ Tcr ohhc hcs trfbflcs mo hfbcrftcrec quo soprcpckok ok osto gursc sck jrfmufhnokto merejemcs< hcs prenorcs gcksestok ok hf ologugek mo ukfs pfutfsnuy motfhhfmfs mo icrnf quo oh ostumefkto vfyf tcnfkmc futcgckiefkzf ok sus fbehemfm oxporenoktfhpfrf er pfsfkmc f nomemf quo fvfkzf oh gursc fgef trfbflcs nokcs merejemcs+

Hcs sojukmcs cblotevcs mo fptetum sck ns ospogiegcs ok iukgek mo hf nftoref y so goktrfk ok hffmquesegek mo ukcs gckcgeneoktcs scbro oh usc y hf fphegfgek mo gcnpckoktos y sestonfs+ _k hfbcrftcrecmo Gerguetcs y Westonfs Hekofhos teoko okgcnokmfmf hf tfrof mo prcpcrgeckfr fh fhunkc hfs orrfneoktfsosokgefhos pfrf sor gfpfz mo fkto uk gerguetc c sestonf hekofh motornekfr nomer y gcnprokmor ohiukgeckfneoktc mo ukf vfrefbho mo sfhemf gcnc rospuostf f ctrf vfrefbho quo mokcnekfroncs mo oktrfmf+F pfrter mo ostfs orrfneoktfs so fbcrmfr oh prcbhonf mo mesoc< motornekfr qu gerguetc c sestonf osgfpfz mo prcgosfr mo hf icrnf mosofmf ukf sofh mo oktrfmf y gckstruerhc+

Osto gursc so f mesofmc pfrf ukf fsejkfturf mo Gerguetcs y Westonfs Hekofhos quo tokjf oh cblotevc momfr ukcs iukmfnoktcs toregcs gcktrfstfmcs gck trfbflcs oxporenoktfhos+ Wek onbfrjc oh okicquo moh toxtc

so fmfptf f mcs setufgeckos gurreguhfros mestektfs fukquo tokmoktos fh nesnc iek+ Gfmf prgtegf (gck osto

Hcs futcros( 24441 Omegecks _TG( 2444+


4/229

0 Ger guetcs y sestonfs he kofhos< gursc mo hfbcr ftcre c

kcnbro so puomok mosejkfr hcs gfptuhcs% mo hfbcrftcrec ost mevememf ok meioroktos otfpfs f er sejueokmcfstf hhojfr fh ncktflo iekfh+ F su voz gfmf ukf mo ostfs prgtegfs ost gcnpuostf pcr tros fpfrtfmcs v. ; v! y pcr tfktc vm8 4quo mf f hf sfhemf vc> .YGG+ We oh vfhcr mo ve bflf fstf quo


17/229

6 Fphe gfgeckos bsegfs moh fnphei egfmcr cporfgeckfh 26

vvc

e

R

R

6

2

YGG

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YH

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R2

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R6

Ygg

y Y@

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R2

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R6

Ygg (6+?%

Y

Y

@

H

Y e

t

Y c

t

Ygg

.Y

gg

v

Y

c

v

GG

GGY

eY YH @

Iej+ 6+6+0 Ger guetc mespfrfmcr mo Wg`nett

ok oso ekstfkto so pfsf f tokor uk vfhcr movm; 4+ Os ok oso ncnoktc gufkmc hf sfhemf (vc% bfsguhf

y tcnf oh vfhcr fhtc moYGG+ Yfrefkmc ctrf voz ve so teoko uk geghc poremegc mo vfhcros hhfnfmc geghc

mo estroses quo so nuostrf ok hf iejurf 6+6+5+ Hcs vfhcros mo hf toksek mo oktrfmf quo prcmugok oh

bfsguhfneoktc mo hf sfhemf sck

Iej+ 6+ 6+5 Geghc mo estroses


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22 Ger guetcs y sestonfs hekofhos< gursc mo hfbcrftcre c

vv

R

R6

2

ce

e

eR2

R6

v

v

R

R6

2

c

e

vm F+vm

v

v

e

6+6+2+2 FC ok zckf hekofh

Ok ostcs ncktflos oh fnpheiegfmcr so rofhenoktf kojftevfnokto (nomefkto fhjk tepc mo gckoxek

oktro hf sfhemf y hf oktrfmf ekvorscrf%+ Wo pcmr fphegfr ok ohhcs uk ntcmc senpheiegfmc mo fkheses

hhfnfmc ntcmc moh gcrtcger guetc vertufh+

Gcnc pcmr gcnprcbfrso hcs gerguetcs sejueoktos pornetok oiogtufr mevorsfscporfgeckosgck hf sofh

(c hfs sofhos% mo oktrfmf+ Mo f oh kcnbro moh mespcsetevc< fnphe iegfmcr cporfgeckfh+

f% Fnpheiegfmcr ekvorscr

Wof oh gerguetc mo hf iejurf 6+6+66 quo os oquevfhokto fh mo hf iejurf 6+6+64 ukf voz sustetuemc oh

fnpheiegfmcr cporfgeckfh pcr su ncmohc oquevfhokto mo hf iejurf 6+6+7+

Iej+ 6+6+64 Fnphe iegfmcr ekvorscr

Iej+ 6+6+66 Ger guetc oquevfhokto moh fnphe ie gfmcr ekvorscr


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6 Fphe gfgeckos bsegfs moh fnphei egfmcr cporfgeckfh 27

e *v

e )Fv

m

R6 /

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ve9 hen

F9=v

c)R2

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(6+9%

Y4

Ye

Ygg

. Ygg

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R 6

Ok osto gfsc oh phfktofneoktc mo hfs hoyos mo Aerg cii mf hujfr f

Hf rohfgek oktro hf toksek mo oktrfmf ve y hf mo sfhemf v4 os ukf rogtf mo pokmeokto kojftevf guycvfhcr veoko flustfmc pcr oh mesofmcr moh gerguetc sojk hf rohfgek oktro hfs rosestokgefs R2 y R6+ Ostf

rogtf ost fgctfmf pcr hfs nxenfs tokseckos quo os gfpfz mo prcpcrgeckfr oh FC f su sfhemf F vm so cbtokmrf vc>=se vm kc iuorf gorc+ Oktckgos hf kegf pcsebehemfm pfrf tokor ukf

sfhemf fgctfmf (kc sfturfmf f hf toksek mo fhenoktfgek moh FC% os quovm9 4+

Ostf gckmegek vm9 4 os ukf mo hfs quo so fphegfk ok oh ntcmc moh gcrtcger guetc ver tufhquo gcksesto

ok supckor e!> e.> e> 4( v m> 4 y vc8 Ysft (iejurfs 6+6+2 y 6+6+7%+ Ostfs supcsegeckos quo so tcnfk

gcnc pfrtemf moh fkheses senpheiegfk gcksemorfbhonokto oh ostumec moh gerguetc+ Fphequoncs fh

olonphc fktorecr moh fnpheiegfmcr ekvorscr oh ntcmc moh gcrtcger guetc vertufh 4^ v!> v. pcr tfktc v.> 4pcr ostfr v! gckogtfmc f nfsf+

e.> 4pcr tfktc eR6! eR2> 4

Gcnbekfkmc hfs mcs ogufgeckos so cbteoko hf fnpheiegfgek mo toksek 4

!

!

S

!

S

vv > v

e

v e

c e

v e

F B

F B

Iej+ 6+6+ 6? Wojuemcr mo toksek

Gcnc vm > 4 os eknomeftc gcnprcbfr quo

Oh oiogtc mo feshfneoktc puomo vorso ok hf iejurf 6+6+69+ Gcnc hf gcrreokto mo oktrfmf fh FC os gorc

oh gerguetc "F" kc so vo porturbfmc ("gfrjfmc"% pcr hf prosokgef moh FC y sus tokseckos y gcrreoktos

so nfkteokok gcnc se oh cporfgeckfh kc ostuveorf prosokto+ Wek onbfrjc oh gerguetc B sejuo veokmc

f su oktrfmf ukf toksek ve hf nesnf quo fy ok hf sfhemf moh gerguetc F+

Iej+ 6+6+ 69 Oiogtc sopfrfmcr moh sojuemcr mo toksek


24/229

20 Ger guetcs y sestonfs hekofhos< gursc mo hfbcrftcre c

v v

R

R

7

c

v

R2

6

6

2

vc

*)R7(

v6

R6

/

v2

R2

% (6+64%

m% Wunfmcr ekvorscr

Gcrrospckmo fh osquonf mo hf sejueokto iejurf+

Iej+ 6+6+6: Bhcquo sunfmcr ekvorscrTcmoncs fprogefr quo pcr suporpcsegek mo hfs mcs iuoktos tokoncs mcs gerguetcs ekvorscros+ Fs

so cbteoko Rtc . f+m] + Tfrf ohhc fhhfr oh oquevfhokto mo ] ovokek moh gerguetc iuokto vestc mosmo

hcs tornekfhos Ys y nfsf (vor hf ihog f ok oh mebulc%+

@fgeokmc hfs pcsebhos fprcxenfgeckos so f mo hhojfr f ukf oxprosek ok hf quo Rt sof

prcpcrgeckfh f Rtc y Yt hc sof f m]+

6+?+6+2 Ohojer hcs vfhcros mo R6 y R2 mo ncmc quo hf rosestokgef mo oktrfmf moh fnpheiegfmcr

ekvorscr vestf mosmo F sof mo 6 A y quo hf fnpheiegfgek mo toksek Yc#Ys sof mo =: (ok

nmuhc%+


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6 Fphe gfgeckos bsegfs moh fnphei egfmcr cporfgeckfh =7

6+?+6+7 Wubstetuer R6 pcr uk gckmoksfmcr mo gfpfgemfm G+ Vu rohfgek fy f crf oktro Yc y hcs

gfnbecs mo tonporfturf m] 3

6+?+2 ]rfbflc mo hfbcrftcrec

6+?+2+6 Flustfr Rp6 mo ncmc quo f tonporfturf fnbeokto hf toksek Yc sof gorc+ Gcnprcbfr quo

uk ekgronoktc mo tonporfturf fgo okgokmor oh hom vormo (mo ncnoktc kc kcs ektorosf oh

hom rclc%+ (Yesufhezfr Yc ok oh csgehcsgcpec%

6+?+2+2 Flustfr Rp2 pfrf quo oh hom rclc so okgeokmf f pfrter mo ukf geortf tonporfturf nemeokmc

fh nesnc teonpc hf toksek ok hf oktrfmf kc ekvorscrf moh fnpheiegfmcr cporfgeckfh knorc

7 (FC7%+

6+?+2+7 Wustetuer R6 pcr uk gckmoksfmcr mo 6 I+ Gcnprcbfr oh iukgeckfneoktc moh gerguetc

gfhoktfkmc y okirefkmc hf K]G (vesufhezfr Yc ok oh csgehcsgcpec%+ Vu ost motogtfkmc

f crf oh gerguetc3+ Rfzckfr hf rospuostf mo fguormc f hc vesufhezfmc y fh iukgeckfneoktc

moh nesnc+

6+9 Trgtegf+ Tfrto Y (cptftevf%

6+9+6 Ostumec provec

Oh sejueokto gerguetc motogtf hf tonporfturf rohftevf oktro mcs puktcs+

6+9+6+6 Cbtokor hf oxprosek mo Yc ok iukgek mo R6 R2 R7 R= Y6 y Y2+


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== Ger guetcs y sestonfs hekofhos< gursc mo hfbcrftcre c

6? Y

6? Y

6? Y

6? Y

6 A?c

6? Y

6? Y

6? Y

6? Y

6? Y

v

v

v

v

RR

RR R

R

R

m

6

2

c

p2 p6

t6t2

2

7

=

(644 A%

R6

H RCLCH YORMO

6? Y

6+9+6+2 @fhhfr hf rohfgek mo rosestokgefs quo porneto ukf ogufgek moh tepc Yc > F+(Y6 . Y2% y

mfr hf oxprosek mo F+

6+9+6+7 Wfbeokmc quo R6 > R7 > 64 AW y F > =: motornekfr oh vfhcr mo hfs rostfktos

rosestokgefs+

6+9+6+= ]okeokmc ok guoktf quo gfmf ukf mo hfs K]G puomo ostfr f mestektf tonporfturf oxphegfr

qu iukgek rofhezf osto gerguetc o ekmegfr gukmc so okgokmor gfmf ukc mo hcs mecmcs homs+

Mo qu ncmc pcmrf senpheiegfrso oh gerguetc fktorecr usfkmc ukf ostrugturf quo onphoo

nokcs fnpheiegfmcros cporfgeckfhos3+


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6 Fphe gfgeckos bsegfs moh fnphei egfmcr cporfgeckfh =?

6+9+2 ]rfbflc mo hfbcrftcrec

6+9+2+6 Ncktfr oh gerguetc fktorecr y fhenoktfrhc+ Gckogtfr oh gfkfh 6 moh csgehcsgcpec ok Y6 y oh

gfkfh 2 ok Y2+

6+9+2+2 Flustfr Rp6 fstf quo hf toksek gcktekuf Y6 sof kuhf+ Ropoter oh prcgosc gck Rp2 pfrf

flustfr Y2+ Ostcs mcs flustos so frk f tonporfturf fnbeokto+

6+9+2+7 Fphegfr meioroktos tonporfturfs f K]G.6 y K]G.2 y gcnprcbfr oh oiogtc scbro hcs homs+


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=9 Ger guetcs y sestonfs hekofhos< gursc mo hfbcrftcre c

Fkoxc 6+F Gurvfs mo vfrefgek mo ukf rosestokgef mo gcoiegeokto motonporfturf kojftevc (K]G% ok iukgek mo hf tonporfturf

Fkoxc 6+B Gfrfgtorstegfs mo hcs fnpheiegfmcros cporfgeckfhos utehezfmcs

Wo okguoktrfk ok icrnftc TMI ok oh GM.rcn fmluktc+ We kc so teoko tokmr quo ekstfhfrso prenorc

Fmcbo Fgrcbft Rofmor 7+4 c suporecr quo so ekghuyo ok oh nesnc GM+


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2 Fkheses mo gerguetcs gck TWpego =:

2 Fkheses mo gerguetcs gck TWpego

Oh cblotevc mo ostcs trfbflcs os ektrcmuger fh fhunkc ok hf utehezfgek mo orrfneoktfs scitwfropfrfoh fkheses mo gerguetcs+ Tfrf ohhc so utehezfr oh prcjrfnf TWpego usfkmc hf ektorifgo Wg onftegs mo

Negrcsen+ Ostf ektorifgo mo gfpturf mo osquonfs jriegcs cirogo ukf ifgehemfm mo roprosoktfgek mohcs gerguetcs mo usc y mo vesufhezfgek mo rosuhtfmcs quo hc fgok fjrfmfbho gcnc prenor gcktfgtcgck hf senuhfgek+ Kc so vfk f fprcvog fr pcr oh ncnoktc tcmfs hfs prostfgeckos moh prcjrfnfTWpego+ Fhjukfs (hf nfycrf% sork trfbflfmfs ok oh hfbcrftcrec gck geortc motfhho ctrfs sorkprosoktfmfs ok osporf mo mosfrrchhfrhfs gufkmc oh gursc ost ns fvfkzfmc+

Oh gckcgeneoktc mo uk prcjrfnf mo senuhfgek ok osto ncnoktc moh gursc teoko hf voktflf moifgehetfr hf vfhemfgek mo ostumecs toregcs mo trfbflcs pcstorecros+ Fmegeckfhnokto fquohhcsfhunkcs quo gursok ctrfs fsejkfturfs rohfgeckfmfs gck oh prosokto gursc puomok usfr ostcsgckcgeneoktcs pfrf gcnprcbfr hf roschugek mo olorgegecs y prcbhonfs+

Fkto osto prenor gcktfgtc gck uk prcjrfnf mo senuhfgek pcmrf guosteckfrso pcrqu ostumefr hcsntcmcs y tgkegfs pfrf cbtokor mosfrrchhcs fkfhtegcs+ We beok hfs voktflfs moh prcjrfnf yf soovemokgefrk ok oh hfbcrftcrec sujorencs fh fhunkc quo roihoxecko scbro hfs henetfgeckos+ Tuomopcr olonphc phfktofrso se oh prcjrfnf os gfpfz pcr se nesnc mo cbtokor ostrugturfs gerguetfhossftesifgor ospogeiegfgeckos mo gcnpcrtfneoktc mo gerguetcs c ok jokorfh oiogtufr ctrfs tfrofs momesoc+ Oh fkheses os seonpro uk nomec ok ekjokeorf porc oh iek os oh mesoc y hf rofhezfgek+

Tcr htenc fy uk pohejrc ok hf senuhfgek quo gckveoko fmvorter ok osto ncnoktc+ Fpfrto mo hfgcncmemfm henpeozf y bflc gcsto mo hfs senuhfgeckos stfs suohok roprcmuger hfs proveseckos quocbtokmrfncs toregfnokto+ Ohhc os gcksoguokgef mo quo oh ncmohc mo senuhfgek os cblotc mosenpheiegfgeckos y fprcxenfgeckos sonolfktos f hfs mo hcs mosfrrchhcs toregcs+ We kc so teoko okguoktf ostc pcmrf supckorso quo hc senuhfmc os seonpro vormfmorc y oxfgtc hhojkmcso f pomerok oh hfbcrftcrec quo hcs sestonfs isegcs so gcnpcrtok gcnc hcs senuhfmcs y kc fh rovs+Ncmohfmcs ekgcnphotcs c oiogtcs pfrsetcs (gcnc hcs quo so vork ns fvfkzfmc oh gursc% hhovfrfk

f gckghuseckos ekgcrrogtfs se shc kcs ierfncs mo hcs rosuhtfmcs mo fhjukfs senuhfgeckos sek nsektorprotfgek mo stcs+

Ok ostcs trfbflcs kc oxesto uk ostumec provec ok oh soktemc fbetufh+ We oh ostumefkto f homc (sekostumefr% osto gfptuhc oh sojueneoktc pcstorecr mo hfs oxphegfgeckos moh prcioscr puomo vorso


44/229

=0 Gerguetcs y sestonfs hekofhos< gursc mo hfbcrftcrec

ifgehetfmc fh fbor ukfs bfsos mo pfrtemf+ Os fsenesnc fgcksolfbho quo so fjf uk fkhesesgufhetftevc mo hcs meioroktos gerguetcs quo so prcpckok pfrf su senuhfgek+

2+6 Ektrcmuggek

Oh prcjrfnf TWpego (TG Wenuhfteck Trcjrfn wet` Ektojrftom Gerguet Onp`fses% porneto hfsenuhfgek mo gerguetcs ohogtrkegcs tfktc hekofhos gcnc kc hekofhos+ Gck h so pcmr ovfhufr ukgerguetc ok oh mcnekec tonpcrfh motornekfr hf rospuostf iroguokgefh oiogtufr fkheses ok gcktekuffs gcnc ctrfs cpgeckos ns fvfkzfmfs+ Ok hcs sejueoktos fpfrtfmcs so fr ukf prosoktfgek yoxpcsegek jokorfh mo hfs pcsebehemfmos moh TWpego+ Wor oh prcpec usufrec queok f bfso mo trfbflfrgck oh prcjrfnf fgfbo mosgubreokmc tcmc su pctokgefh+

Hfs hebrorfs mo gcnpckoktos gck hfs quo trfbflf TWpego sck nuy fvfkzfmfs hc quo f og c quoosto prcjrfnf ost fnphefnokto ostfkmfrezfmc y sof fgoptfmc f kevoh prcioseckfh tfktc ok goktrcsmo ekvostejfgek y ukevorsemfmos gcnc ok hf ekmustref+ Fmons hcs prekgepfhos ifbregfktos mo

gcnpckoktos y gerguetcs ektojrfmcs ifgehetfk ncmohcs TWpego mo sus prcmugtcs fggosebhos vfEktorkot+

Hf icrnf gckgrotf mo ologutfr oh prcjrfnf mopokmor moh hujfr isegc mckmo so fyf ekstfhfmc okgfmf hfbcrftcrec ekicrntegc c ok gfmf crmokfmcr porsckfh gcsf quo yf so oxpckmr ok hfs ghfsosprgtegfs+ _kf voz moktrc moh prcjrfnf Wg onftegs hfs meioroktos tfrofs f oiogtufr pfrf senuhfr ukgerguetc so vfk mosgrebeokmc ok hcs sejueoktos fpfrtfmcs+

2+2 Gnc mebulfr

Oh prenor pfsc fktos mo senuhfr uk gerguetc sor jokorfr oh osquontegc moh nesnc+ Ostc so fgo

ologutfkmc hf egckf sg`onftegs+ _kf voz og c ostc fpfrogor ukf voktfkf mo trfbflc gcnc hf mo hfiejurf 2+6+

Hcs gcnpckoktos quo puomok sor ekgcrpcrfmcs f uk gerguetc pfrf su pcstorecr fkheses ostkonpfquotfmcs ok hebrorfs+ Os enpcrtfkto mestekjuer mcs tepcs mo hebrorfs< hfs hebrorfs gck hfmosgrepgek jriegf moh gcnpckokto (oxtoksek +shb% y ctrfs gck hf mosgrepgek ohogtrkegf(oxtoksek + h eb%+ Hcs gerguetcs jokorfmcs pcr sg`onftegsteokok oxtoksek +sg`+ Tcstorecrnoktomurfkto hf senuhfgek y vesufhezfgek mo rosuhtfmcs so jokorfk ukcs ieg orcs ektornomecs< +kot + ger+fhsy +cut+

Tfrf mebulfr oh gerguetc fkfhezfr so mobo fgumer fMr fw#Jot Kow Tfrty sohoggeckfr oh gcnpckoktomosofmc moktrc mo hfs meioroktos hebrorfs mespckebhos+ Tcr olonphc hcs gcnpckoktos quo so puomok

okgcktrfr ok hf hebrorfFKFHCJ(iejurf 2+2% sck hcs ohonoktcs mo gerguetc ns fbetufhos+


45/229

2 Fkheses mo gerguetcs gck TWpego =5

Iej+ 2+6 ]fbhorc mo trfbflc mo Tspego

Fhjukcs mo hcs ohonoktcs quo os pcsebho ekgcrpcrfr f kuostrc osquontegc (y oh mosejkfmcrgcrrospckmeokto% sck 4

. teonpc mo mogfeneoktc > 4

. vfhcr mo toksek ok oh kevoh bflc > 4

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