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Обработка результатов экспериментов и наблюдений

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Prusakov Danil.

Ia?aaioea ?acoeueoaoia yenia?eiaioa

Eceiaeaiu iaeioi?ua ?acaeaeu iaoaiaoe/aneie ia?aaioee ?acoeueoaoia
iaaethaeaiee e yenia?eiaioia i aeaenoaeyo ni neo/aeiuie aaee/eiaie,
ii?aaeaeaiey e ioeaiee caeiiia eo ?ani?aaeaeaiey, aiaeeoe/aneiai e
a?aoe/aneiai ioia?aaeaiey ?acoeueoaoia.AAAAeAIEA

I?e enneaaeiaaiee oaoie/aneeo nenoai iiaoo eniieueciaaoueny
oai?aoe/aneea e yiie?e/aneea iaoiaeu iiciaiey. Eaaeaeia ec yoeo
iai?aaeaiee iaeaaeaao ioiineoaeueiie naiinoiyoaeueiinoueth, eiaao naie
aeinoieinoaa e iaaeinoaoee. A iauai neo/aa, oai?aoe/aneea iaoiaeu a
aeaea iaoaiaoe/aneeo iiaeaeae iicaieytho iienuaaoue e iauyniyoue
acaeiinayce yeaiaioia eco/aaiie nenoaiu eee iauaeoa a ioiineoaeueii
oe?ieeo aeeaiaciiao eciaiaiey ia?aiaiiuo aaee/ei. Iaeiaei i?e iino?iaiee
oai?aoe/aneeo iiaeaeae iaecaaaeii aaaaeaiea eaeeo-eeai ia?aie/aiee,
aeiiouaiee, aeiioac e o.i. Iiyoiio aicieeaao caaea/a ioeaiee
aeinoiaa?iinoe ( aaeaeaaoiinoe ) iieo/aiiie iiaeaee ?aaeueiiio i?ioeanno
eee iauaeoo. Aeey yoiai i?iaiaeeony yenia?eiaioaeueiay i?iaa?ea
?ac?aaioaiiuo oai?aoe/aneeo iiaeaeae. I?aeoeea yaeyaony ?aoathuae
iniiaie iao/iiai iiciaiey. A ?yaea neo/aaa eiaiii ?acoeueoaou
yenia?eiaioaeueiuo enneaaeiaaiee aeatho oie/ie e oai?aoe/aneiio
iaiauaieth eco/aaiiai yaeaiey. Yenia?eiaioaeueiia enneaaeiaaiea aeaao
aieaa oi/iia niioaaonoaea iaaeaeo eco/aaiuie ia?aiao?aie. Ii ia neaaeoao
e i?aoaaee/eaaoue ?acoeueoaou yenia?eiaioaeueiuo enneaaeiaaiee, eioi?ua
ni?aaaaeeeau oieueei a i?aaeaeao oneiaee i?iaaaeaiiiai yenia?eiaioa.

Oaeei ia?acii, oai?aoe/aneea e yenia?eiaioaeueiua enneaaeiaaiey
aeiiieiytho ae?oa ae?oaa e yaeythony ninoaaiuie yeaiaioaie i?ioeanna
iiciaiey ie?oaeathuaai ian ie?a.

Eae i?aaeei, ?acoeueoaou yenia?eiaioaeueiuo enneaaeiaaiee ioaeaeathony
a ii?aaeaeaiiie iaoaiaoe/aneie ia?aaioea. A ianoiyuaa a?aiy i?ioeaaeo?a
ia?aaioee yenia?eiaioaeueiuo aeaiiuo aeinoaoi/ii oi?ioi oi?iaeeciaaia e
enneaaeiaaoaeth iaiaoiaeeii oieueei aa i?aaeeueii eniieueciaaoue. E?oa
aii?inia, ?aoaaiuo i?e ia?aaioea ?acoeueoaoia yenia?eiaioa, ia oae oae
aaeee. Yoi ( aii?inu iiaeai?a yiie?e/aneeo oi?ioe e ioeaiea eo
ia?aiao?ia, aii?inu ioeaiee enoeiiuo cia/aiee ecia?yaiuo aaee/ei e
oi/iinoe ecia?aiee, aii?inu enneaaeiaaiey ei??aeyoeeiiiuo caaeneiinoae e
iaeioi?ua ae?oaea.

Ianoiyuaa o/aaiia iiniaea ia i?aoaiaeoao ia i?eaeiaeueiinoue. Iii
niaea?aeeo iaeioi?ua ?acoeueoaou ooiaeaiaioaeueiuo e i?eeeaaeiuo ?aaio a
iaeanoe ia?aaioee ?acoeueoaoia yenia?eiaioaeueiuo enneaaeiaaiee
[1…13(. Iiniaea iiaeao neoaeeoue i?aeoe/aneei ?oeiaiaenoaii ii
ia?aaioea ?acoeueoaoia yenia?eiaioa eae nooaeaioai, oae e iao/iui
nio?oaeieeai e eiaeaia?ai.

1. IOEAEE ECIA?AIEE

Iniiaie anaai anoanoaiciaiey yaeyaony iaaethaeaiea e yenia?eiaio.

Iaaethaeaiea ( yoi nenoaiaoe/aneia, oeaeaiai?aaeaiiia aini?eyoea oiai
eee eiiai iauaeoa eee yaeaiey aac aicaeaenoaey ia eco/aaiue iauaeo eee
yaeaiea. Iaaethaeaiea iicaieyao iieo/eoue ia?aiia/aeueioth eioi?iaoeeth
ii eco/aaiiio iauaeoo eee yaeaieth.

Yenia?eiaio ( iaoiae eco/aiey iauaeoa, eiaaea enneaaeiaaoaeue aeoeaii e
oeaeaiai?aaeaiii aicaeaenoaoao ia iaai iooai nicaeaiey eneonnoaaiiuo
oneiaee eee eniieuecoao anoanoaaiiua oneiaey, iaiaoiaeeiua aeey
auyaeaiey niioaaonoaothueo naienoa. Aeinoieinoaaie yenia?eiaioa ii
n?aaiaieth n iaaethaeaieai ?aaeueiiai yaeaiey eee iauaeoa yaeyaony:

1. Aiciiaeiinoue eco/aiey a «/enoii aeaea», aac aeeyiey iiai/iuo
oaeoi?ia, caoaiiythueo iniiaiie i?ioeann;

2. A yenia?eiaioaeueiuo oneiaeyo iiaeii iieo/eoue ?acoeueoao aieaa
auno?i e oi/ii;

3. I?e yenia?eiaioa iiaeii i?iaiaeeoue eniuoaiey noieueei ?ac, neieueei
yoi iaiaoiaeeii.

?acoeueoao yenia?eiaioa eee ecia?aiey anaaaea niaea?aeeo iaeioi?oth
iia?aoiinoue. Anee iia?aoiinoue iaea, oi ath iiaeii i?aiaa?a/ue. Iaeiaei
i?e yoii iaecaaaeii aicieeatho aeaa aii?ina: ai(ia?auo, /oi iiieiaoue
iiae iaeie iia?aoiinoueth, e, ai(aoi?uo, eae ioeaieoue aaee/eio
iia?aoiinoe. Oi anoue, e ?acoeueoaou yenia?eiaioa ioaeaeathony a
ii?aaeaeaiiii oai?aoe/aneii iniuneaiee.

1.1. Oeaee iaoaiaoe/aneie ia?aaioee ?acoeueoaoia yenia?eiaioa

Oeaeueth ethaiai yenia?eiaioa yaeyaony ii?aaeaeaiea ea/anoaaiiie e
eiee/anoaaiiie nayce iaaeaeo enneaaeoaiuie ia?aiao?aie, eeai ioeaiea
/eneaiiiai cia/aiey eaeiai-eeai ia?aiao?a.

A iaeioi?uo neo/ayo aeae caaeneiinoe iaaeaeo ia?aiaiiuie aaee/eiaie
ecaanoai ii ?acoeueoaoai oai?aoe/aneeo enneaaeiaaiee. Eae i?aaeei,
oi?ioeu, au?aaeathuea yoe caaeneiinoe, niaea?aeao iaeioi?ua iinoiyiiua,
cia/aiey eioi?uo e iaiaoiaeeii ii?aaeaeeoue ec iiuoa.

Ae?oaei oeiii caaea/e yaeyaony ii?aaeaeaiea iaecaanoiie ooieoeeiiaeueiie
nayce iaaeaeo ia?aiaiiuie aaee/eiaie ia iniiaa aeaiiuo yenia?eiaioa.
Oaeea caaeneiinoe iacuaatho yiie?e/aneeie.

Iaeiicia/ii ii?aaeaeeoue iaecaanoioth ooieoeeiiaeueioth caaeneiinoue
iaaeaeo ia?aiaiiuie iaaiciiaeii aeaaea a oii neo/aa, anee au ?acoeueoaou
yenia?eiaioa ia eiaee ioeaie. Oai aieaa ia neaaeoao yoiai iaeeaeaoue,
eiay ?acoeueoaou yenia?eiaioa, niaea?aeauea ?acee/iua ioeaee ecia?aiey.

Iiyoiio neaaeoao /aoei iiieiaoue, /oi oeaeueth iaoaiaoe/aneie ia?aaioee
?acoeueoaoia yenia?eiaioa yaeyaony ia iaoiaeaeaiea enoeiiiai oa?aeoa?a
caaeneiinoe iaaeaeo ia?aiaiiuie eee aaniethoiie aaee/eiu eaeie-eeai
eiinoaiou, a i?aaenoaaeaiea ?acoeueoaoia iaaethaeaiee a aeaea iaeaieaa
i?inoie oi?ioeu n ioeaieie aiciiaeiie iia?aoiinoe aa eniieueciaaiey.

1.2. Aeaeu ecia?aiee e i?e/eiu ioeaie

Iiae ecia?aieai iiieiatho n?aaiaiea ecia?yaiie aaee/eiu n ae?oaie
aaee/eiie, i?eiyoie ca aaeeieoeo ecia?aiey.

?acee/atho aeaa oeia ecia?aiee: i?yiua e einaaiiua. I?e i?yiii ecia?aiee
ecia?yaiay aaee/eia n?aaieaaaony iaiin?aaenoaaiii ni naiae aaeeieoeae
ia?u. Iai?eia?, ecia?aiea iee?iiao?ii eeiaeiiai ?acia?a, i?iiaaeooea
a?aiaie i?e iiiiue /aniauo iaoaieciia, oaiia?aoo?u ( oa?iiiao?ii, neeu
oiea ( aiia?iao?ii e o.i. Cia/aiea ecia?yaiie aaee/eiu ion/eouaaaony i?e
yoii ii niioaaonoaothuae oeaea i?eai?a.

I?e einaaiiii ecia?aiee ecia?yaiay aaee/eia ii?aaeaeyaony (au/eneyaony)
ii ?acoeueoaoai ecia?aiee ae?oaeo aaee/ei, eioi?ua naycaiu n ecia?yaiie
aaee/eiie ii?aaeaeaiiie ooieoeeiiaeueiie caaeneiinoueth. Iai?eia?,
ecia?aiea nei?inoe ii i?ieaeaiiiio iooe e cao?a/aiiiio a?aiaie,
ecia?aiea ieioiinoe oaea ii ecia?aieth iannu e iauaia, oaiia?aoo?u i?e
?acaiee ii yeaeo?iaeaeaeouae neea, aaee/eiu neeu ( ii oi?oaei
aeaoi?iaoeeyi e o.i.

0,5 ii ia eciaieoue anee i?eiaiei eoio aeey ?anniao?eaaiey oeaeu.
Aiaeiae/ii i?ienoiaeeo ecia?aiea e i?e eniieueciaaiee ae?oaeo
ecia?eoaeueiuo n?aaenoa.

E?iia i?eai?iie iia?aoiinoe ia ?acoeueoao ecia?aiey aeeyao aua ?yae
iauaeoeaiuo e noauaeoeaiuo i?e/ei, iaoneaaeeaathueo iiyaeaiea ioeaee
ecia?aiey ( ?aciinoe iaaeaeo ?acoeueoaoii ecia?aiey e enoeiiui cia/aieai
ecia?yaiie aaee/eiu. Ioeaea ecia?aiey iau/ii iaecaanoia, eae iaecaanoii
e enoeiiia cia/aiea ecia?yaiie aaee/eiu. Eneeth/aiea ninoaaeytho
ecia?aiey ecaanoiuo aaee/ei i?e ii?aaeaeaiee oi/iinoe ecia?eoaeueiuo
i?eai?ia eee eo oa?e?iaea. Iiyoiio iaeiie ec aaaeiaeoeo caaea/
iaoaiaoe/aneie ia?aaioee ?acoeueoaoia yenia?eiaioa e yaeyaony ioeaiea
enoeiiiai cia/aiey ecia?yaiie aaee/eiu ii aeaiiui yenia?eiaioa n
aiciiaeii iaiueoae ioeaeie.

1.3. Oeiu ioeaie ecia?aiey

E?iia i?eai?iie iia?aoiinoe ecia?aiey (ii?aaeaeyaiie iaoiaeii ecia?aiey)
nouanoaotho e ae?oaea, eioi?ua iiaeii ?acaeaeeoue ia o?e oeia:

1. Nenoaiaoe/aneea iia?aoiinoe iaoneaaeeaathony iinoiyiii aeaenoaothueie
oaeoi?aie. Iai?eia?, niauaiea ia/aeueiie oi/ee ion/aoa, aeeyiea
iaa?aaaiey oae ia eo oaeeeiaiea, eciin ?aaeouaai eacaey e o.i.
Nenoaiaoe/aneea ioeaee auyaeytho i?e niioaaonoaothuae oa?e?iaea i?eai?ia
e iioiio iie iiaoo auoue o/oaiu i?e ia?aaioea ?acoeueoaoia ecia?aiee.

2. Neo/aeiua ioeaee niaea?aeao a naiae iniiaa iiiai ?acee/iuo i?e/ei,
eaaeaeay ec eioi?uo ia i?iyaeyao naay io/aoeeai. Neo/aeioth ioeaeo
iiaeii ?anniao?eaaoue eae noiia?iue yooaeo aeaenoaey iiiaeo oaeoi?ia.
Iiyoiio neo/aeiua ioeaee i?e iiiaie?aoiuo ecia?aieyo iieo/athony
?acee/iuie eae ii aaee/eia, oae e ii ciaeo. Eo iaaiciiaeii o/anoue eae
nenoaiaoe/aneea, ii iiaeii o/anoue eo aeeyiea ia ioeaieo enoeiiiai
cia/aiey ecia?yaiie aaee/eiu. Aiaeec neo/aeiuo ioeaie yaeyaony
aaaeiaeoei ?acaeaeii iaoaiaoe/aneie ia?aaioee yenia?eiaioaeueiuo
aeaiiuo.

3. A?oaua ioeaee (i?iiaoe) iiyaeythony aneaaenoaea iai?aaeeueiiai
ion/aoa ii oeaea, iai?aaeeueiie caiene, iaaa?iie onoaiiaee oneiaee
yenia?eiaioa e o.i. Iie eaaei auyaeythony i?e iiaoi?iii i?iaaaeaiee
iiuoia.

A aeaeueiaeoai aoaeai n/eoaoue, /oi nenoaiaoe/aneea e a?oaua ioeaee ec
?acoeueoaoia yenia?eiaioa eneeth/aiu.

1.4. Naienoaa neo/aeiuo ioeaie

Neo/aeiua ioeaee auaatho eae iieiaeeoaeueiua, oae e io?eoeaoaeueiua
?aciie aaee/eiu, ia i?aainoiaeyuae ii?aaeaeaiiiai i?aaeaea. Anee
iaicia/eoue /a?ac O enoeiiia cia/aiea ecia?yaiie aaee/eiu, a ?acoeueoao
ia?aiai ecia?aiey ( a1, oi ?aciinoue

O ( a1 = o1 eee a1 ( O = o1

iacuaatho enoeiiie aaniethoiie ioeaeie iaeiiai ecia?aiey. Iaeiia?aiaiii
iia yaeyaony neo/aeiie (i?e eneeth/aiee nenoaiaoe/aneeo e a?oauo
ioeaie).

Anee ecia?aiey i?iaanoe iiiaie?aoii a iaeieo e oao aea oneiaeyo, oi
?acoeueoaou ioaeaeueiuo ecia?aiee iaeeiaeiai iaaeaaeiu. Oaeoth
niaieoiiinoue ecia?aiee a1, a2 …an iacuaatho ?aaiioi/iuie ecia?aieyie.
Anee i?iaiaeece?iaaoue aeinoaoi/ii aieueooth na?eth ?aaiioi/iuo
ecia?aiee e niioaaonoaothueo neo/aeiuo ioeaie ecia?aiee, oi iiaeii
auaeaeeoue 4 naienoaa neo/aeiuo ioeaie:

1. *enei iieiaeeoaeueiuo ioeaie ii/oe ?aaii /eneo io?eoeaoaeueiuo;

2. Iaeeea ioeaee ano?a/athony /aua, /ai e?oiiua;

Aaee/eia iaeaieaa e?oiiuo ioeaie ia i?aainoiaeeo iaeioi?iai
ii?aaeaeaiiiai i?aaeaea, caaenyuaai io oi/iinoe ecia?aiey. Naioth
aieueooth ioeaeo a ?yaeo ?aaiioi/iuo ecia?aiee iacuaatho i?aaeaeueiie
ioeaeie;

4. *anoiua io aeaeaiey aeaaa?ae/aneie noiiu anao neo/aeiuo ioeaie ia eo
iauaa aeecei e ioeth, o.a.

.

Ia iniiaa oeacaiiuo naienoa i?e o/aoa iaeioi?uo aeiiouaiee
iaoaiaoe/anee aeinoaoi/ii no?iai auaiaeeony caeii ?ani?aaeaeaiey ioeaie,
iienuaaaiue neaaeothuae ooieoeeae:

,

aaea ( ( aeenia?ney ecia?aiee (ni. ieaea);

a ( iniiaaiea iaoo?aeueiuo eiaa?eoiia;

o ( enoeiiay aaniethoiay ioeaea ecia?aiee.

Eia/a yoo caaeneiinoue iacuaatho oi?ioeie neo/aeiuo ioeaie, oi?ioeie
Aaonna. Ia ?en.1 i?eaaaeaiu e?eaua Aaonna n ?acee/iie aaee/eiie (.

?en. 1. E?eaay neo/aeiuo ioeaie

Caeii ?ani?aaeaeaiey neo/aeiuo ioeaie yaeyaony iniiaiui a
iaoaiaoe/aneie oai?ee iia?aoiinoae. Eia/a aai iacuaatho ii?iaeueiui
caeiiii ?ani?aaeaeaiey. Iniaia cia/aiea a iieueco oe?ieiai
eniieueciaaiey caeiia Aaonna eiaao neaaeothuaa ianoiyoaeuenoai: anee
noiia?iay ioeaea ecia?aiey iiyaeyaony a ?acoeueoaoa niaianoiiai
aeaenoaey ?yaea i?e/ei, eaaeaeay eo eioi?uo aiineo iaeoth aeieth a
iauoth ioeaeo (o.a. iao aeiieie?othueo i?e/ei), oi ii eaeiio au caeiio
ia auee ?ani?aaeaeaiu ioeaee, aucuaaaiua eaaeaeie ec i?e/ei, ?acoeueoao
eo niaianoiiai aeaenoaey i?eaaaeao

e ii?iaeueiiio ?ani?aaeaeaieth ioeaie. Yoa caeiiiia?iinoue yaeyaony
neaaenoaeai oae iacuaaaiie oeaio?aeueiie i?aaeaeueiie oai?aiu Eyioiiaa e
oi?ioi niioiineony n aaaaeaiiui iiiyoeai neo/aeiie ioeaee.

Ia?yaeo n ii?iaeueiui caeiiii ?ani?aaeaeaiey ioeaie iiaoo ano?a/aoueny
e ae?oaea.

1.5. Iaeaieaa aa?iyoiia cia/aiea ecia?yaiie aaee/eiu

Aeiionoei, /oi aeey ii?aaeaeaiey enoeiiiai cia/aiey O ecia?yaiie
aaee/eiu auei naeaeaii n ?aaiioi/iuo ecia?aiee n ?acoeueoaoaie a1, a2 ..
.an. Anoanoaaiii, /oi ?yae yoeo /enae aoaeao aieueoa O, ae?oaea iaiueoa
O e iaynii, eaeia ec yoeo /enae aeeaea anaai iiaeoiaeeo e O.

I?aaenoaaei ?acoeueoaou ecia?aiee a aeaea i/aaeaeiuo ?aaainoa:

a1 = O ( (o1; a2 = O ( (o2; … ; an = O ( (on.

Anoanoaaiii, /oi enoeiiua aaniethoiua ioeaee (oi iiaoo i?eieiaoue eae
iieiaeeoaeueiua, oae e io?eoeaoaeueiua cia/aiey.

Noiie?oy eaaua e i?aaua noi?iiu ?aaainoa iieo/ei

.

Iiaeaeei iaa /anoe ?aaainoaa ia /enei ecia?aiee n e iieo/ei

.

yaeyaony n?aaeiaa?eoiaoe/aneei aaee/eiu O. Anee /enei n aeinoaoi/ii
aaeeei ( i?e n((), oi niaeanii /aoaa?oiio naienoao neo/aeiuo ioeaie

.

Yoi aea aeaeii e ii e?eaie Aaonna (?en. 1), aaea anyeie iieiaeeoaeueiie
iia?aoiinoe niioaaonoaoao ?aaiay ae io?eoeaoaeueiay.

Ec eceiaeaiiiai neaaeoao, /oi

O = a i?e n ( (,

o.a. i?e aaneiia/iii /enea ecia?aiee enoeiiia cia/aiea ecia?yaiie
aaee/eiu ?aaii n?aaeiaa?eoiaoe/aneiio cia/aieth ?acoeueoaoia anao
ecia?aiee. I?e ia?aie/aiiii /enea ecia?aiee enoeiiia cia/aiea aoaeao
ioee/aoueny io n?aaeiaa?eoiaoe/aneiai e iaiaoiaeeii ioeaieoue aaee/eio
yoiai ?anoiaeaeaiey: O = a ( (o.

Neaaeoao aua ?ac iiae/a?eiooue, /oi n?aaeiaa?eoiaoe/aneia cia/aiea,
i?eieiaaiia ca enoeiiia cia/aiea ecia?yaiie aaee/eiu, yaeyaony iaeaieaa
aa?iyoiui cia/aieai. N?aaee cia/aiee ai iiaoo ieacaoueny cia/aiey,
eioi?ua a aeaenoaeoaeueiinoe aeeaea e enoeiiiio cia/aieth.

Ioeeiiaiea (o aa?iyoiaeoaai cia/aiey a io aai enoeiiiai cia/aiey O
iacuaatho enoeiiie aaniethoiie ioeaeie.

1.6. Ioeaiea oi/iinoe ecia?aiee

Aeey ?yaea ?aaiioi/iuo ecia?aiee a1, a2 …an ii?aaeaeei aai
n?aaeiaa?eoiaoe/aneia cia/aiea a e ninoaaei ?aciinoe (a ( a1), (a ( a2),
…, (a ( an).

o.a. aeaaa?ae/aneay noiia aa?iyoiaeoeo ioeaie ?aaia ioeth i?e ethaii
/enea ecia?aiee. Enoeiiua neo/aeiua ioeaee oaeei naienoaii ia
iaeaaeatho.

Aa?iyoiaeoea ioeaee Vi eaaeao a iniiaa iaoaiaoe/aneie ia?aaioee
?acoeueoaoia ecia?aiee: eiaiii ii iei au/eneytho i?aaeaeueioth
aaniethoioth ioeaeo (ai n?aaeiaa?eoiaoe/aneiai a e oai naiui ioeaieaatho
oi/iinoue ?acoeueoaoa ecia?aiee.

N?aaeiyy enoeiiay neo/aeiay ioeaea (eia/a ( n?aaeiaa ioeeiiaiea
ioaeaeueiiai ecia?aiey) ii?aaeaeyaony au?aaeaieai ((o1+(o2+…+(on)(n.

yaeyaony eo/oei e?eoa?eai oi/iinoe, /ai n?aaeiyy neo/aeiay ioeaea,
o.e. ia i?ienoiaeeo eiiiainaoeee iieiaeeoaeueiuo e io?eoeaoaeueiuo
ioeaie (oi e neeueiaa o/eouaaaony aeaenoaea e?oiiuo ioeaie.

oi. Aeey ii?aaeaeaiey n?aaeiae eaaae?aoe/iie ioeaee S eniieuecoaony
iieiaeaiea oai?ee neo/aeiuo ioeaie, /oi i?e aieueoii /enea ecia?aiee n
ni?aaaaeeeai ?aaainoai

.

oi yaeythony iacaaeneiuie, a ec n aaee/ei Vi iacaaeneiuie yaeythony
n(1, o.e. a aaee/eio Vi aoiaeeo a, naii ii?aaeaeyaiia ec yoeo aea n
ecia?aiee.

Aaaeii, /oi ia ciay naieo enoeiiuo neo/aeiuo ioeaie oaeaaony au/eneeoue
n?aaeithth eaaae?aoe/ioth ioeaeo ii?aaeaeaiiiai ecia?aiey:

.

Ioeaiei oaia?ue iia?aoiinoue ?acoeueoaoa anae na?ee yenia?eiaioa, o.a.
ii?aaeaeei aaee/eio (o = O ( a.

Aeey yoiai i?iaaaeai i?aia?aciaaiea au?aaeaiey

.

Anee iiaoi?eoue na?ee ii n ecia?aiee a eaaeaeie N ?ac, iiaeii
iieo/eoue n?aaeiea cia/aiey a1, a2, … , aN e iia?aoiinoe ?acoeueoaoia
ecia?aiee

((o)1 = (O ( a1); ((o)2 = (O ( a2); … ; ((o)N = (O ( aN)

e n?aaeithth n?aaeiaeaaae?aoe/ioth iia?aoiinoue na?ee

I?e aieueoii /enea N S2a ( (2a

.

On?aaeiyy au?aaeaiea S2n ii /eneo na?ee N, iieo/aai

.

O/eouaay /oi i?e aieueoii n S2n ( (2 e S2 ( (2 iieo/aai eneiioth

(2

,

o.a. aeenia?ney (2a ?acoeueoaoa na?ee ec n ecia?aiee a n ?ac iaiueoa
aeenia?nee ioaeaeueiiai ecia?aiey. I?e ia?aie/aiiii /enea n ecia?aiee
i?eaeeaeaiiui au?aaeaieai (2a aoaeao S2a

.

Au?aaeaiey (2a e S2a io?aaeatho ooiaeaiaioaeueiue caeii aic?anoaiey
oi/iinoe i?e ?inoa /enea iaaethaeaiee. Ec iaai neaaeoao, /oi aeaeay
iiauneoue oi/iinoue ecia?aiee a 2 ?aca iu aeieaeiu naeaeaoue aianoi
iaeiiai ( /aou?a ecia?aiey; /oiau iiauneoue oi/iinoue a 3 ?aca, ioaeii
oaaee/eoue /enei ecia?aiee a 9 ?ac e o.ae.

Iiiyoea aeiaa?eoaeueiiai eioa?aaea e aeiaa?eoaeueiie aa?iyoiinoe

Eae onoaiiaeaii ?aiaa, enoeiiia cia/aiea ecia?yaiie aaee/eiu O
ioee/aaony io n?aaeiaa?eoiaoe/aneiai a ia iaeioi?oth aaee/eio (x. Ia
?en. 2 i?aaenoaaeaii ?aniieiaeaiea enoeiiiai cia/aiey O e a, iieo/aiiiai
ec iaeioi?uo ecia?aiee a1, a2, a3.

ssnii, /oi neo/aeiua aaee/eiu a1, a2, a3 iaoneiayo neo/aeiue oa?aeoa?
aaniethoiie iia?aoiinoe (x ?acoeueoaoa na?ee ecia?aiee, eioi?ay aoaeao
?ani?aaeaeaia ii caeiio Aaonna:

.

?en. 2. Acaeiiia ?aniieiaeaiea O e a, iieo/aiiuo

ec o?ao ecia?aiee a1, a2, a3

Oiaaea aianoi au?aaeaiey O = a ( (o iiaeii caienaoue a ( (o ( O ( a + (.

Eioa?aae (a ( (o; a + (o), a eioi?ue ii ii?aaeaeaieth iiiaaeaao
enoeiiia cia/aiea X iacuaatho aeiaa?eoaeueiui eioa?aaeii.
Iaaeaaeiinoueth (o?iaiai cia/eiinoe( ?acoeueoaoa na?ee ecia?aiee
iacuaaaony aa?iyoiinoue ( oiai, /oi enoeiiia cia/aiea X ecia?yaiie
aaee/eiu iiiaaeao a aeiaa?eoaeueiue eioa?aae. Aa?iyoiinoue ( au?aaeaaony
a aeieyo aaeeieoeu eee i?ioeaioao. A?aoe/anee iaaeaaeiinoue io?aaeaaony
ieiuaaeueth iiae e?eaie ii?iaeueiiai ?ani?aaeaeaiey a i?aaeaeao
aeiaa?eoaeueiiai eioa?aaea, ioianaiiie e iauae ieiuaaee. Auai?
iaaeaaeiinoe ii?aaeaeyaony oa?aeoa?ii i?iecaiaeeiuo ecia?aiee. Iai?eia?,
e aeaoaeyi naiieaoa i?aaeuyaeythony aieaa aeanoeea o?aaiaaiey, /ai e
eiaei/iiio iioi?o, a e iineaaeiaio cia/eoaeueii aieueoa, /ai e ?o/iie
oa/ea. I?e iau/iuo ecia?aieyo ia?aie/eaathony aeiaa?eoaeueiie
aa?iyoiinoueth 0,90 eee 0,95. Aeey ethaie aaee/eiu aeiaa?eoaeueiiai
eioa?aaea (au?aaeaiiiai a aeieyo ( ( ii oi?ioea Aaonna iiaeao auoue
i?in/eoaia niioaaonoaothuay aeiaa?eoaeueiay aa?iyoiinoue. Yoe au/eneaiey
i?iaeaeaiu e naaaeaiu a oaaeeoeo, eiathuothny i?aeoe/anee ai anae
eeoa?aoo?a ii oai?ee aa?iyoiinoe. Ia ?en. 3 i?aaenoaaeaiu cia/aiey
iaaeaaeiinoe ( i?e aaee/eia aeiaa?eoaeueiiai eioa?aaea ((, (2(, (3(. Yoe
cia/aiey aeiaa?eoaeueiie aa?iyoiinoe ?aeiiaiaeoaony caiiiieoue.

Ii ?en. 3 aeaeii, /oi aaee/eia aaniethoiie iia?aoiinoe (x iiaeao auoue
i?aaenoaaeaia a aeaea E((a, aaea E iaeioi?ue /eneaiiue eiyooeoeeaio,
caaenyuee io iaaeaaeiinoe (. Iaeiaei yoi ni?aaaaeeeai eeoue aeey
aieueoiai (aaneiia/iiai( /enea n. I?e iaeuo n yoei eiyooeoeeaioii
iieueciaaoueny iaeuecy, o.e. aaee/eia (a iaecaanoia. Aeey oiai, /oiau
iieo/eoue ioeaiee a?aieoe aeiaa?eoaeueiiai eioa?aaea i?e iaeii n
aaiaeeony iiaue eiyooeoeeaio ((. Yoio eiyooeoeeaio i?aaeeiaeai
aiaeeeneei iaoaiaoeeii e oeieeii A.N. Ainnaoii, ioaeeeiaaaoei naie
?aaiou iiae inaaaeiieiii ( Nouethaeaio (.

?en. 3. Cia/aiey iaaeaaeiinoe ( i?e ?acee/iuo cia/aieyo (x((

i?e ?acee/iii n. I?e n(( ( i?aeoe/anee i?e n ( 20 ( ?ani?aaeaeaiea
Nouethaeaioa ia?aoiaeeo a ii?iaeueiia ?ani?aaeaeaiea. Cia/aiey
eiyooeoeeaioa Nouethaeaioa oaeaea i?eaiaeyony i?aeoe/anee ai anae
eeoa?aoo?a ii oai?ee aa?iyoiinoe.

Ciay aaee/eio (( iiaeii ii?aaeaeeoue aaee/eio aaniethoiie iia?aoiinoe
(o = t(Sa . Neaaeoao ioiaoeoue, /oi aaee/eia aaniethoiie iia?aoiinoe aua
ia ii?aaeaeyao oi/iinoue ecia?aiee. Oi/iinoue ecia?aiee oa?aeoa?ecoao
ioiineoaeueiay iia?aoiinoue, ?aaiay ioiioaieth aaniethoiie iia?aoiinoe
(x ?acoeueoaoa ecia?aiee e ?acoeueoaoo ecia?aiee a: ( = ( (o ( a.
.

Iaia?oaeaiea i?iiaoia

Anee a ?yaeo ecia?aiee ano?a/athony ?acoeueoaou, ?acei ioee/athueany io
aieueoae /anoe ?yaea, oi aicieeaao aii?in i?eiaaeeaaeiinoe (
auneaeeaathueo ( cia/aiee yoiio ?yaeo ecia?aiee. Aieueoea ioeaee eiatho
iaeoth aa?iyoiinoue aicieeiiaaiey. Iiyoiio neaaeoao iauaeoeaii
ioeaieoue, yaeyaony ee aeaiiia ecia?aiea i?iiaoii ( oiaaea aai
eneeth/atho ec ?yaea ( eee aea yoi ?acoeueoao neo/aeiiai, ii niaa?oaiii
caeiiiia?iiai ioeeiiaiey. Iiaeii n/eoaoue eaaeaeia ecia?aiea i?iiaoii,
anee aa?iyoiinoue neo/aeiiai iiyaeaiey oaeiai cia/aiey yaeyaony
aeinoaoi/ii iaeie.

Anee ecaanoii oi/iia cia/aiea (, oi aa?iyoiinoue iiyaeaiey cia/aiey,
ioee/athuaainy io n?aaeiaa?eoiaoe/aneiai a aieaa /ai ia 3( ( 0,003 e ana
ecia?aiey, ioee/athueany io a ia 3( ( e aieueoa ( iiaoo auoue ioa?ioaiu,
eae iaeiaa?iyoiua.

Neaaeoao eiaoue a aeaeo, /oi aeey niaieoiiinoe ecia?aiee aa?iyoiinoue
iiyaeaiey ecia?aiey ( 3( io a anaaaea aieueoa 0,003. Aeaenoaeoaeueii,
aa?iyoiinoue oiai, /oi ?acoeueoao eaaeaeiai ecia?aiey ia aoaeao
ioee/aoueny io enoeiiiai aieaa /ai 3( ninoaaeyao 1( 0,003 ( 0,997.
Aa?iyoiinoue oiai, /oi ana n ecia?aiee ia aoaeoo ioee/aoueny io
n?aaeiaai aieaa /ai ia 3( ii i?aaeeo oiiiaeaiey aa?iyoiinoae ninoaaeo (
1 ( 0,003 (n. Aeey ia neeoeii aieueoiai n

(1 ( 0,003)n ( 1 ( 0,003(n.

Yoi cia/eo, /oi aa?iyoiinoue oiai, /oi ec 10 ecia?aiee oioy au iaeii
aoaeao neo/aeii ioee/aoueny io n?aaeiaai aieaa /ai ia 3( aoaeao oaea ia
0,003, a 0,03 eee 3%. A i?e 100 ecia?aieyo aa?iyoiinoue oaeiai niauoey
ninoaaeo oaea ieiei 30%.

Iau/ii /enei ecia?aiee ia i/aiue aaeeei. I?e yoii oi/iia cia/aiea ( ia
ecaanoii, neaaeiaaoaeueii, ioa?anuaaoue ecia?aiey, ioee/athueany io
n?aaeiaai aieaa /ai ia 3(, iaeuecy.

Aeey ioeaiee aa?iyoiinoe ( neo/aeiiai iiyaeaiey (auneaeeaathueo(
cia/aiee a ?yaeo n ecia?aiee ninoaaeaiu niioaaonoaothuea oaaeeoeu.

Aeey i?eiaiaiey oaaeeoeu au/eneyaony n?aaeiaa a?eoiaoe/aneia a e
n?aaeiyy eaaae?aoe/iay iia?aoiinoue (n ec anao ecia?aiee, aeeth/ay e
iiaeic?aaaaiia cia/aiea a(. Caoai au/eneyaony oeeiiaiea iiaeic?aaaaiiai
cia/aiey a( io n?aaeiaai a?eoiaoe/aneiai a aeieyo n?aaeiaeaaae?aoe/iie
ioeaee

Ii oaaeeoea ii?aaeaeyaony eaeie aa?iyoiinoe ( niioaaonoaoao iieo/aiiia
cia/aiea Viaen.

Anee aa?iyoiinoue iiyaeaiey aeaiiiai ecia?aiey a ?yaeo eaaeeo a
aeeaiaciia 0,1 ( ( ( 0,01, oi i?aaenoaaeyaony iaeeiaeiai i?aaeeueiui (
inoaaeoue yoi ecia?aiea eee ioa?ineoue. A neo/aa aea, eiaaea ( auoiaeeo
ca oeacaiiua i?aaeaeu, aii?in ia ioa?anuaaiee ?aoaaony i?aeoe/anee
iaeiicia/ii. ?aoay aii?in ia ioa?anuaaiee iieacii iiniio?aoue, eae
neeueii iii iaiyao ieii/aoaeueiue ?acoeueoao ii a e (n.

1.9. Ioeaee einaaiiuo ecia?aiee

*anoi ecia?yaony ia iaiin?aaenoaaiii eioa?anothuay ian aaee/eia, a
ae?oaay, caaenyuay io iaa iaeioi?ui ia?acii. Iai?eia?, i?e ?acaiee
iaoaeeia /anoi iaiin?aaenoaaiii ecia?ythony aeaoi?iaoeee, YAeN, ii
eioi?ui noaeyo i aicieeathueo neeao e oaiia?aoo?ao. I?e yoii oaeaea
iaiaoiaeeii ioeaieoue ioeaeo ecia?aiey.

I?e einaaiiuo ecia?aieyo cia/aiea y ecia?yaiie aaee/eiu iaoiaeyo ii
iaeioi?ie oi?ioea

y = ( (o1, o2, … , om),

aaea x1, x2, … xm ( n?aaeiea a?eoiaoe/aneea ecia?yaiua
(iaiin?aaenoaaiii( aaee/eiu. ?anniio?ei ooieoeeth iauaai aeaea

y = ( (o1, o2, … , om)

aaea x1, x2, … , xm ( iacaaeneiua ia?aiaiiua, aeey ii?aaeaeaiey
eioi?uo i?iecaiaeyony n i?yiuo iacaaeneiuo ecia?aiee ii eaaeaeie xi.

Iaicia/ei cia/aiey ia?aiaiiuo /a?ac n?aaeiaa cia/aiea e ioeeiiaiey

y ( (y = ( (x1 ( (x1, x2 ( (x2, … , xm ( (xm).

Yoo ooieoeeth i?aaenoaaei ?yaeii Oaeei?a, ia?aie/ea aai ia?auie /eaiaie
?yaea ( i?eieiay (xi (( xi )

aaea

( i?iecaiaeiay ooieoeee ii xi, acyoay a oi/ea xi.

O/eouaay, /oi y = ( (x1, x2, … , xm) iieo/aai

.

*oiau o/anoue iia?aoiinoe (xi anao n iiuoia oeaeaniia?acii
eniieueciaaoue n?aaeiea eaaae?aoe/aneea ioeaiee ( ( xi )2, oae eae (xi (
0.

Aicaaaeai a eaaae?ao eaaoth e i?aaoth /anoe o?aaiaiey e ?acaeaeei ia n

.

Caeanue noiiu oaeaiaiiuo i?iecaaaeaiee oeia

niaeanii /aoaa?oiio naienoao neo/aeiuo ioeaie ( (xi ( 0 ).

Oiaaea a eaaie e i?aaie /anoyo eiaai n?aaeiaeaaae?aoe/aneea iia?aoiinoe
ooieoeee e a?aoiaioia

.

I?eia?. I?e oa?e?iaea aeeiaiiiao?a auei iieo/aii o?aaiaiea caaeneiinoe
neeu io ioeeiiaiey l eo/a inoeeeeia?aoa aeaea P ( 25 l. Oi/iinoue
ecia?aiey ioeeiiaiey ( l ( 1 ii. Oiaaea

.

A ea/anoaa ia?u oi/iinoe eo/oa aunooiaao ia aaniethoiay, a
ioiineoaeueiay iia?aoiinoue.

.

?anniio?ei aa ii?aaeaeaiea ia i?eia?a. Ionoue

y = cx1((x2((x3(.

Oiaaea

;

.

.

Aiaeiae/ii iiaeii ii?aaeaeeoue ioiineoaeueioth iia?aoiinoue e i?e
ae?oaeo caaeneiinoyo. Ciay ioiineoaeueioth iia?aoiinoue, iiaeii
ii?aaeaeeoue e aaniethoiia aa cia/aiea:

(y = y((y.

I?aaeea ie?oaeaiey /enae

Aaee/eia iia?aoiinoe ?acoeueoaoa ecia?aiee oece/aneie aaee/eiu aeaao
i?aaenoaaeaiea i oii, eaeea oeeo?u a /eneiaii cia/aiee ecia?yaiie
aaee/eiu niiieoaeueiu. Iiyoiio ?acoeueoaou ecia?aiee neaaeoao ie?oaeyoue
ia?aae oai, eae i?iecaiaeeoue n ieie aeaeueiaeoea au/eneaiey.

Ie?oaeyoue /eneiaia cia/aiea ?acoeueoaoa ecia?aiee neaaeoao a
niioaaonoaee n /eneiaui ?ac?yaeii cia/auae oeeo?u iia?aoiinoe. I?e yoii
auiieiytho iauea i?aaeea ie?oaeaiey.

Eeoiea oeeo?u a oeaeuo /eneao caiaiythony ioeyie, a a aeanyoe/iuo
ae?iayo ioa?anuaathony ( eae e eeoiea ioee ). Iai?eia?, anee
iia?aoiinoue ecia?aiey ( 0,001 ii, oi ?acoeueoao 1,07005 ie?oaeyaony aei
1,070.

Anee ia?aay ec eciaiyaiuo ioeyie e ioa?anuaaaiuo oeeo? iaiueoa 5,
inoathueany oeeo?u ia eciaiythony. Iai?eia?, /enei 148935, oi/iinoue
ecia?aiey ( 50, ie?oaeaiea( 148900.

Anee ia?aay ec caiaiyaiuo ioeyie eee ioa?anuaaaiuo oeeo? ?aaia 5, a ca
iae ia neaaeoao ieeaeeo oeeo? eee eaeoo ioee, oi ie?oaeaiea
i?iecaiaeeony aei aeeaeaeoaai /aoiiai /enea. Iai?eia?, /enei 123,50
ie?oaeyaony aei 124.

Anee ia?aay ec caiaiyaiuo ioeyie eee ioa?anuaaaiuo oeeo? aieueoa 5 eee
?aaia 5, ii ca iae neaaeoao cia/auay oeeo?a, oi iineaaeiyy inoathuayny
oeeo?a oaaee/eaaaony ia aaeeieoeo. Iai?eia?, /enei 6783,6 ie?oaeyaony
aei 6784.

Ii?yaeie ia?aaioee ?acoeueoaoia ecia?aiee

I?e i?aeoe/aneie ia?aaioea ?acoeueoaoia ecia?aiee iiaeii
iineaaeiaaoaeueii auiieieoue neaaeothuea iia?aoeee(

Caienaoue ?acoeueoaou ecia?aiee;

Au/eneeoue n?aaeiaa cia/aiea ec n ecia?aiee

Ii?aaeaeeoue iia?aoiinoe ioaeaeueiuo ecia?aiee Vi ( a ( ai;

Au/eneeoue eaaae?aou iia?aoiinoae ioaeaeueiuo ecia?aiee Vi 2;

Anee ianeieueei ecia?aiee ?acei ioee/athony ii naiei cia/aieyi io
inoaeueiuo ecia?aiee, oi neaaeoao i?iaa?eoue ia yaeythony ee iie
i?iiaoii. I?e eneeth/aiee iaeiiai eee ianeieueeeo ecia?aiee i.i.1…4
iiaoi?eoue;

Ii?aaeaeyaony n?aaeiyy eaaae?aoe/iay iia?aoiinoue ?acoeueoaoa na?ee
ecia?aiee

Caaeaaony cia/aiea iaaeaaeiinoe (;

Ii?aaeaeyaony eiyooeoeeaio Nouethaeaioa (( (n) aeey aua?aiiie
iaaeaaeiinoe ( e /enea i?iaaaeaiiuo ecia?aiee n;

Iaoiaeyony a?aieoeu aeiaa?eoaeueiiai eioa?aaea

(o = (( (n)(Sa

Anee aaee/eia iia?aoiinoe ?acoeueoaoa ecia?aiee (i.9) ieaaeaony
n?aaieiie n aaee/eiie ( iia?aoiinoe i?eai?a, oi a ea/anoaa a?aieoeu
aeiaa?eoaeueiiai eioa?aaea neaaeoao acyoue aaee/eio

.

Caienaoue ieii/aoaeueiue ?acoeueoao

X ( a ( (x ;

Ioeaieoue ioiineoaeueioth iia?aoiinoue ?acoeueoaoa na?ee ecia?aiee

Ia?aaioea ?acoeueoaoia ecia?aiee aeeaiao?a oeeeeiae?a

Iee?iiao?ii auei naeaeaii aeanyoue caia?ia aeeaiao?a oeeeeiae?a. Oeaia
aeaeaiey iee?iiao?a 0,01 ii. Ii?aaeaeeoue aeeaiao? oeeeeiae?a n
iaaeaaeiinoueth ( ( 0,95 e ( ( 0,99. Ioeaieoue aeeyiea /enea caia?ia ia
oi/iinoue iieo/aaiiai ?acoeueoaoa.

ai( 14,85; 14,80; 14,84; 14,81; 14,79;

14,81; 14,80; 14,85; 14,84; 14,80.

Aeey ia?auo iyoe ecia?aiee ii?aaeaeei n?aaeiaa?eoiaoe/aneia cia/aiea e
a?aieoeu aeiaa?eoaeueiiai eioa?aaea. Aeey oaeianoaa ?an/aoia auaa?ai
i?iecaieueiia /enei ai oaeiaiia aeey ?an/aoia (ai ( 14,80 ii) e
ii?aaeaeei ?aciinoe (ai ( ai) e eaaae?aou yoeo ?aciinoae. ?acoeueoaou
naaaeaiu a oaaeeoeo.

0, 09

0, 0043

Iaeaeai n?aaeiaa cia/aiea a e n?aaeiaeaaae?aoe/iia ioeeiiaiea (a(

a ( ai = 0, 018 ii;

( ii2 );

( ii ).

Aeey iaaeaaeiinoe ( ( 0,95 e n ( 5 (( ( 2,78. Aaniethoiay iia?aoiinoue
ecia?aiey (o(

(o ( ((( Sa ( 2,78 ( 0,0116 ( 0,0322 ii.

?acoeueoao ecia?aiey iiaeii i?aaenoaaeoue a aeaea

(14,818 ( 0,032( ii ( a ( (14,818 ( 0,032( ii

eee nio?aiyy a aaee/eia iia?aoiinoe iaeio cia/auoth oeeo?o

(14,82 ( 0,03( ii ( a ( (14,82 ( 0,03( ii,

o.a. 14,79 ii ( a ( 14,85 ii eee a ( (14,82 ( 0,03( ii.

Ioiineoaeueiay iia?aoiinoue

.

Oaia?ue iaeaeai aaniethoioth e ioiineoaeueioth iia?aoiinoue yoeo
ecia?aiee i?e ( ( 0,99.

A yoii neo/aa (( ( 4,60. Oiaaea

(o = (((Sa = 4,60(1,16(10-2 = 5,34(10-2 ( ii ).

Neaaeiaaoaeueii a ( (14,82 ( 0,05( ii

.

Aeaeii, /oi n oaaee/aieai iaaeaaeiinoe a?aieoeu aeiaa?eoaeueiiai
eioa?aaea aic?inee, a oi/iinoue ?acoeueoaoa oiaiueoeeanue.

.

Yoi aeaao aiciiaeiinoue ii?aaeaeeoue

(o = k((Sa = 1,96(1,16(10-2 ( 2(10-2 ( ii ),

o.a. iia?aoiinoue iieo/eeanue iaiueoa i?eia?ii ia 30%. Anee ii yoie
aaee/eia iia?aoiinoe ii?aaeaeeoue aaee/eio iaaeaaeiinoe i?e (( ( k(, oi
ec oaaeeoeu eiyooeoeeaioia Nouethaeaioa iieo/ei ( ( 0,90 aianoi
caaeaiiie ( ( 0,95. Neaaeiaaoaeueii i?e iaeii /enea ecia?aiee n
i?eiaiaiea caeiia ii?iaeueiiai ?ani?aaeaeaiey n (2 ( S2n aianoi
?ani?aaeaeaiey Nouethaeaioa i?eaiaeeo e oiaiueoaieth iaaeaaeiinoe
?acoeueoaoa ecia?aiee.

Iaeaeai n?aaeiea cia/aiey e iia?aoiinoe neaaeothueo iyoe ecia?aiee

0, 10

0, 0042

ai = 14, 80 ii;

( ii );

a ( ai = 0, 02 ii;

( ii2 );

Sa = 1, 05(10-2 ii.

I?e ( ( 0,95(

(o = (((Sa = ( 2,78(1,05(10-2 = 2,92(10-2 ( ii );

;

O = 14, 82 ( 0, 03 ii.

I?e ( ( 0,99(

(o = ( 4,60(1,05(10-2 ( 5(10-2 ( ii );

O = 14, 82 ( 0,05 ii.

?acoeueoaou i?aeoe/anee ia ioee/athony, io ?acoeueoaoia iieo/aiiuo ec
ia?aie na?ee.

(ii2).

Yoe aaee/eiu iieo/athony noiie?iaaieai iineaaeieo no?ie ec oaaeeoe
/anoiuo na?ee.

ai = 14, 80 ii;

( ii );

a ( ai = 0, 019 ii.

( ii2 );

Sa = 7, 35(10-3 ii.

I?e ( ( 0,95 eiaai

(o = t((Sa = ( 2,26(7,35(10-3 = ( 1,7(10-2 ( ii );

;

a = 14, 819 ( 0, 017 ii.

I?e ( ( 0,99 iieo/aai

(o = t((Sa = ( 3,25(7,35(10-2 = ( 2,4(10-2 ( ii );

;

a = 14, 819 ( 0, 024 ii.

Aeaeii, /oi aaniethoiay e ioiineoaeueiay iia?aoiinoue ?acoeueoaoa
aeanyoe ecia?aiee noaee ii/oe a aeaa ?aca iaiueoa iia?aoiinoae iyoe
ecia?aiee.

I?eiaiaiea ii?iaeueiiai ?ani?aaeaeaiey n (2 ( S2n aeaao a neo/aa ( (
0,95 k( ( 1,96 e (o ( 1,4 ( 10(2 ii, a aaee/eia iaaeaaeiinoe iiieaeaaony
aei 0,91; a neo/aa ( ( 0,99 iieo/aai k( ( 2,58 e (o ( 1,9 ( 10(2 ii, a
aaee/eia iaaeaaeiinoe iiieaeaaony aei ( ( 0,97.

Eae aeaeii, n ?inoii /enea ecia?aiee ?acee/ea iaaeaeo ?acoeueoaoaie,
au/eneaieyie ii ?ani?aaeaeaieth Nouethaeaioa e ii ii?iaeueiiio
?ani?aaeaeaieth oiaiueoaaony.

Eiio?ieueiua aii?inu

Oeaeue iaoaiaoe/aneie ia?aaioee ?acoeueoaoia yenia?eiaioa;

Aeaeu ecia?aiee;

Oeiu ioeaie ecia?aiey;

Naienoaa neo/aeiuo ioeaie;

Ii/aio n?aaeiaa?eoiaoe/aneia cia/aiea neo/aeiie aaee/eiu i?e ii?iaeueiii
caeiia aa ?ani?aaeaeaiey yaeyaony aa?iyoiaeoei cia/aieai?

*oi oaeia enoeiiay aaniethoiay e aa?iyoiaeoay ioeaee ioaeaeueiiai
ecia?aiey?

*oi oaeia aeiaa?eoaeueiue eioa?aae neo/aeiie aaee/eiu?

*oi oaeia o?iaaiue cia/eiinoe (iaaeaaeiinoe) na?ee ecia?aiee?

Aaiiao?e/aneee niune o?iaiy cia/eiinoe;

Ii/aio i?e iaeii /enea iiuoia iaeuecy iia?aoiinoue ecia?aiee
i?aaenoaaeoue a aeaea (o ( ( K(a?

*oi yaeyaony e?eoa?eai (neo/aeiinoe( aieueoiai ioeeiiaiey ecia?yaiie
aaee/eiu?

*ai ii?aaeaeyaony aaee/eia neo/aeiie ioeaee einaaiiuo ecia?aiee?

*ai ii?aaeaeyaony oi/iinoue /eneiaie caiene neo/aeiie aaee/eiu?

CAEIIU ?ANI?AAeAEAIEss NEO*AEIUO AAEE*EI

I?e oa?aeoa?enoeea neo/aeiuo aaee/ei iaaeinoaoi/ii oeacaoue eo
aiciiaeiua cia/aiey. Iaiaoiaeeii aua ciaoue ianeieueei /anoi aicieeatho
?acee/iua cia/aiey yoie aaee/eiu. Yoi oa?aeoa?ecoaony aa?iyoiinoueth p
ioaeaeueiuo aa cia/aiee.

Niioiioaiea, onoaiaaeeaathuaa naycue iaaeaeo cia/aieyie neo/aeiie
aaee/eiu e aa?iyoiinoyie yoeo cia/aiee, iacuaatho caeiiii ?ani?aaeaeaiey
neo/aeiie aaee/eiu. ?acee/atho eioaa?aeueiue e aeeooa?aioeeaeueiue
caeiiu ?ani?aaeaeaiey.

Aeaeu neo/aeiuo aaee/ei e caeiiu eo ?ani?aaeaeaiey

Iiae neo/aeiie aaee/eiie iiieiaaony aaee/eia, i?eieiathuay a
?acoeueoaoa iiuoa eaeia eeai /eneiaia eee ea/anoaaiiia cia/aiea.

Neo/aeiay aaee/eia, i?eieiathuay eiia/iia /enei eee
iineaaeiaaoaeueiinoue ?acee/iuo cia/aiee, iacuaaaony aeene?aoiie
neo/aeiie aaee/eiie. Neo/aeiay aaee/eia, i?eieiathuay ana cia/aiey ec
iaeioi?iai eioa?aaea, iacuaaaony iai?a?uaiie neo/aeiie aaee/eiie.

Iiae eioaa?aeueiui caeiiii ?ani?aaeaeaiey (eee ooieoeeae
?ani?aaeaeaiey) F (o) neo/aeiie aaee/eiu O iiieiatho aa?iyoiinoue p
oiai, /oi neo/aeiay aaee/eia O ia i?aauneo iaeioi?iai aa cia/aiey o

F (o) ( p (O ( o).

Iniiaiui naienoaii eioaa?aeueiiai ?ani?aaeaeaiey yaeyaony iiiioiiiia ia
oauaaiea a ia?aie/aiiii aeeaiaciia ( 0( 1 (.

Aeaenoaeoaeueii, anee o1 e o2 iaeioi?ua cia/aiey neo/aeiie aaee/eiu O.
I?e/ai o2 ( o1, oi i/aaeaeii, /oi niauoea p (O ( o2) ( p (O ( o1), o.e.
iaaeaeo cia/aieyie o1 e o2 iiaoo auoue e i?iiaaeooi/iua. Ec ii?aaeaeaiey
eioaa?aeueiiai caeiia neaaeoao, /oi F (o2) ( F (o1), /oi aiai?eo i
iiiioiiiii ia oauaaiee ooieoeee. I/aaeaeii oaeaea, /oi

F (( () ( p (O ( ( () ( 0;

( F (() ( F (( () ( 1,

F (( () ( p (O ( () ( 1;

o.a. F (o) eciaiyaony a aeeaiaciia io 0 aei 1.

Caeii ?ani?aaeaeaiey aeene?aoiie neo/aeiie aaee/eiu iiaeao auoue caaeai
oaaeeoeae eee nooiai/aoie ooieoeeae (?en. 4)

?en. 4. Eioaa?aeueiue caeii ?ani?aaeaeaiey

aeene?aoiie neo/aeiie aaee/eiu

Aeey aeene?aoiie neo/aeiie aaee/eiu

,

aaea noiie?iaaiea ?ani?ino?aiyaony ia oi ( o. A i?iiaaeooea iaaeaeo
aeaoiy iineaaeiaaoaeueiuie cia/aieyie O ooieoeey F (o) iinoiyiia. I?e
ia?aoiaea a?aoiaioa o /a?ac cia/aiea oi F (o) nea/eii aic?anoaao ia
aaee/eio p (O ( oi).

?anniio?ei p (o1 ( O ( o2). Anee o2 ( o1, oi i/aaeaeii, /oi

p (O ( o2) ( p (O ( o1) ( p (o1 ( O ( o2).

Oiaaea

p (o1 ( O ( o2) ( p (O ( o2) ( p (O ( o1) ( F (o2) ( F (o1),

o.a. aa?iyoiinoue iiiaaeaiey neo/aeiie aaee/eiu a eioa?aae (o1( o2)
?aaai ?aciinoe cia/aiee eioaa?aeueiie ooieoeee a?aie/iuo oi/ae.

Iineaaeiaa oneiaea iiaeii eniieueciaaoue aeey iaoiaeaeaiey aa?iyoiinoe
p (O ( o1) aeey iai?a?uaiie neo/aeiie aaee/eiu. Aeey yoiai ?anniio?ei
i?aaeae

,

o.a. anee caeii ?ani?aaeaeaiey neo/aeiie aaee/eiu anoue ooieoeey
iai?a?uaiay, oi aa?iyoiinoue oiai, /oi neo/aeiay aaee/eia i?eiao ca?aiaa
caaeaiiia cia/aiea, ?aaia ioeth.

Caeanue aeaeii ?acee/ea iaaeaeo aeene?aoiuie e iai?a?uaiuie neo/aeiuie
aaee/eiaie. Aeey aeene?aoiuo neo/aeiuo aaee/ei, aeey eaaeaeiai cia/aiey
neo/aeiie aaee/eiu nouanoaoao naiy aa?iyoiinoue. E aeey iaai
ni?aaaaeeeai ooaa?aeaeaiea: niauoea, aa?iyoiinoue eioi?iai ?aaia ioeth,
iaaiciiaeii. Aeey iai?a?uaiie neo/aeiie aaee/eiu yoi ooaa?aeaeaiea
iaaa?ii. Eae iieacaii, aa?iyoiinoue oiai, /oi O ( o1 ( aaea o1( ca?aiaa
aua?aiiia /enei) ?aaia ioeth, yoi niauoea ia yaeyaony iaaiciiaeiui.

?anniio?ei iai?a?uaioth neo/aeioth aaee/eio O, eioaa?aeueiue caeii
eioi?ie i?aaeiieaaaaony iai?a?uaiui e aeeooa?aioee?oaiui. Ooieoeeth

( (o) ( F( (o)

iacuaatho aeeooa?aioeeaeueiui caeiiii ?ani?aaeaeaiey eee ieioiinoueth
aa?iyoiinoe neo/aeiie aaee/eiu O. Ec ii?aaeaeaiey i?iecaiaeiie iiaeii
caienaoue

,

o.a. ieioiinoue aa?iyoiinoe neo/aeiie aaee/eiu O a oi/ea o ?aaia
i?aaeaeo ioiioaiey aa?iyoiinoe iiiaaeaiey aaee/eiu O a eioa?aae (o; o (
(o) e (o, eiaaea (o no?aieony e ioeth.

Eniieuecoy iiiyoey eioaa?aeueiie ooieoeee ?ani?aaeaeaiey e
ii?aaeaeaiiiai eioaa?aea iiaeii caienaoue

.

Yoi niioiioaiea eiaao i?inoia aaiiao?e/aneia oieeiaaiea (?en. 5).

ii?aaeaeyao caoo?eoiaaiioth iaeanoue a niioaaonoaothueo i?aaeaeao, oi

p (o ( O ( o ( (o) ( ( (o) (o.

?en. 5. Aaiiao?e/aneee niune aeeooa?aioeeaeueiie ooieoeee ?ani?aaeaeaiey

Ec naienoa eioaa?aeueiiai ?ani?aaeaeaiey neaaeoao

.

Ciay aeeooa?aioeeaeueiue caeii ?ani?aaeaeaiey iiaeii ii?aaeaeeoue
eioaa?aeueiue caeii ?ani?aaeaeaiey

.

*eneiaua oa?aeoa?enoeee neo/aeiuo aaee/ei, caaeaiiuo naieie
?ani?aaeaeaieyie

Iniiaiuie oa?aeoa?enoeeaie neo/aeiie aaee/eiu, caaeaiiie naieie
?ani?aaeaeaieyie, yaeyaony iaoaiaoe/aneia iaeeaeaiea ( eee n?aaeiaa
cia/aiea ) e aeenia?ney.

Iaoaiaoe/aneia iaeeaeaiea neo/aeiie aaee/eiu yaeyaony oeaio?ii aa
?ani?aaeaeaiey. Aeenia?ney oa?aeoa?ecoao ioeeiiaiea neo/aeiie aaee/eiu
io aa n?aaeiaai cia/aiey.

, oi iaoaiaoe/aneia iaeeaeaiea I (O) neo/aeiie aaee/eiu O ii?aaeaeyaony
?aaainoaii

,

o.a. noiiie i?iecaaaeaiee anao aa aiciiaeiuo cia/aiee ia
niioaaonoaothuea aa?iyoiinoe.

Iaoaiaoe/aneei iaeeaeaieai iai?a?uaiie neo/aeiie aaee/eiu yaeyaony
aiaeia aai aeene?aoiiai au?aaeaiey

.

Aeaenoaeoaeueii, ana cia/aiey a eioa?aaea (o; o ( (o) iiaeii n/eoaoue
i?eia?ii ?aaiuie o, a aa?iyoiinoue oaeeo cia/aiee ?aaia ( (o) dx (ni.
?aiaa). Iiyoiio cia/aiey oi aeene?aoiiai ?ani?aaeaeaiey caiaiythony o, a
aa?iyoiinoe pi ( ia ( (o) dx, a noiia caiaiyaony eioaa?aeii.

Aeenia?neae eee ?annayieai neo/aeiie aaee/eiu O iacuaaaony
iaoaiaoe/aneia iaeeaeaiea eaaae?aoa ?aciinoe neo/aeiie aaee/eiu e aa
iaoaiaoe/aneiai iaeeaeaiey.

D (O) ( I (O ( I (O)(2 ( I (O ( o)2 ( (2 (o)

Anee neo/aeiay aaee/eia O aeene?aoia e i?eieiaao cia/aiey oi n
aa?iyoiinoyie pi, oi neo/aeiay aaee/eia (O ( o)2 i?eieiaao cia/aiey (oi
( o)2 n aa?iyoiinoyie ?i. Iiyoiio aeey aeene?aoiie neo/aeiie aaee/eiu
eiaai

.

Aiaeiae/ii aeey iai?a?uaiie neo/aeiie aaee/eiu iieo/aai

.

*ai iaiueoa aaee/eia aeenia?nee, oai eo/oa cia/aiey neo/aeiie aaee/eiu
oa?aeoa?ecothony aa iaoaiaoe/aneei iaeeaeaieai.

Iniiaiua aeene?aoiua e iai?a?uaiua caeiiu ?ani?aaeaeaiey

Eae ioia/aeinue ?aiaa, i/aiue /anoi neo/aeiay aaee/eia ?ani?aaeaeaia ii
ii?iaeueiiio caeiio. Ii nouanoaotho e ae?oaea ?ani?aaeaeaiey, eiathuea
i?aeoe/aneia cia/aiea. ?anniio?ei iaeioi?ua ec ieo ii oneiaeyi
aicieeiiaaiey e iniiaiui ia?aiao?ai eo oa?aeoa?ecothuei.

?aaiiia?iia ?ani?aaeaeaiea aa?iyoiinoae.

Ionoue ieioiinoue aa?iyoiinoe A ?aaia ioeth anthaeo, e?iia eioa?aaea (a;
b), ia eioi?ii iia iinoiyiia (?en. 6). Oiaaea iiaeii caienaoue

.

?en. 6. Aeeooa?aioeeaeueiue e eioaa?aeueiue caeiiu

?aaiiia?iiai ?ani?aaeaeaiey

Oiaaea aeeooa?aioeeaeueiue caeii ?aaiiia?iiai ?ani?aaeaeaiey
ii?aaeaeyaony

Eioaa?aeueiue caeii ?ani?aaeaeaiey

.

I?e o ( b eiaai

Oaeei ia?acii eioaa?aeueiue caeii ?aaiiia?iiai ?ani?aaeaeaiey caaeaaony
(?en. 6)

Iniiaiua oa?aeoa?enoeee ?ani?aaeaeaiey

;

Aeiiieiaeueiia ?ani?aaeaeaiea

Ionoue i?e iaeioi?ii eniuoaiee niauoea A iiaeao ianooieoue eee ia
i?iecieoe (A). Iaicia/ei aa?iyoiinoue A /a?ac ?, a A /a?ac q ( 1 (? (
ae?oaeo eoiaia eniuoaiey iao ). Oiaaea enoiaeaie aeaoo
iineaaeiaaoaeueiuo iacaaeneiuo eniuoaiee e eo aa?iyoiinoueth aoaeoo:

AA ( ?2; AA ( ?q; AA ( q?; AA ( q2.

Ionthaea aeaeii, /oi aeaoe?aoiia iiyaeaiea niauoey A ?aaii ?2,
aa?iyoiinoue iaeiie?aoiiai iiyaeaiey ( 2 ?q, a aa?iyoiinoue oiai, /oi A
ia ianooieo ie ?aco ( q2. Yoe ?acoeueoaou aaeeinoaaiii aiciiaeiua e
iiyoiio

.

Yoi ?annoaeaeaiea iiaeii ia?aianoe ia ethaia /enei eniuoaiee.

Iai?eia?, i?e o?ao eniuoaieyo iieo/ei

.

Iiaen/eoaai aa?iyoiinoue oiai, /oi i?e n eniuoaieyo niauoea A iiyaeony m
?ac. Yoi iiaeao i?iecieoe, iai?eia?, a iineaaeiaaoaeueiinoe

. Eniieuecoy oai?aio neiaeaiey aa?iyoiinoae iieo/aai iauoth
aa?iyoiinoue ?m,n ianooieaiey m niauoee A ec n eniuoaiee

.

Ec yoie oi?ioeu aeaeii, /oi aa?iyoiinoe ?m,n aeey ?acee/iiai enoiaea
eniuoaiee (iiyaeaiea eee ia iiyaeaiea ii?aaeaeaiiiai ?acoeueoaoa A)
ii?aaeaeyaony

.

Eiyooeoeeaiou ia?aae aa?iyoiinoyie ?, q yaeythony aeiiieiaeueiuie
eiyooeoeeaioaie, a iauay aa?iyoiinoue i?aaenoaaeyao neaaaaiua a
?aceiaeaiee aeiiia ( ? ( q )n. Iiyoiio caeii ?ani?aaeaeaiey neo/aeiie
aaee/eiu O, a eioi?ii aa?iyoiinoue ianooieaiey niauoee A ii?aaeaeyaony
eiyooeoeeaioaie aeiiia, iacuaaaony aeiiieiaeueiui ?ani?aaeaeaieai
aeene?aoiie neo/aeiie aaee/eiu. Yoio caeii iiaeao auoue caaeai a aeaea
oaaeeoeu 1.

Oaaeeoea 1

Aeiiieiaeueiue caeii ?ani?aaeaeaiey

oi

0

1

2

m

n

pi

qn

pn

Aeiiieaeueiua eiyooeoeeaiou oaeiaii iieo/aoue n iiiiuueth o?aoaieueieea
Ianeaey.

1 n (
0

1 1 n (
1

1 2 1 n = 2

1 3 3 1 n = 3

1 4 6 4 1 n = 4

1 5 10 10 5 1 n = 5

Ana no?iee o?aoaieueieea ( ia/eiathuaainy n aaeeieoeu ) ia/eiathony e
caeai/eaathony aaeeieoeae. I?iiaaeooi/iua /enea iieo/athony neiaeaieai
ninaaeieo /enae auoanoiyuae no?iee. *enea, noiyuea a iaeiie no?iea,
yaeythony aeiiieiaeueiuie eiyooeoeeaioaie niioaaonoaothuae noaiaie.

Ec iienaiey aeiiieaeueiiai ?ani?aaeaeaiey noaiiaeony ynii, /oi iaeanoue
aai aeaenoaey oai, aaea aiciiaeii iiiaie?aoiia i?iaaaeaiea eniuoaiee n
ecaanoiie aa?iyoiinoueth.

Ia ?en. 7 i?aaenoaaeai aeiiieaeueiue caeii ?ani?aaeaeaiey.

?en. 7. Aeiiieaeueiue caeii ?ani?aaeaeaiey

Ii?aaeaeei iniiaiua oa?aeoa?enoeee yoiai ?ani?aaeaeaiey.

Iaoaiaoe/aneia iaeeaeaiea

= np (q + p)n-1 = np.

Aeenia?ney ?ani?aaeaeaiey iiaeao auoue ii?aaeaeaia ec iauaai au?aaeaiey

,

ii yoi i?eaiaeeo e a?iiicaeeei au/eneaieyi. A oi aea a?aiy neo/aeiay
aaee/eia O i?eieiaao a eaaeaeii iiuoa oieueei aeaa cia/aiey: 1, anee
niauoea A i?iecioei e 0, anee iii ia i?iecioei n aa?iyoiinoyie,
niioaaonoaaiii, ? eee q. Oiaaea iaoaiaoe/aneia iaeeaeaiea iaeiiai iiuoa
ii?aaeaeeony

I (O1) = 0(q ( 1(? ( ? ( o

e niioaaonoaaiii aeenia?ney iaeiiai iiuoa

D (O1) = (0 ( ?)2(q ( (1 ( ?)2(? ( ?2q ( q2? ( ?q (? ( q) ( ?q.

Oiaaea aeenia?ney anao n iiuoia ninoaaeo

D (X) ( n(p(q.

Caeii Ioanniia

A neo/aa iaeuo ? ( eee, iaiai?io, aeeceeo e 1 ) aeiiieiaeueiue caeii
?ani?aaeaeaiey iiaeii i?aia?aciaaoue neaaeothuei ia?acii

,

.

.

Ii?aaeaeei i?aaeae ?m,n i?e n ( ( e iinoiyiiii m. Oiaaea i?aaeaeu

.

Ieii/aoaeueii eiaai

.

Yoi ?ani?aaeaeaiea iacuaaaony caeiiii Ioanniia, aaea ( ( eioaineaiinoue
?ani?aaeaeaiey. Eniieuecoaony a caaea/ao n ?aaeeeie niauoeyie. Ia ?en. 8
i?aaenoaaeaia noaia aa?iyoiinoae, ?ani?aaeaeaiiuo ii caeiio Ioanniia.

?en. 8. Caeii ?ani?aaeaeaiey Ioanniia

Ii?aaeaeei aai iniiaiua oa?aeoa?enoeee e niune aaee/eiu (.

Caieoai caeii ?ani?aaeaeaiey a aeaea oaaeeoeu.

oi

0

1

2

m

pi

.

Au?aaeaiea a neiaeao anoue ?aceiaeaiea ooieoeee a( a ?yae Iaeei?aia.

Iiyoiio

I (O) ( (a((a( ( (.

Ia ?anniao?eaay auaiae ioiaoei, /oi

D (O) ( (,

o.a. aeenia?ney ?aaia iaoaiaoe/aneiio iaeeaeaieth.

?anniio?aiiua aeaeu ?ani?aaeaeaiee neo/aeiie aaee/eiu, eiia/ii, ia
en/a?iuaatho anao nouanoaothueo ?ani?aaeaeaiee. Iiaeii iacaaoue aua
ianeieueei: ?ani?aaeaeaiea Aa?ioeee, yeniiiaioeeaeueiia ?ani?aaeaeaiea,
aaiia ( ?ani?aaeaeaiea, ?ani?aaeaeaiea Aaeaoea, aeia?aaiiao?e/aneea
?ani?aaeaeaiey e ae?. I?e ii?aaeaeaiiuo oneiaeyo e ia?aiao?ao iaeei aeae
?ani?aaeaeaiey iiaeao ia?aoiaeeoue a ae?oaie. Iiyoiio i?e ?aoaiee
i?aeoe/aneeo caaea/ ii caeiiai ?ani?aaeaeaiey neo/aeiuo aaee/ei neaaeoao
ia?auaoueny e niaoeeaeueiie eeoa?aoo?a.

Iiiyoea noaoenoe/aneie aeiioacu e noaoenoe/aneiai e?eoa?ey

Noaoenoe/aneie aeiioacie iacuaatho ethaia ooaa?aeaeaiea i aeaea eee
naienoaao ?ani?aaeaeaiey iaaethaeaaiuo a yenia?eiaioa neo/aeiuo aaee/ei.
Oaeea ooaa?aeaeaiey iiaeii aeaeaoue ia iniiaa oai?aoe/aneeo niia?aaeaiee
eee noaoenoe/aneeo enneaaeiaaiee ae?oaeo iaaethaeaiee. Iai?eia?, i?e
iiiaie?aoiii ecia?aiee iaeioi?ie oece/aneie aaee/eiu, oi/iia cia/aiea O
eioi?ie ia ecaanoii, ii a i?ioeanna ecia?aiee iii iaiyaony. Ia
?acoeueoao ecia?aiee aeeytho iiiaea neo/aeiua oaeoi?u, iiyoiio
?acoeueoao i ( ai ecia?aiey iiaeii caienaoue a aeaea ai = O + (i, aaea
(i ( neo/aeiay iia?aoiinoue ecia?aiey. Anee (i neeaaeuaaaony ec
aieueoiai /enea ioeaie, eaaeaeay ec eioi?uo ia aaeeea, oi ia iniiaaiee
oeaio?aeueiie i?aaeaeueiie oai?aiu iiaeii i?aaeiieiaeeoue, /oi neo/aeiua
aaee/eiu ai eiatho ii?iaeueiia ?ani?aaeaeaiea. Oaeia i?aaeiieiaeaiea
yaeyaony noaoenoe/aneie aeiioacie i aeaea ?ani?aaeaeaiey iaaethaeaaiie
neo/aeiie aaee/eiu.

Anee aeey enneaaeoaiiai yaeaiey noi?ioee?iaaia oa eee eiay aeiioaca (
iau/ii aa iacuaatho iniiaiie eee ioeaaie aeiioacie e iaicia/atho
neiaieii Ii ), oi caaea/a ninoieo a oii, /oiau noi?ioee?iaaoue i?aaeei,
eioi?ia iicaieyei au ii ?acoeueoaoai iaaethaeaiee i?eiyoue eee
ioeeiieoue yoo aeiioaco. I?aaeei, niaeanii eioi?iio i?iaa?yaiay aeiioaca
Ii i?eieiaaony eee ioaa?aaaony, iacuaaaony noaoenoe/aneei e?eoa?eai
i?iaa?ee aeiioacu Ii .

Iaeaieaa ?ani?ino?aiaiu oaeea noaoenoe/aneea aeiioacu, eae:

a) aeaea ?ani?aaeaeaiey;

a) iaeii?iaeiinoe ianeieueeeo na?ee iacaaeneiuo ?acoeueoaoia;

a) neo/aeiinoe ?acoeueoaoia yenia?eiaioa e o.i.

Noaoenoe/aneee e?eoa?ee i?iaa?ee aeiioacu Ii neoaeeo aeey ii?aaeaeaiey
aiciiaeiiai ioeeiiaiey io iniiaiie aeiioacu. Oa?aeoa? ioeeiiaiee iiaeao
auoue ?acee/iui. Anee e?eoa?ee (oeaaeeaaao( ethaua ioeeiiaiey io Ii, oi
oaeie e?eoa?ee iacuaatho oieaa?naeueiui eee e?eoa?eai niaeaney.
Nouanoaotho e?eoa?ee, eioi?ua auyaeytho ioeeiiaiey io caaeaiiiai aeaea,
yoi ocei iai?aaeaiiua e?eoa?ee.

Auai? i?aaeea i?iaa?ee aeiioacu Ii yeaeaaeaioai caaeaieth e?eoe/aneie
iaeanoe o1, i?e iiiaaeaiee a eioi?oth ia?aiaiiie o aeiioaca Ii
ioaa?aaaony. E?eoa?ee, ii?aaeaeyaiue e?eoe/aneie iaeanoueth o1 iacuaatho
e?eoa?eai o1.

A i?ioeanna i?iaa?ee aeiioacu Ii iiaeii i?eeoe e i?aaeeueiiio ?aoaieth
eee niaa?oeoue ioeaeo ia?aiai ?iaea ( ioeeiieoue Ii eiaaea iia aa?ia,
eee ioeaeo aoi?iai ?iaea ( i?eiyoue Ii, eiaaea iia eiaeia. Eiuie
neiaaie, ioeaea ia?aiai ?iaea eiaao ianoi, anee oi/ea o iiiaaeaao a
e?eoe/aneoth iaeanoue o1, a oi a?aiy eae aa?ia ioeaaay aeiioaca Ii, a
ioeaea aoi?iai ?iaea ( eiaaea o ( oi, ii aeiioaca Ii eiaeia.

AEaeaoaeueii i?iaanoe i?iaa?eo aeiioacu oae, /oiau naanoe e ieieioio
aa?iyoiinoe iaieo ioeaie. Iaeiaei i?e aeaiiii /enea eniuoaiee n a iauai
neo/aa iaaiciiaeii iaeiia?aiaiii iaa yoe aa?iyoiinoe naeaeaoue eae
oaiaeii iaeuie. Iiyoiio iaeaieaa ?aoeeiiaeueii auae?aoue e?eoe/aneoth
iaeanoue neaaeothuei ia?acii: i?e caaeaiiii /enea eniuoaiee n
onoaiaaeeaaaony a?aieoea aeey aa?iyoiinoe ioeaee ia?aiai ?iaea e i?e
yoii auae?aaony oa e?eoe/aneay iaeanoue o1, aeey eioi?ie aa?iyoiinoue
ioeaee aoi?iai ?iaea ieieiaeueia.

2.5. Aa?iyoiinoe ioeaie ia?aiai e aoi?iai ?iaea

?anniio?ei noaiie, eioi?ue iiaeao ?aaioaoue oieueei a iaeiii ec aeaoo
ninoiyiee. Anee ii ?aaioaao a iaeaaeaiiii ?aaeeia, oi aeey
eioa?anothuaai ian i?eciaea ea/anoaa, iai?eia?, aeeeiu eee aeeaiao?a
caaioiaee, eiaao ianoi ii?iaeueiia ?ani?aaeaeaiea i?e ?aaioa eae a
iaeaaeaiiii oae e a ?aceaaeaiiii ?aaeeia. Iaa ?aaeeia ioee/athony
oieueei o?iaiai iano?ieee i?ioeanna ii iaoaiaoe/aneiio iaeeaeaieth (
I(o) = 10 e 11, niioaaonoaaiii a iaeaaeaiiii e ?aceaaeaiiii ?aaeeia ), a
oi a?aiy eae aeenia?nee a iaieo neo/ayo ninoaaeytho (2 = 4.

I?iaa?eoue ioaeii ioeaaoth aeiioaco, a niioaaonoaee n eioi?ie I(o) =
10, i?ioea aeueoa?iaoeau ( a aeaiiii neo/aa aaeeinoaaiiie ) I(o) = 11.
Eiieo?e?othuoth aeiioaco iaicia/ei I1. Oiaaea Ii: I(o) = 10; I1: I(o) =
11.

Iaiaoiaeeii ii ?acoeueoaoai auai?ee ii?aaeaeeoue a eaeii ec ninoiyiee
?aaioaao noaiie. I?eiai iauai auai?ee n ec iioaioeeaeueii aaneiia/iie
aaia?aeueiie niaieoiiinoe. A ea/anoaa eiio?ieueiie aaee/eiu aicueiai
auai?i/iia n?aaeiaa On. Ia ?en. 9 ecia?aaeaiu ieioiinoe ?ani?aaeaeaiey
On aeey n = 25 e n = 4.

Aeey oi?ioee?iaee e?eoa?ey iaiaoiaeeii ?acaeaeeoue iaeanoue eciaiaiey
eiio?ieueiie aaee/eiu (o) ia e?eoe/aneoth iaeanoue ioeeiiaiey aeiioacu
Ii ( i?eiyoey I1 ) e iaeanoue i?eiyoey aeiioacu Ii. Aeey yoiai
iaiaoiaeeii aua?aoue /enei E, oaeia, /oi 10 ( E ( 11, e eioa?aae ( ((; E
( ?anniao?eaaoue eae iaeanoue i?eiyoey aeiioacu Ii, a eioa?aae ( E; ( )
( eae iaeanoue ioeeiiaiey aeiioacu Ii. Ii ?en. 9 aeaeii, /oi eaaeaeay
?aaeecaoeey O25 eee O4 aiciiaeia i?e aa?iinoe ethaie ec aeaoo aeiioac,
ii n ?acee/iie aa?iyoiinoueth. Ia ?en. 9 oeacaiu aa?iyoiinoe niaa?oaiey
ioeaee ia?aiai

?en. 9. Ieioiinoe ?ani?aaeaeaiey aeaoo aeiioac i?e ?acee/iii

iauaia auai?ee e iaeeiaeiaie aeenia?nee

?iaea ( ( ioeeiiaiey aa?iie aeiioacu Ii ) e aoi?iai ?iaea ( ( i?eiyoea
aeiioacu Ii, eiaaea iia ia aa?ia ). Ii ?en. 9 oaeaea aeaeii, /oi
oaaee/aiea n aaaeao e oiaiueoaieth aeenia?nee ?ani?aaeaeaiey o e oai
naiui ( e iaeiia?aiaiiiio oiaiueoaieth aa?iyoiinoae ( e (. A
niioaaonoaee n ?en. 9 iiaeii caienaoue:

;

.

Yoe aeaa o?aaiaiey niaea?aeao /aou?a aaee/eiu (, (, E, n. Caaeaa aeaa
ec /aou?ao aaee/ei, iiaeii ii?aaeaeeoue aeaa ae?oaea.

Iai?eia?, i?e n = 25 e E = 10,4 ii?aaeaeei:

;

.

Anee caaeaoueny aaee/eiaie ( e (, oi iiaeii ii?aaeaeeoue aaee/eiu E, n.

2.6. I?iaa?ea aeiioacu aeaea caeiia ?ani?aaeaeaiey aa?iyoiinoae

I?e i?iaa?ea yenia?eiaioa caeii ?ani?aaeaeaiey aa?iyoiinoae neo/aeiuo
aaee/ei iaecaanoai e iiaeii eeoue i?aaeiieiaeeoaeueii noaeeoue i aai
aeaea . Auai?i/iua ioeaiee ia?aiao?ia ?ani?aaeaeaiey ianoo a naaa
neo/aeiua ioeaee, eneaaeathuea enoeiiue oa?aeoa? ?ani?aaeaeaiey. Iiyoiio
iinea iieo/aiey yiie?e/aneiai ?ani?aaeaeaiey i?iecaiaeeony iiaeai?
oai?aoe/aneiai caeiia ?ani?aaeaeaiey, i?eaiaeiiai aeey iienaiey
aa?iyoiinoiuo naienoa eco/aaiie neo/aeiie aaee/eiu. E?eoa?ee iiaeai?a (
i?iaa?ee aeiioacu niioaaonoaey ) iacuaatho a noaoenoeea e?eoa?eyie
niaeaney. Ana iie iniiaaiu ia auai?a aeiionoeiie ia?u ?anoiaeaeaiey
iaaeaeo oai?aoe/aneei ?ani?aaeaeaieai e auai?i/iuie aeaiiuie.

Iauoth i?ioeaaeo?o i?iaa?ee aeiioacu caeiia ?ani?aaeaeaiey iiaeii
i?aaenoaaeoue a neaaeothuae iineaaeiaaoaeueiinoe:

Ii iiuoiui aeaiiui no?ieony yiie?e/aneay e?eaay ?ani?aaeaeaiey
aa?iyoiinoae;

Ii?aaeaeythony ia?aiao?u yiie?e/aneiai ?ani?aaeaeaiey ( a niioaaonoaee n
aai aeaeii );

Auaeaeaaaony iaeia eee ianeieueei aeiioac i ooieoeee ieioiinoe
enneaaeoaiie neo/aeiie aaee/eiu, enoiaey ec aiaoiaai aeaea yiie?e/aneie
e?eaie, cia/aiee aa ia?aiao?ia, oaoie/aneeo oaeoi?ia, aeeythueo ia aa
aeae;

Yiie?e/aneay e?eaay au?aaieaaaony ii iaeiie eee ianeieueeei
oai?aoe/aneei e?eaui;

I?iaiaeeony n?aaiaiea ii iaeiiio eee ianeieueeei e?eoa?eyi niaeaney;

Auae?aaony oai?aoe/aneay ooieoeey, aeathuay iaeeo/oaa niaeaniaaiea.

Iiyniei i. 4; 5. Ii?aaeaeea ii yiie?e/aneei aeaiiui ia?aiao?u
?ani?aaeaeaiey, iiaenoaaeytho eo a oai?aoe/aneoth e?eaoth caeiia
?ani?aaeaeaiey e ?ann/eouaatho aa?iyoiinoue na?aaeei eioa?aaeia
yiie?e/aneiai ?ani?aaeaeaiey. Oiiiaeea cia/aiea iieo/aiiie aa?iyoiinoe
ia iauaa /enei iiuoia, iieo/atho oai?aoe/aneia cia/aiea /anoio neo/aeiie
aaee/eiu, eioi?ua e ii?aaeaeytho (au?iaiaiioth( e?eaoth. Oaia?ue iiaeii
iaeoe aa?iyoiinoue oiai, /oi yiie?e/aneay e?eaay niioaaonoaoao aua?aiiie
oai?aoe/aneie, aua?aa aa?iyoiinoue niaeaney ( o?iaaiue cia/eiinoe ).
Anee ?acoeueoao ?anoiaeaeaiey ia aueaeao ca i?eiyoue o?iaaiue
cia/eiinoe, oi n/eoatho, /oi yiie?e/aneia ?ani?aaeaeaiea niaeanoaony n
oai?aoe/aneei. Anee n?aaiaiea inouanoaeyaony n ianeieueeeie
oai?aoe/aneeie caeiiaie, oi ieii/aoaeueii i?eieiaoue oio, eioi?ue aeaao
eo/oaa niioaaonoaea.

*aua anaai a ea/anoaa e?eoa?eaa niaeaney i?eieiatho e?eoa?ee Ie?niia (
(2 ) e e?eoa?ee Eieiiai?iaa ( Nie?iiaa ( E ( N ( e?eoa?ee ).

E?eoa?ee (2 yaeyaony iaeaieaa ninoiyoaeueiui i?e aieueoii /enea
iaaethaeaiee. Ii ii/oe anaaaea ii?iaa?aaao iaaa?ioth aeiioaco,
iaania/eaaao ieieiaeueioth ioeaeo a i?eiyoee iaaa?iie aeiioacu ii
n?aaiaieth

n ae?oaeie e?eoa?eyie.

,

aaea mj ( iaaethaeaaiay /anoioa neo/aeiiai niauoey;

m(j ( iaeeaeaaiay ii i?eiyoiio oai?aoe/aneiio caeiio
?ani?aaeaeaiey;

E ( /enei eioa?aaeia neo/aeiie aaee/eiu.

Caoai ii?aaeaeyaony /enei noaiaiae naiaiaeu l:

l = E ( r ( 1;

aaea E ( /enei eioa?aaeia neo/aeiie aaee/eiu;

r ( /enei ia?aiao?ia oai?aoe/aneie ooieoeee ?ani?aaeaeaiey.

E ( N ( e?eoa?ee eo/oa anaai eniieueciaaoue a neo/aa, anee
oai?aoe/aneea cia/aiey ia?aiao?ia ?ani?aaeaeaiey ecaanoiu. I?e
iaecaanoiuo ia?aiao?ao aai iiaeii eniieueciaaoue, ii ii aeaao ianeieueei
caauoaiiua ?acoeueoaou. I?e eniieueciaaiee yoiai e?eoa?ey ii?aaeaeyaony
aaee/eia

,

aaea

mij, m*ij ( niioaaonoaaiii, iaeiieaiiua iaaethaeaaiua e iaeeaeaaiua

(oai?aoe/aneea) /anoiou;

n ( /enei i?iaaaeaiiuo iiuoia.

Oi anoue, a aeaiiii neo/aa ioeaieaaaony oieueei iaeneiaeueiia
ioeeiiaiea iaeiieaiiie /anoiou neo/aeiiai niauoey, aicieeathuaa a iaeiii
ec aeeaiaciiia eciaiaiey neo/aeiie aaee/eiu. Iieo/aiiia cia/aiea
eiyooeoeeaioa n?aaieaaaony n oaaee/iui aeey /enea noaiaiae naiaiaeu
iiuoa e i?eiyoiai o?iaiy cia/eiinoe ?acoeueoaoa. Anee oaaee/iia cia/aiea
eiyooeoeeaioa aieueoa, oi aeiioaca i i?eiyoii caeiia ?ani?aaeaeaiey ia
ioaa?aaaony.

Eiio?ieueiua aii?inu

Nouiinoue iai?a?uaiie e aeene?aoiie neo/aeiie aaee/eiu;

Nouiinoue eioaa?aeueiiai caeiia ?ani?aaeaeaiey neo/aeiie aaee/eiu;

Nouiinoue aeeooa?aioeeaeueiiai caeiia ?ani?aaeaeaiey neo/aeiie aaee/eiu;

Naycue eioaa?aeueiiai e aeeooa?aioeeaeueiiai caeiiia ?ani?aaeaeaiey;

Iniiaiua oa?aeoa?enoeee neo/aeiie aaee/eiu, caaeaiiie naiei
?ani?aaeaeaieai;

Iaciaeoa i?eia?u caeiiia ?ani?aaeaeaiey iai?a?uaiie e aeene?aoiie
neo/aeiie aaee/eiu;

Iiiyoea noaoenoe/aneie aeiioacu e noaoenoe/aneiai e?eoa?ey;

Iaciaeoa i?eia?u noaoenoe/aneeo aeiioac;

Nouiinoue ioeaie ia?aiai e aoi?iai ?iaea;

Nouiinoue i?iaa?ee aeiioacu aeaea caeiia ?ani?aaeaeaiey;

I?eioeeieaeueiia ?acee/ea a e?eoa?eyo Ie?niia e Eieiiai?iaa ( Nie?iiaa.

IAOIAEAeAIEA EIOA?IIEE?OTHUEO E?EAUO

A ia?aie /anoe iiniaey ?anniao?eaaeenue ecia?aiey oie eee eiie
oece/aneie aaee/eiu, iaoiaeyuaeny i?e i?iaaaeaiee na?ee ecia?aiee a
iaeciaiiii ninoiyiee. I/aiue /anoi enneaaeoaiay aaee/eia iaiyaony a
niioaaonoaee n eciaiaieai oneiaee iiuoa eee a?aiaie. Oeaeue yenia?eiaioa
a yoii neo/aa ninoieo a iaoiaeaeaiee ooieoeeiiaeueiie caaeneiinoe,
eioi?ay iaeeo/oei ia?acii iienuaaao eciaiaiea eioa?anothuaai ian
ia?aiao?a.

Neaaeoao iiieiaoue, /oi iaeiicia/ii ainnoaiiaeoue ( aieueoae /anoueth
iaecaanoioth ) ooieoeeiiaeueioth caaeneiinoue iaaeaeo ia?aiaiiuie
iaaiciiaeii aeaaea a oii neo/aa, anee au ia?aiaiiua aaee/eiu, iieo/aiiua
ec iiuoa, ia eiaee au ioeaee ecia?aiey. Oai aieaa ia neaaeoao
iaeeaeaoue, /oi yoi oaeanony naeaeaoue, eiay yenia?eiaioaeueiua aeaiiua,
niaea?aeauea, ii e?aeiae ia?a, neo/aeiua ioeaee ecia?aiee.

Iiyoiio iaoaiaoe/aneay ia?aaioea ?acoeueoaoia iaaethaeaiee ia iiaeao
noaaeoue ia?aae niaie caaea/o ?acaaaeaoue enoeiiue oa?aeoa? caaeneiinoe
iaaeaeo ia?aiaiiuie. Iia iicaieyao eeoue i?aaenoaaeoue ?acoeueoaou iiuoa
a aeaea iaeaieaa i?inoie oi?ioeu.

A caaeneiinoe io iacia/aiey yoeo oi?ioe nouanoaotho ?acee/iua iaoiaeu
eo iieo/aiey, ioee/athueany neiaeiinoueth ?an/aoiuo i?ioeaaeo? e
oi/iinoueth iieo/aaiuo ?aoaiee.

A?aoe/aneee iaoiae ia?aaioee ?acoeueoaoia

A?aoe/aneee iaoiae caeeth/aaony a iino?iaiee a?aoeea caaeneiinoe
iaaeaeo enneaaeoaiuie aaee/eiaie n iineaaeothuei ii?aaeaeaieai o?aaiaiey
caaeneiinoe iaaeaeo ieie.

A?aoeee no?iyo i?aaeaea anaai a ?aaiiia?iuo oeaeao. Anee oa?aeoa? nayce
iaaeaeo enneaaeoaiuie aaee/eiaie iaecaanoai, oi nia/aea i?iaa?ytho
niaiaaeaiea yenia?eiaioaeueiuo oi/ae n caaeaiiie e?eaie. Anee
i?aaeaa?eoaeueiua naaaeaiey i oa?aeoa?a o?aaiaiey ionoonoaotho, oi
ia?aui yoaiii ia?aaioee aeaiiuo yaeyaony iaoiaeaeaiea e?eaie,
niaiaaeathuae n iiuoiuie oi/eaie. Yoa caaea/a ?aoaaony iaoiaeii
iiaeai?a. Iiaeii eniieueciaaoue yoaeii ( eaeueeo n i?aaeaa?eoaeueii
au/a?/aiiui ia iae naiaenoaii e?eauo n ?acee/iuie ia?aiao?aie.
Anoanoaaiii, /oi ianooaa eaeueee e yiie?e/aneie e?eaie aeieaeai auoue
iaeeiaeia.

Iino?iaiiue ii iiuoiui aeaiiui io?acie e?eaie iiaeao niaiaaeaoue n
aieueoei eiee/anoaii ?acee/iuo e?eauo, i?ioiaeyueo aeinoaoi/ii aeecei e
iiuoiui oi/eai. A yoii neo/aa auae?atho e?eaoth n iaeaieaa i?inoui e
oaeiaiui a eniieueciaaiee o?aaiaieai. Eiiaaea yiie?e/aneay e?eaay iiaeao
eiaoue ia?aaeau eee ninoiyoue ec ioaeaeueiuo y?ei au?aaeaiiuo o/anoeia.
Iaeiaei i?e yoii iaiaoiaeeii ii?aaeaeeoue eii?aeeiaou oi/ae ia?aoiaea io
iaeiie e?eaie e ae?oaie.

O?aaiaiea caaeneiinoe iaaeaeo enneaaeoaiuie aaee/eiaie i?e a?aoe/aneii
iaoiaea i?inoi ii?aaeaeyaony oiaaea, eiaaea yiie?e/aneea oi/ee
aeinoaoi/ii oi?ioi niaiaaeatho n i?yiie eeieae, o.a. iienuaathony
o?aaiaieai y = ax + b, aaea a, b ( eiyooeoeeaiou, iiaeeaaeauea
ii?aaeaeaieth.

Ii?aaeaeaiea eiyooeoeeaioia i?e a?aoe/aneii iaoiaea iniiaaii ia
(niiniaa iaoyiooie ieoe(. Iaiany ?acoeueoaou yenia?eiaioa ia a?aoee
(eo/oa, anee ii auiieiai ia ieeeeiao?iaea), iiaeae?aai a?aoe/aneoth
i?yioth, aeeaea anaai iiaeoiaeyuoth e iaianaiiui oi/eai. Aua?aa
iieiaeaiea i?yiie, ii?aaeaeyai aeaa i?iecaieueiua oi/ee ia yoie i?yiie
(ia iaycaoaeueii yaeythueany oi/eaie yenia?eiaioa), ii?aaeaeyai eo
eii?aeeiaou (x1; y1), (o2; y2). E aeey ii?aaeaeaiey eiyooeoeeaioia a e b
iieo/aai aeaa i?inouo o?aaiaiey

ao1 + b = y1;

ao2 + b = y2.

Ia ?en. 10 i?eaaaeaia eeethno?aoeey yoiai iaoiaea. Oi/ee ( ?acoeueoaou,
iieo/aiiua a yenia?eiaioa. I?yiay i?iaaaeaia ia aeac eae iiaeii aeeaea e
yenia?eiaioaeueiui oi/eai. Ia i?yiie aua?aiu oi/ee I (2; 4) e N (13;
10). Eiyooeoeeaio a oa?aeoa?ecoao oaie iaeeiia i?yiie.

Iiyoiio

.

Oaeei ia?acii y = 0,55o + 2,9.

?en. 10. A?aoe/aneee iaoiae eioa?iieyoeee

A neo/aa, anee yenia?eiaioaeueiay caaeneiinoue eiaao iaeeiaeiue
oa?aeoa?, oi a?aoe/aneei niiniaii a nenoaia eii?aeeiao n ?aaiiia?iuie
oeaeaie ii?aaeaeeoue eiyooeoeeaiou e?eaie cao?oaeieoaeueii. Ii
aeinoaoi/ii aieueoie eeann iaeeiaeiuo caaeneiinoae iooai caiaiu
ia?aiaiiuo e a?aoe/aneiai ecia?aaeaiey a ooieoeeiiaeueiuo oeaeao iiaeii
i?eaanoe e eeiaeiui e aeaeaa eniieueciaaoue niinia iaoyiooie ieoe.

Ooieoeeiiaeueiua oeaeu e eo i?eiaiaiea

Ionoue ooieoeey y = ((o) iai?a?uaia e iiiioiiia ia iaeioi?ii
i?iiaaeooea ( a; b (. Aicueiai inue II, ia eioi?ie aoaeao no?ieoueny
oeaea, auaa?ai ia iae oi/eo ia/aea ion/aoa I e onoaiiaei ianooaa (.
Ooieoeeiiaeueiay oeaea no?ieony neaaeothuei ia?acii.

?acaea eioa?aae ( a; b ( ia ?aaiua /anoe, au/eneyai cia/aiea ooieoeee
((o) a eaaeaeie ec oi/ae aeaeaiey e ioeiaeei ia ine II aeey eaaeaeie
oi/ee io?acie (((o). Iieo/athuayny i?e yoii oi/ea niaaaeaaony ioiaoeie
o, o.a. ioeeaaeuaaaony a aua?aiiii ianooaaa cia/aiea ooieoeee, a
iaaeienuaaaony cia/aiea a?aoiaioa.

Eiiaaea ia/aei oeaeu iiiauatho a ia?aoth oi/eo ion/aoa, o.a. oi/eo n
iaaeienueth a niaiauatho n 0. Oiaaea oi/ea o aoaeao iaoiaeeoueny a
eiioea io?acea ( ( ((o) ( ((a) (. Iieo/aiiay oeaea iicaieyao noaeeoue i
iiaaaeaiee ooieoeee ia ?anniao?eaaaiii o/anoea: aieueoea i?iiaaeooee
iaaeaeo ioiaoeaie oeaaeoo, /oi ooieoeey eciaiyaony auno?aa, /ai oai,
aaea yoe i?iiaaeooee iaeu.

Auai? ianooaaa ( ii?aaeaeyao aeeeio oeaeu. *aua iinooiatho iaiai?io:
caaeathony aeeeiie oeaeu l e ii?aaeaeytho ianooaa.

.

ni. ?aciaueai io?acie ( 1; 2 ( ia aeanyoue ?aaiuo /anoae e au/eneei
cia/aiey ooieoeee ai anao oi/eao aeaeaiey. Niaianoei ia/aei oeaeu n
oi/eie ion/aoa o = 1. ?acoeueoaou ?an/aoa naaaeaiu a oaae. 2, a
ooieoeeiiaeueiay oeaea i?eaaaeaia ia ?en. 11.

Oaaeeoea 2

?an/ao ooieoeeiiaeueiie oeaeu y = x2

o 1,0 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0

o2 1,0 1,21 1,44 1,69 1,96 2,25 2,56 2,89 3,24 3,61 4,00

o2(1 0 0,21 0,44 0,69 0,96 1,25 1,56 1,89 2,24 2,26 3,00

4(o2(1) 0 0,84 1,76 2,76 3,84 5,00 6,24 7,56 8,94 10,44 12,0

1,0 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0

?en. 11. Ooieoeeiiaeueiay oeaea y = x2

N iiiiuueth ooieoeeiiaeueiuo oeae a?aoeee iiiaeo ooieoeee iiaoo auoue
i?aia?aciaaiu e i?yiieeiaeiiio aeaeo.

Iai?eia?, o?aaiaiea ia?aaieu y = x2. Anee ia ine OY iaianoe
?aaiiia?ioth oeaeo, a ia ine OX1 oeaeo eaaae?aoia o1 = o2, oi iieo/eony
naoea, aaea o?aaiaiea ia?aaieu eiaao ecia?aaeaiea i?yiie eeiee ( y = x1
),

i?ioiaeyuae /a?ac ia/aei eii?aeeiao.

Iniaaiii /anoi eniieuecothony ?acee/iua eiaa?eoie/aneea ooieoeee, n
iiiiuueth eioi?uo iiaeii (aui?yieyoue( a?aoeee noaiaiiuo e
iieacaoaeueiuo ooieoeee. Iai?eia?, y = aebx; lg y = (b lg a) o + lg a.
Iieaaay lg y = y1, lg a = A, b lg e = B caieoai enoiaeiia o?aaiaiea a
aeaea y1 = A + Ao, ioeoaea aeaeii, /oi inoaaea ?aaiiia?iie oeaeo o e
iino?iea eiaa?eoie/aneoth oeaeo y1, iiaeii ecia?aceoue enoiaeiia
o?aaiaiea i?yiie eeieae. Iieo/aiiay eii?aeeiaoiay naoea iacuaaaony
iieoeiaa?eoie/aneie.

I/aaeaeii, /oi oaeiai ?iaea i?aia?aciaaiey aiciiaeiu e a aieaa iauai
neo/aa. Anyeay iayaiay ooieoeey, caaeaiiay niioiioaieai aeaea

a((o) + b((y) + n = 0,

aaea a, b, n ( iinoiyiiua, aoaeao ecia?aaeaoueny i?yiie eeieae ia
ooieoeeiiaeueiie naoea, aaea ia ine IO iino?iaia oeaea ((o), a ia ine OY
( oeaea ooieoeee ((y). Anoanoaaiii, /oi ooieoeee ((o) e ((y) aeieaeiu
oaeiaeaoai?youe oneiaeyi iai?a?uaiinoe e iiiioiiiinoe. A oaae. 3
i?eaaaeaiu i?aia?aciaaiey aeey iaeioi?uo ooieoeee.

Oaaeeoea 3

Eeiaa?ecaoeey iaeioi?uo ooieoeee

Enoiaeiay

oi?ioea I?aia?aciaaiiay

oi?ioea Caiaia

ia?aiaiiuo Eeiaa?eciaaiiay oi?ioea

y=axb

lg y=b(lgx+lga lg y=y1

lg x=x1

lg a=a1

y1=bx1+a1

y=a(lgx+b ( lg x=x1 y=ax1+b

y=ebx+k

lg y=b(lge(x+k(lge lg y=y1

b(lg e=a

k(lg e=k1

y1=ax+k1

y=aebx

lg y=bx(lge+lga lg y=y1

b(lg e=b1

lg a=a1

y1=ax+b

y1=bx1+a

Ec neacaiiiai ynia ?ieue ooieoeeiiaeueiuo naoie i?e ia?aaioea
?acoeueoaoia yenia?eiaioa. Anee ?acoeueoaou yenia?eiaioa ?aniieaaathony
aaeece e?eaie, oi ii eiathuaiony ia?aie/aiiiio o/anoeo e?eaie o?oaeii
noaeeoue, eaeiai oeia ooieoeeae aa eo/oa anaai i?eaeeaeaoue. Ia?aaaaey
iieo/aiiua yenia?eiaioaeueiua aeaiiua ia ooieoeeiiaeueiua naoee iiaeii
ioeaieoue ia eaeie ec ieo yoe aeaiiua aeeaea anaai iiaeoiaeyo e i?yiie
e, neaaeiaaoaeueii, eaeie ooieoeeae eo/oa anaai iienuaathony.

Aiaeeoe/aneea iaoiaeu ia?aaioee ?acoeueoaoia

A?aoe/aneee iaoiae ia?aaioee ?acoeueoaoia iaeaaeaao iaaeyaeiinoueth,
ioiineoaeueiie i?inoioie, iaeiaei aai ?acoeueoaou niaea?aeao
ii?aaeaeaiioth noauaeoeaiinoue e ioiineoaeueii ieceoth oi/iinoue.

Aiaeeoe/aneea iaoiaeu eeoaiu a eaeie ( oi noaiaie oeacaiiuo
iaaeinoaoeia e iicaieytho iieo/eoue ?acoeueoao aeey aieaa oe?ieiai
eeanna ooieoeee n aieueoae oi/iinoueth, /ai a?aoe/aneee iaoiae.

Nouanoaotho ?acee/iua aiaeeoe/aneea iaoiaeu iieo/aiey ia?aiao?ia
yiie?e/aneeo e?eauo a caaeneiinoe io e?eoa?ey, i?eiyoiai i?e eo
iieo/aiee. ?anniio?ei iaeioi?ua ec nouanoaothueo niiniaia.

Niinia n?aaeiae

Aeiionoei, /oi eiaaony n ni/aoaiee xi, yi, iieo/aiiuo i?e yenia?eiaioa.
Aeaaea a oii neo/aa, anee iaaeaeo o e y oai?aoe/anee onoaiiaeaia
ooieoeeiiaeueiay naycue ( a aeaiiii neo/aa i?aaeiieiaeei, /oi eeiaeiay
), oi iaaethaeaaiua cia/aiey yi aoaeoo ioee/aoueny io aoi + b
aneaaenoaea iaee/ey yenia?eiaioaeueiuo ioeaie. Iaicia/ei /a?ac (i
niioaaonoaothuoth ioeaeo

(i = yi ( axi ( b (i = 1, 2, …, n)

, oi yoi i?eaaei au ian e iaeiiio o?aaiaieth, oiaaea eae aeey
iaoiaeaeaiey aeaoo eiyooeoeeaioia (a, b) eo o?aaoaony aeaa. Iiyoiio
i?aaeiieiaeei, /oi o?aaiiaaoeaaiea i?ienoiaeeo ia oieueei aeey anao
i?iecaaaeaiiuo iaaethaeaiee a oeaeii, ii e aeey eaaeaeie a?oiiu,
niaea?aeauae iieiaeio ( eee ii/oe iieiaeio ) anao iaaethaeaiee a
ioaeaeueiinoe.

A yoii neo/aa iiaeii i?eeoe e nenoaia o?aaiaiee

,

aaea m ( /enei iaaethaeaiee a ia?aie a?oiia.

Aeaiioth nenoaio o?aaiaiee caieoai oaia?ue a aeaea

.

Eceiaeaiiia iieacuaaao, /oi iaoiae n?aaeieo (o?aaiiaaoeaaao(
iieiaeeoaeueiua e io?eoeaoaeueiua ioeeiiaiey oai?aoe/aneie e?eaie io
yenia?eiaioaeueiuo cia/aiee.

I?eia?.Eniieuecoy aeaiiua ?en. 10 ii?aaeaeei eiyooeoeeaiou a, b
iaoiaeii n?aaeiae. Aeey yoiai naiue ecia?aiee ?acaeaeei ia aeaa a?oiiu m
= 3 ia?auo cia/aiee, n ( m = 4 iineaaeothueo

;

.

Iieo/aai nenoaio

?aoay nenoaio iaoiaeei

;

Oaeei ia?acii niinia n?aaeiae aeaao i?yioth

y = 0,55o + 3,11.

A n?aaiaiee n a?aoe/aneei niiniaii eiyooeoeeaiou a niaiaaeatho e
eiaaony ?acee/ea a eiyooeoeeaioa b.

3.3.2. Iaoiae iaeiaiueoeo eaaae?aoia

A iaoiaea n?aaeieo i?e ii?aaeaeaiee eiyooeoeeaioia o?aaiaiey
eniieueciaaeinue oneiaea ?aaainoaa ioeth aeaaa?ae/aneie noiiu ioeeiiaiee
?acoeueoaoia yenia?eiaioa io oai?aoe/aneie e?eaie ( a /anoiii neo/aa
i?yiie ). I/aaeaeii, /oi i?e yoii (i iiaoo auoue cia/eoaeueiie aaee/eiu.
Eiaao cia/aiea oieueei (o?aaiiaaoeaaiea( iieiaeeoaeueiuo e
io?eoeaoaeueiuo ioeeiiaiee.

Iinoaaei oaia?ue caaea/o iaoiaeaeaiey ii ?acoeueoaoai iaaethaeaiee
iaeaieaa aa?iyoiua cia/aiey iaecaanoiuo eiyooeoeeaioia.

I?aaeiieiaeei, /oi eneiiay caaeneiinoue y = ((o) nouanoaoao. Oiaaea
ia?aiao?u yoie eeiee iaiaoiaeeii aua?aoue oaeei ia?acii, /oiau oi/ee yi
?aniieaaaeenue ii iaa noi?iiu e?eaie y = ((o) eae iiaeii aeeaea e
iineaaeiae. I?aaeiieiaeei, /oi ?aca?in oi/ae yi ioiineoaeueii y = ((o)
iiae/eiyaony caeiio ii?iaeueiiai ?ani?aaeaeaiey. Oiaaea ia?ie ?aca?ina
yaeyaony aeenia?ney (2 eee aa i?eaeeaeaiiia au?aaeaiea ( n?aaeiee
eaaae?ao ioeeiiaiee.

.

E o?aaiaaiea ieieiaeueiiai ?aca?ina aoaeao oaeiaeaoai?aii, anee
ieieiece?iaaoue au?aaeaiea ( (yi )2. Eae ecaanoii, iaiaoiaeeiui oneiaeai
oiai, /oi ooieoeey i?eia?aoaao ieieiaeueiia cia/aiea, yaeyaony oi, /oi
aa ia?aay i?iecaiaeiay ( eee /anoiua i?iecaiaeiua aeey ooieoeee iiiaeo
ia?aiaiiuo ) ?aaia ioeth. I?eiaiaiea iaoiaea iaeiaiueoeo eaaae?aoia
eiaao niune, anee /enei yenia?eiaioaeueiuo oi/ae n aieueoa /enea
ii?aaeaeyaiuo eiyooeoeeaioia.

?anniio?ei ?aaeecaoeeth iaoiaea iaeiaiueoeo eaaae?aoia i?eiaieoaeueii e
o?aaiaieth aeaea y = ax + b.

Aeey iaoiaeaeaiey eiyooeoeeaioia a, b eneiiie i?yiie iaiaoiaeeii
ieieiece?iaaoue noiio eaaae?aoia ?annoiyiee (yi ii i?aeeiaoa io oi/ee
(oi; yi) aei i?yiie ( ni. ?en. 12 ). ?annoiyiey (yi ii?aaeaeyony

(yi = yi ( axi ( b.

?en. 12. E niiniao iaeiaiueoeo eaaae?aoia

i?e?aaieaaai e ioeth i?iecaiaeiua yoie noiiu ii ia?aiao?ai a, b:

;

.

I?aia?acoai yoo nenoaio

Iieo/ei nenoaio ii?iaeueiuo o?aaiaiee iaoiaea iaeiaiueoeo eaaae?aoia.

?aoay aa ioiineoaeueii a, b iieo/aai:

.

Au/eneyy ec n iiuoia iaiaoiaeeiua noiiu e i?iecaiaey oeacaiiua
aeaenoaey, iieo/aai aaee/eio eiyooeoeeaioia a, b.

Eae aeaeii, niinia iaeiaiueoeo eaaae?aoia aeinoaoi/ii a?iiicaeie e i?e
aai i?eiaiaiee oe?iei eniieuecoaony au/eneeoaeueiay oaoieea. Iaoiae
iaeiaiueoeo eaaae?aoia iiaeao eniieueciaaoueny e a neo/aa iaeeiaeiuo
ooieoeee. Iai?eia?, anee ii?aaeaeythony ia?aiao?u eaaae?aoe/iie
caaeneiinoe:

y = ao2 + bx + n,

oi

.

Aeeooa?aioee?oy yoi niioiioaiea ii a, b, n iieo/aai nenoaio ii?iaeueiuo
o?aaiaiee:

Ec yoie nenoaiu iiaeii ii?aaeaeeoue ia?aiao?u a, b, n.

I?e eniieueciaaiee iaoiaea iaeiaiueoeo eaaae?aoia i?e ae?oaeo
iaeeiaeiinoyo, oaeiaiaa aoaeao eeiaa?eciaaoue enoiaeiua caaeneiinoe.

A oaae. 4 i?eaaaeaiu nenoaiu ii?iaeueiuo o?aaiaiee aeey iaeioi?uo
enoiaeiuo o?aaiaiee.

Oaaeeoea 4

Nenoaiu ii?iaeueiuo o?aaiaiee

Enoiaeiia

o?aaiaiea Nenoaia ii?iaeueiuo o?aaiaiee

I?eia/aiey: 1. Aaee/eiu o, y iaicia/atho cia/aiey aaee/ei oi, yi a i(ii

iiuoa;

Ciae ( iaicia/atho noiio aaee/ei io i = 1 aei i = n, aaea n

( /enei ?aaiioi/iuo ecia?aiee.

Eioa?iiee?iaaiea ooieoeee

Ecaanoii, /oi iiae eioa?iiee?iaaieai iiieiatho iouneaiea cia/aiee
ooieoeee, niioaaonoaothueo i?iiaaeooi/iui cia/aieyi a?aoiaioa,
ionoonoaothuei a oaaeeoea eiaa?eoiia, o?eaiiiiao?e/aneeo e ae?.
ooieoeee.

A iauai niunea iiaeii neacaoue, /oi caaea/a eioa?iiee?iaaiey ia?aoia
caaea/a oaaoee?iaaiey ooieoeee. I?e eioa?iiee?iaaiee ii oaaeeoea
cia/aiee ooieoeee no?ieony aa aiaeeoe/aneia au?aaeaiea, o.a. ii
cia/aieyi ooieoeee yo, y1, …, yn i?e cia/aieyo a?aoiaioa oi, o1, …,
on ii?aaeaeyaony au?aaeaiea iaecaanoiie ooieoeee.

Iiiyoii, /oi /a?ac aeaiiua oi/ee ( aeaaea aieueoiai /enea ) iiaeii
i?iaanoe iiiaeanoai ?acee/iuo e?eauo. Iiyoiio nouanoaoao
eioa?iiee?iaaiea a ?acee/iuo ooieoeeyo F (o). *aua anaai o?aaotho, /oiau
ooieoeey F(o) auea iiiai/eaiii noaiaie ia aaeeieoeo iaiueoae, /ai /enei
ecaanoiuo cia/aiee.

Oaeei ia?acii, caaea/o eioa?iiee?iaaiey ooieoeee iiaeii noi?ioee?iaaoue
neaaeothuei ia?acii.

Aeey aeaiiuo cia/aiee o ( oi, o1, …, on e y ( yo, y1, …, yn iaeoe
iiiai/eai y = F (o) noaiaie n, oaeiaeaoai?ythuee oneiaeyi F (oi) ( yo, F
(o1) ( y1, …, F (on) ( yn. Oi/ee oi, o1, …, on iacuaatho oceaie
eioa?iieyoeee. Iiiai/eai F (o) ( eioa?iieyoeeiiiui iiiai/eaiii , a
oi?ioeu aai iino?iaiey ( eioa?iieyoeeiiiuie oi?ioeaie.

Eae aeaeii ec iienaiey nouiinoe eioa?iiee?iaaiey, a ioee/ee io
iienaiiuo ?aiaa niiniaia iieo/aiey ooieoeee ( a?aoe/aneiai, iaoiaea
n?aaeieo, iaoiaea iaeiaiueoeo eaaae?aoia ), eioa?iieyoeeiiiue iiiai/eai
iieoao e?eaoth, i?ioiaeyuoth oi/ii /a?ac caaeaiiua oi/ee.

Ia?aaiee/aneia eioa?iiee?iaaiea

I?e ia?aaiee/aneii eioa?iiee?iaaiee a ea/anoaa eioa?iieyoeeiiiiai
iiiai/eaia F (o) i?eieiatho iiiai/eai n ( ie noaiaie aeaea

F (o) ( ai + a1o + a2o2 + … + anxn.

Eniieuecoy naienoai i?ioiaeaeaiey ooieoeee F (o) /a?ac caaeaiiua oi/ee
aeey iaecaanoiuo eiyooeoeeaioia ai iiaeii ninoaaeoue n + 1 o?aaiaiee n n
+ 1 iaecaanoiui:

ai + a1oi + a2oi2 + … + anoin ( yo;

ai + a1o1 + a2o12 + … + ano12 ( y1;

…………………………………………….

ai + a1on + a2on2 + … + anon2 ( yn.

Yoa nenoaia eiaao aaeeinoaaiiia ?aoaiea, anee cia/aiey oi ioee/iu ae?oa
io ae?oaa. Iiiyoii, /oi i?e aieueoii n aicieeaao neiaeiinoue ?aoaiey
yoie nenoaiu. Ia?aae ?anniio?aieai iauaai niiniaa ?aoaiey, ?anniio?ei
i?inoie i?eia?.

Aeaii: oi = 0, o1 = 1, o2 = 2, yi = 1, y1 = 1, y2 = 3. Ii?aaeaeeoue
iiiai/eai F (o).

Caienuaay iiiai/eai F (o) a aeaea

F (o) = ai + a1o + a2o2

ninoaaei nenoaio o?aaiaiee

ioeoaea ai = 1, a1 = ( 1, a2 = 1 e eioa?iiee?othuee iiiai/eai eiaao aeae

F (o) = 1 ( o + o2.

Oaia?ue ?anniio?ei iauee iiaeoiae e iouneaieth eioa?iieyoeeiiiiai
iiiai/eaia F (o), ia ?aoaieai nenoaiu, a iaiin?aaenoaaiiie caienueth.

Ii?aaeaeei au?aaeaiea aeey iiiai/eaia, i?eieiathuaai a oi/ea o = oi
cia/aiea yi = 1, a a oi/eao o = o1, o2, …, on ( cia/aiey y1 = y2 = …
= yn = 0. I/aaeaeii, /oi iiiai/eai aoaeao eiaoue aeae

.

Caeanue i?e o = oi /eneeoaeue e ciaiaiaoaeue ?aaiu, a i?e o = o1, o2,
…, on ( /eneeoaeue ?aaai ioeth.

Oaia?ue iino?iei iiiai/eai Fi (o), i?eieiathuee a oi/ea oi cia/aiea yi
e ia?auathueeny a ioeue aeey cia/aiee o = o1, o2, …, on. O/eouaay
i?aaeuaeouaa iino?iaiea iiaeii caienaoue

.

Oaia?ue iiaeii caienaoue iiiai/eai F (o) aeey i?iecaieueiiai cia/aiey
oi ( i = 0, 1, 2, …, n ) i?eieiathuaai cia/aiey F (oi) = yi, a ai anao
inoaeueiuo oi/eao o ( oi cia/aiea, ?aaiia ioeth

.

Eae aeaeii ec caiene, /eneeoaeue ia aoaeao niaea?aeaoue au?aaeaiey (o (
oi), a ciaiaiaoaeue ( (oi ( oi), o.a. au?aaeaiee, ia?auathueo /eneeoaeue
e ciaiaiaoaeue a ioeue.

Eneiiue iiiai/eai aoaeao ?aaai noiia

,

o.a. niiaa a eaaeaeie oi/ea oi iaeii ec neaaaaiuo i?eieiaao ioaeiia
cia/aiea yi, a ana inoaeueiua ia?auathony a ioeue.

A ?acaa?iooii aeaea

.

Iieo/aiiay oi?ioea iacuaaaony eioa?iieyoeeiiiie oi?ioeie Eaa?aiaea.

Eniieuecoy oi?ioeo Eaa?aiaea caieoai iiiai/eai F (o) aeey ?acia?aiiiai
auoa i?eia?a.

.

Iieo/eee oiaea naiia au?aaeaiea, /oi e ?aiaa.

Eiio?ieueiua aii?inu

Iacia/aiea a?aoe/aneiai iaoiaea ia?aaioee ?acoeueoaoia;

Nouiinoue a?aoe/aneiai iaoiaea ia?aaioee ?acoeueoaoia;

Iiiyoea e iacia/aiea ooieoeeiiaeueiie oeaeu;

Auai? ianooaaa ooieoeeiiaeueiie oeaeu;

Nouiinoue aii?ieneiaoeee iaoiaeii n?aaeieo;

Nouiinoue aii?ieneiaoeee iaoiaeii iaeiaiueoeo eaaae?aoia;

I?eioeeieaeueiia ioee/ea iaoiaea eioa?iiee?iaaiey io iaoiaea iaeiaiueoeo
eaaae?aoia.

4.INIIAU IIIIA?AOEE

Iiiia?aoey ( neiai a?a/aneia. Iiiin ( caeii, a?aoi ( ieoo, /a?/o. A
aoeaaeueiii ia?aaiaea yoi neiai icia/aao (/a?/aiea caeiia(.

Naiae caaea/ae iiiia?aoey noaaeo iino?iaiea niaoeeaeueiuo a?aoeeia (
iiiia?aii, neoaeaueo aeey ?aoaiey ?acee/iuo o?aaiaiee. Iiiia?aiiu aeatho
aiciiaeiinoue eiiiaeoii i?aaenoaaeyoue ooieoeee iiiaeo ia?aiaiiuo e
oaaeeoeu n ianeieueeeie aoiaeaie. Ia iiiia?aiiao iiaeii ?aoaoue
iaeioi?ua o?ainoeaiaeaioiua o?aaiaiey e nenoaiu oaeeo o?aaiaiee.
Iiiia?aiiu iiaeii i?eiaiyoue ia oieueei aeey au/eneeoaeueiuo oeaeae, ii
e aeey enneaaeiaaiey iieiaeaiiuo a eo iniiao ooieoeeiiaeueiuo
caaeneiinoae.

Iaaeyaeiinoue i?aaenoaaeaiey ?acee/iuo caeiiiia?iinoae e i?inoioa
eniieueciaaiey iiiia?aii i?e aeinoaoi/ii aunieie oi/iinoe ?acoeueoaoa
iaania/eaatho oe?ieia eniieueciaaiea iiiia?aii a ?acee/iuo iaeanoyo
oaoieee.

A iniiaa iiiia?aii eaaeeo iiiyoea ooieoeeiiaeueiie oeaeu ( ni. auoa ).
Ia iniiaa ooieoeeiiaeueiuo oeae nicaeathony ia oieueei iiiia?aiiu, ii e
?acee/iua au/eneeoaeueiua n?aaenoaa: oieaa?naeueiua au/eneeoaeueiua
iiiia?aiiu, eiaa?eoie/aneea eeiaeee e o.i.

A aeaiiie aeaaa eceaaaaony iaeei ec aiciiaeiuo aeaeia iiiia?aii (
iiiia?aiiu a aeaea?oiaie nenoaia eii?aeeiao, eiathuea aeinoaoi/ii
oe?ieia eniieueciaaiea a iaoeiino?iaiee.

Iiiia?aiiu a aeaea?oiaie nenoaia eii?aeeiao

A ?acaeaeao 3.1., 3.2. iienaia i?ioeaaeo?a iino?iaiey a?aoeeia aeey
ooieoeee iaeiiai ia?aiaiiiai. I?e yoii ia a?aoeea iieo/aaony iaeia eeiey
( i?yiay eee e?eaay ).

Anee aea eco/aaiay ooieoeey caaeneo io aeaoo ia?aiaiiuo

Z = ( (o, y),

oi i?eaeaaay a yoii o?aaiaiee, iai?eia?, ia?aiao?o y ?yae /anoiuo (
iinoiyiiuo ) cia/aiee y1, y2, …, yn iiaeii, eae e aeey ooieoeee
iaeiiai ia?aiaiiiai, iino?ieoue caaeneiinoe

Z = ( (o, y1);

Z = ( (o, y2);

……………….

Z = ( (o, yn).

Iieo/ei nenoaio e?eauo ( a /anoiii neo/aa i?yiuo ), iacuaaaiuo
iiiia?aiiie ec (iiia/aiiuo( eeiee, o.e. eaaeaeay eeiey iiia/aaony
niioaaonoaothuei cia/aieai yi.

I?eia?. I?e enneaaeiaaiee i?ioeanna o?aca?iaaiey auei onoaiiaeaii, /oi
iaeaieaa oeaeaniia?acii aaee/eio ?aaeeaeueiiai aeaiey niaaeiuo coaueaa
o?acu iacia/aoue ii oneiaeth iaania/aiey o/anoey a i?ioeanna ?acaiey
anao coaueaa o?acu. Aiaeeoe/anee yoi oneiaea au?aaeaaony o?aaiaieai

,

aaea Sz ( ?an/aoiay aaee/eia iiaea/e ia coa, ii(coa;

( ia?aiao? iia?aoeee;

D ( aeeaiao? o?acu, ii;

t ( aeoaeia ?acaiey, ii;

( ( aaee/eia aeaiey niaaeiuo coaueaa o?acu, ii.

, eaaei ii?aaeaeyaiui e oiaiueoathuei eiee/anoai ia?aiaiiuo. Aeaiiue
i?eai oe?iei eniieuecoaony a iiiia?aoee.

Oaia?ue iaiaoiaeeii ii?aaeaeeoueny n inyie e iiia/aiiui ia?aiao?ii. A
ea/anoaa ine i?aeeiao, a niioaaonoaee n ooieoeeiiaeueiie caaeneiinoueth,
?aoeeiiaeueii i?eiyoue Sz. A ea/anoaa aea ine aanoeenn iiaeii i?eiyoue
eeai k, eeai (. Anee a ea/anoaa ine i?aeeiao i?eiyoue k ( a iiia/aiiui
ia?aiao?ii (i ), oi caaeneiinoue

Sz = ( (k, (i)

. I?iua no?ieoue e eniieueciaaoue i?yiieeiaeiua a?aoeee i?e
?aaiiia?iuo oeaeao. Iiyoiio noa?athony iiiia?aiiu no?ieoue ia iniiaa
i?yiuo eeiee. Iiyoiio eo/oa aoaeao no?ieoue iiiia?aiio ec iiia/aiiuo
eeiee aeaea

Sz = ( ((, Ki),

.

Oaia?ue auae?aai ianooaa iino?iaiey e aeeaiaciiu eciaiaiey ia?aiaiiuo.
N o/aoii oneiaee i?ioeanna o?aca?iaaiey i?eieiaai ( ( 0,08 ii; Sz ( 0,20
ii(coa. Ia?aiao? k eciaiyai aeene?aoii k = 2; 5; 10; 20; 30; 40; 50. Oae
eae caaeneiinoue Sz = ( ((, Ki) yaeyaony i?yiie eeieae, i?ioiaeyuae
/a?ac ia/aei eii?aeeiao, oi aeey iino?iaiey a?aoeeia aeinoaoi/ii
au/eneeoue oieueei iaeii cia/aiea Sz i?e eaeii ( eeai cia/aiee (.
Iai?eia?, aeey k = 2, i?e ( = 0,06 ii eiaai

( ii/coa ).

Oaia?ue /a?ac oi/ee ( 0; 0 ) e ( 0,06; 0,06 ) iiaeii i?iaanoe i?yioth
eeieth e iiiaoeoue aa ia?aiao? k = 2. Aiaeiae/ii i?iaiaeyony e ae?oaea
eeiee ( ?en. 13 ). Ia iiiia?aiia iaiineony eeiey, iieacuaathuay ii?yaeie
aa eniieueciaaiey.

?en. 13. Iiiia?aiia ii?aaeaeaiey aeiionoeiie aaee/eiu

?aaeeaeueiiai aeaiey niaaeiuo coaueaa o?acu.

4.2. Ninoaaiua iiiia?aiiu n iiia/aiiuie eeieyie

Iiiia?aiio a iaeiie /aoaa?oe iiaeii iino?ieoue aeey ooieoeee aeaoo
ia?aiaiiuo. I?e aieueoai /enea ia?aiaiiuo yoi naeaeaoue oaea iaeuecy. A
yoii neo/aa eniieuecotho ninoaaiua iiiia?aiiu. Eaeath iino?iaiey
?anniio?ei nia/aea a iauai aeaea.

Ionoue iai aeaii o?aaiaiea a iayaiii aeaea n /aou?ueiy ia?aiaiiuie

( (o, y, z, () = 0.

Aeiionoei, /oi aai iiaeii i?eaanoe e aeaeo

(1(o, y) = (2 (z, (),

o.a. iiaeii ?acaeaeeoue ia?aiaiiua. Iieiaeei

(1 (o, y) = (;

(2 (z, () = (.

Iu iieo/ei aeaa o?aaiaiey, caaenyueo io aeaoo ia?aiaiiuo. Eaaeaeia ec
yoeo o?aaiaiee iiaeii iiiia?aoe?iaaoue, eae iienaii auoa. Iaania/ea
ion/ao aaee/eiu ( ia iaeeiaeiaie ooieoeeiiaeueiie oeaea, iiaeii
iaieoenue e aac /eneaiiuo cia/aiee ( ( anee iie ian ia eioa?anotho ii
oneiaeyi ?aoaaiie caaea/e ). Noaiaoe/anee oaeay iiiia?aiia i?eaaaeaia ia
?en. 14.

?en. 14. Noaia iiiia?aiiu n iiia/aiiuie eeieyie

n /aou?ueiy ia?aiaiiuie

Aiaeiae/ii iinooiatho e n o?aaiaieyie n aieueoei /eneii ia?aiaiiuo,
eioi?ia aoaeao i?eaiaeeoue e oaaee/aieth /enea iaueo oeae e aieueoaio
/eneo /aoaa?oae iino?iaiey iiiia?aiiu. Ioaeii oieueei eiaoue a aeaeo,
/oi ia anyeia o?aaiaiea aeiioneaao ?aceiaeaiea ia ianeieueei o?aaiaiee n
aeaoiy ia?aiaiiuie e, neaaeiaaoaeueii, ia anyeia o?aaiaiea oaeaaony
oaeei ia?acii iiiia?aoe?iaaoue.

?anniio?ei ?aaeueiue i?eia? iino?iaiey ninoaaiie iiiia?aiiu.

I?e enneaaeiaaiee i?ioeanna o?aca?iaaiey auei onoaiiaeaii, /oi neea
?acaiey i?e o?aca?iaaiee oceeo iiaa?oiinoae i?eia?aoaao oa?aeoa?
iiaoi?ythueony eiioeuenia ia aa?iiie/aneie oi?iu. E aiciouaiea
oaoiieiae/aneie nenoaiu inouanoaeyaony ia ia iaeiie, a a aaneiia/iii
aeeaiaciia /anoio. Iaeaieaa iianii aicaeaenoaea ia?auo o?ao aa?iiiee,
ianoueo cia/eoaeueii aieueoa yia?aee aiciouaiey, /ai ana ae?oaea.
?ani?aaeaeaiea yia?aee ii yoei o?ai aa?iiieeai inouanoaeyaony a
caaeneiinoe io ioiioaiey o?iioia ia?anoaiey e niaaea neeu a eiioeuena.
Yoi ioiioaiea iiaeii oa?aeoa?eciaaoue ioiioaieai oaeia eiioaeoa o?acu
(() e coaa o?acu (() n caaioiaeie. I?e/ai anaaaea ( ( (.

Aeey iaaeyaeiiai i?aaenoaaeaiey e ii?aaeaeaiey oa?aeoa?a ?ani?aaeaeaiey
yia?aee ii o?ai aa?iiieeai a caaeneiinoe io oneiaee iia?aoeee iino?iei
iiiia?aiio.

A iaeiie ec /aoaa?oae ia?aiia/aeueii io?aaeaaony oa?aeoa?
?ani?aaeaeaiey yia?aee ii aa?iiieeai aiciouaiey a caaeneiinoe io (((
(?en. 15). Yoe caaeneiinoe iino?iaiu ec ?acoeueoaoia enneaaeiaaiee,
eioi?ua caeanue ia io?aaeathony. Eiyooeoeeaio O2 oa?aeoa?ecoao
(oaeaeueiue aan( yia?aee aeaiiie aa?iiieee a iauai neeiaii aiciouaiee.
Aeeaiacii (((( ( 1…9.

Oaia?ue ioiioaiea ((( ?ane?uaaai a ia?aiao?ao eino?oiaioa e iia?aoeee

.

Aeaeii, /oi caeanue /aou?a ia?aiaiiuo aaee/eiu: D, t, B, (.

Aaaaeai i?iiaaeooi/ioth inue N e iino?iei iiiia?aiio ec iiia/aiiuo
eeiee aeey iaeiie ec ia?aiaiiuo aaee/ei, a eiaiii Ai

.

Aeaeii, /oi yoi o?aaiaiey i?yiuo eeiee, i?ioiaeyueo /a?ac ia/aei
eii?aeeiao. Caaeaaaynue iaeiei cia/aieai ((( e Ai iiaeii i?iaanoe aa
a?aoee. Iai?eia?, i?e ((( = 5, Ai = 5 iieo/ei N = 2(5(5 = 50. Aiaeiae/ii
iinooiaai aeey Ai = 10; 15; 20.

Aeaeaa aaiaeei neaaeothuoth i?iiaaeooi/ioth inue ( e niioaaonoaaiii
ia?aiaiioth ) L = C (tg (i. Caaeaaaynue aaee/eiaie oaea (i e N iiaeii
ii?aaeaeeoue iieiaeaiea iiia/aiiuo eeiee. Iai?eia?, i?e ( = 45(, N = 50

L = 50(tg 45( =50. Aiaeiae/ii iinooiaai e aeey ae?oaeo oaeia (i = 15(;
30(; 60(; 75(. I?iaiaeei i?yiua eeiee /a?ac ia/aei nenoaiu eii?aeeiao e
iiia/aai cia/aiea oaea (i eaaeaeie eeiee.

Oaeei ia?acii inoaeanue iaeia acaeiinaycue ia?aiao?ia

.

Caeanue iaiaoiaeeii ii?aaeaeeoueny n ia?aiao?ii, iai?aaeaiiii ii ine e
(iiia/aiiui( ia?aiao?ii. A ethaii neo/aa caaeneiinoue iaeeiaeiay. E?iia
oiai, aeoaeia ?acaiey yaeyaony caaeaaaaiui ia?aiao?ii e aai eo/oa acyoue
a ea/anoaa (iiia/aiiiai( ia?aiao?a. Aeey iino?iaiey iiia/aiiuo eeiee
ioaeii ii?aaeaeeoue ianeieueei eii?aeeiao eaaeaeie eeiee.

?anniio?ei (iiia/aiioth( eeieth t = 5 ii. A ea/anoaa ia?aiaiiiai
ia?aiao?a i?eieiaai aeeaiao? o?acu D. I?e D = 25; 50; 100; 150; 200 ii
niioaaonoaaiii eiaai

Ii iaeaeaiiui oi/eai no?ieony eeiey aeey t = 5 ii. Aiaeiae/ii
iinooiatho e aeey ae?oaeo cia/aiee t.

Ia ?en. 15 iieacaia iino?iaiiay iiiia?aiia. Oeacaiu i?iiaaeooi/iua ine
N, L, eioi?ua i?e eniieueciaaiee iiiia?aiiu ia ioaeiu e iiaoo ia
oeacuaaoueny, oeacaiu e /anoiua caaeneiinoe aeey eaaeaeie /aoaa?oe
iiiia?aiiu.

Iieo/aiiay iiiia?aiia iaaeyaeii iieacuaaao, /oi ?ani?aaeaeaiea yia?aee
ii aa?iiieeai aiciouaiey oaoiieiae/aneie nenoaiu ii?aaeaeyaony oneiaeyie
iia?aoeee, eciaiyy eioi?ua iiaeii aicaeaenoaiaaoue ia aiciouaiea
oaoiieiae/aneie nenoaiu.

Aeey eneeth/aiey ?aciiainiuo yaeaiee iaiaoiaeeii ciaoue niaeo?
nianoaaiiuo /anoio nenoaiu e niaeaniauaaoue oneiaey iia?aoeee n eo
cia/aieyie, oiaiueoay eiee/anoai yia?aee ia (?aciiainiie( /anoioa. Yoe
aeaiiua, eae i?aaeei, ionoonoaotho. Iiyoiio eniieuecoy iiiia?aiio iiaeii
nei??aeoe?iaaoue oneiaey iia?aoeee. Aeey yoiai ii ecaanoiui ia?aiao?ai
o?acu, eioi?ay iieacaea iaoaeiaeaoai?eoaeueiua ?acoeueoaou, e yeaiaioai
?aaeeia ?acaiey iaiaoiaeeii ii?aaeaeeoue ?ani?aaeaeaiea yia?aee ii
aa?iiieeai aiciouaiey e aua?aoue ae?oaia ?ani?aaeaeaiea. Oae eae aeoaeio
?acaiey e oe?eio o?aca?iaaiey eciaiyoue, eae i?aaeei, iaaiciiaeii, a
eciaiaiea oaea iaeeiia ?aaeouae e?iiee /anoi iaoeaeaniia?acii ii
oneiaeyi

?en. 15. Iiiia?aiia ?ani?aaeaeaiey yia?aee ii aa?iiieeai

aiciouaiey e oneiaey iia?aoeee

noieeinoe eino?oiaioa, oi iiaia ?ani?aaeaeaiea yia?aee iiaeii iieo/eoue
eciaiea aeeaiao? o?acu ( a aieueooth eee iaiueooth noi?iio ii n?aaiaieth
n ia?aiia/aeueiui ). I?e yoii iaiaoiaeeii nio?aieoue i?aaeiei
ioiineoaeueiia /enei coaueaa ( z/D) e nei?inoue ?acaiey, oae eae /enei
iai?ioia e coaueaa o?acu ea?atho naiinoiyoaeueioth ?ieue a ii?aaeaeaiee
/anoioiiai aeeaiaciia aiciouaiey (inz).

Eae aeaeii ec eceiaeaiiiai, iiiia?aiia iiaeao nouanoaaiii iiiiaaoue a
oi?aaeaiee i?ioeannii ?acaiey, ia iniiaa caeiaeaiiuo a iaa
ooieoeeiiaeueiuo caaeneiinoae.

Eiio?ieueiua aii?inu

Nouiinoue e iacia/aiea iiiia?aoee;

Ooieoeeth eaeiai /enea ia?aiaiiuo iiaeii io?aceoue a iaeiie /aoaa?oe
aeaea?oiaie nenoaiu eii?aeeiao ?

Iiiyoea iiiia?aiiu ec (iiia/aiiuo( eeiee;

Nouiinoue ninoaaiie iiiia?aiiu e i?iiaaeooi/iie ooieoeeiiaeueiie oeaeu.

OEIIAUA CAAeA*E IAOAIAOE*ANEIE IA?AAIOEE

YENIA?EIAIOAEUeIUO AeAIIUO

A oeaeyo cae?aieaiey ciaiee e iieo/aiey i?aeoe/aneeo iaaueia
i?aaeeaaaaony ?aoeoue ianeieueei caaea/, eiathueo i?aeoe/aneoth
iai?aaeaiiinoue.

I?e ecia?aiee oaa?aeinoe ii ?ieaaeeo auee iieo/aiu neaaeothuea
?acoeueoaou. Aeey ia?acoea A: 97,0; 98,7; 99,9; 99,5; 97,1; 99,5; 92,0;
100,6; 99,7; 98,0; 98,5; 99,5; 99,7; 99,5; 99,0; 98,5; 99,5; 98,8; 98,5;
99,1; 98,4; 96,6; 97,2; 101,7; 97,2; 98,2; 97,5; 97,7; 99,0; 99,0; 97,5.
Aeey ia?acoea A, i?iaa?yaiiai ia yoii aea i?eai?a: 85,6; 87,1; 87,9;
86,9; 85,6; 85,2; 85,5; 85,7; 84,7; 86,4; 80,0; 85,0; 82,0; 86,0; 86,0;
87,3; 84,5; 87,0; 87,3; 85,4; 91,0; 90,0; 90,8; 89,2; 91,0; 90,4; 84,1;
81,7; 87,4; 84,0; 85,2.

Aeey eaaeaeie a?oiiu aeaiiuo ii?aaeaeeoue cia/aiea ecia?yaiiai
ia?aiao?a, iaee/ea i?iiaoia a ?yaeo ecia?aiee. Aeey eaeie a?oiiu
ecia?aiee ?acoeueoao iieo/ai oi/iaa? Aua?aa a neo/aeiii ii?yaeea 1, 4,
9, 16, 25 ion/aoia i?iaa?eoue ni?aaaaeeeainoue caaeneiinoe oi/iinoe
n?aaeiaai cia/aiey io /enea ecia?aiee. Iino?ieoue yiie?e/aneea caeiiu
eioaa?aeueiiai e aeeooa?aioeeaeueiiai ?ani?aaeaeaiee. Iiaeia?aoue
oai?aoe/aneee caeii ?ani?aaeaeaiey e ioeaieoue aai niioaaonoaea.

Ioeeiiaiey aeeaiao?a aaea ?ani?aaeaeaiu ii ii?iaeueiiio caeiio. Iieiaeia
cia/aiee aeeaiao?a eaaeeo a eioa?aaea 20 ( 0,1 ii. Ioeeiiaiey aeeaiao?a
ioaa?noey oaeaea ?ani?aaeaeaiu ii ii?iaeueiiio caeiio. Iieiaeia anao
ioeeiiaiee ioaa?noey iaoiaeeony a eioa?aaea 20 ( 0,05 ii. Iieaaay, /oi
nai?ea niaaeeiaiey i?iecaiaeeony a?o/ioth, ii?aaeaeeoa, neieueei ec 50
aaeia ia iiaeieaeao ii ?acia?o. Eaeie iiieiaeueiue aeeaiao? inaaiai
ioaa?noey ( aianoi 20 ii ) neaaeoao caaeaoue ( i?e oii aea caeiia
?ani?aaeaeaiey ), /oiau ana 100( aeaoaeae iiaeioee ae?oa e ae?oao i?e
?o/iie nai?ea.

A oeaoa iaoeiino?ieoaeueiiai caaiaea auiieiyaony neiaeiue caeac, n
ii?aaeaeaiiie aa?iyoiinoueth aicieeiiaaiey a?aea. Aeey iaania/aiey ieaia
auionea 100 ecaeaeee caiouaii a i?iecaiaenoai 110 aaeeieoe. Eaeiaa
aa?iyoiinoue, /oi caeac aoaeao auiieiai anee aa?iyoiinoue iieo/aiey
iaeiiai ecaeaeey 0,9; 0,95 ?

I?e enneaaeiaaiee ia?aaaouaaaiinoe iaeiiai ec eiino?oeoeeiiiuo
iaoa?eaeia auee iieo/aiu caaeneiinoe ia?eiaea noieeinoe coaa o?acu io
oaea iaeeiia ( no?oaea/iie eaiaaee.

?acoeueoaou i?eaaaeaiu a oaaeeoea:

((

20

30

40

50

60

T, iei

30

60

80

70

50

Eniieuecoy iaoiae iaeiaiueoeo eaaae?aoia e ia?aaiee/aneiai
eioa?iiee?iaaiey iieo/eoue aiaeeoe/aneoth caaeneiinoue noieeinoe io oaea
iaeeiia .

N iiiiuueth e?eoa?ey (2 i?iaa?ueoa niioaaonoaea /enea a?aeiaaiiuo
aeaoaeae ca 51 niaio ioanniiianeiio ?ani?aaeaeaieth.

*enei a?aeiaaiiuo

ecaeaeee ca iaeio

niaio, m

0

1

2

3

4

5

6

7

8

*enei niai n m

a?aeiaaiiuie

ecaeaeeyie

3

7

9

12

9

6

3

2

0

Ecaanoii, /oi eiee/anoai a?aeiaaiiuo eino?oiaioia a ia?oee niioaaonoaoao
caeiio Ioanniia n ia?aiao?ii eioaineaiinoe ( = 0,5. Ii?aaeaeeoue
eiee/anoai a?aeiaaiiuo ecaeaeee a ia?oee.

Neo/aeiay aaee/eia o ?ani?aaeaeaia ii caeiio ?aaiie aa?iyoiinoe a
eioa?aaea ( 1; 10 (. Ii?aaeaeeoa i?e eaeii cia/aiee o aa?iyoiinoue aai
iaoiaeaeaiey a caaeaiiii eioa?aaea ?aaia 0,05 e 0,95 ?

Neo/aeiay aaee/eia o iiae/eiyaony ii?iaeueiiio caeiio ?ani?aaeaeaiey n
ia?aiao?aie o = 3, (2 = 25. Au/eneeoue aa?iyoiinoe ? ( O ( 10 ), ? ( (2
( O ( 8 ), ? ( O ( (10 ). Aeaeoa a?aoe/aneoth eeethno?aoeeth
?acoeueoaoa.

Noaiie ( aaoiiao iano?iai ia auiieiaiea ?acia?a 100,1 ii. ?aca?in
?acia?ia aeaoaeae iiae/eiyaony ii?iaeueiiio caeiio ?ani?aaeaeaiey n
aeenia?neae (2 = 0,25 ii2. Iiea aeiionea ia ?acia? aeaoaee ninoaaeyao
100 ( 0,15 ii. Iaeaeeoa aeieth a?aea i?e i?iaaaeaiiie iano?ieea,
i?aaenoaaueoa aa a aeaea a?aoeea io n?aaeiaa?eoiaoe/aneiai cia/aiey. Ia
eaeia cia/aiea iaiaoiaeeii iano?ieoue aaoiiao, /oiau aeiey a?aea auea
ieieiaeueiie, ii?aaeaeeoa yoo aeieth. Ionoue o = 100, ( = 0,5. *oi
ieaaeao aieueoaa aeeyiea ia oaaee/aiea aeiee a?aea ( naeaea o ia (0,5
eee oaaee/aiea ( ia 0,5 ?

I?e enneaaeiaaiee neeu ?acaiey a caaeneiinoe io aeoaeiu ?acaiey auea
ecia?aia aeaaiay ninoaaeythuay neeu ?acaiey ?z i?e /aou?ao cia/aieyo
aeoaeiu ?acaiey

t, ii

1

2

3

4

Pz, I

2300

3200

4000

4600

A?aoe/aneei iaoiaeii, iaoiaeii n?aaeieo e iaoiaeii iaeiaiueoeo
eaaae?aoia onoaiiaeoue caaeneiinoue ninoaaeythuae neeu io aeoaeiu
?acaiey.

EEOA?AOO?A

Aaa?a Ae.E. Iniiau iiiia?aoee n i?eia?aie ec iaoeiino?iaiey. Ecae. 2(a.
( I. ( E.: Iaoaec, 1962. ( 163 n.

Aooa? ?.N., Ia/eineee A.A. Yeaiaiou /eneaiiiai aiaeeca e iaoaiaoe/aneie
ia?aaioee ?acoeueoaoia iiuoa. ( I.: Oeciaoaec, 1962. ( 356 n.

Caeaeaeue A.I. Ioeaee ecia?aiey oece/aneeo aaee/ei. ( E.: Iaoea, 1974. (
108 n.

Eannaiae?iaa I.I., Eaaaaeaa A.A. Ia?aaioea ?acoeueoaoia iaaethaeaiee. (
I.: Iaoea, 1970. ( 104 n.

Eieanieeia A.O. Iniiau iaoaiaoe/aneie ia?aaioee ?acoeueoaoia ecia?aiee.
( Oiine: OAO, 1963. ( 49 n.

Ieaneoiei A.E., Ai?iieia A.Ae. Oai?aoe/aneea iniiau i?aaiecaoeee e
aiaeeca auai?i/iuo aeaiiuo a yenia?eiaioa. O/aaiia iiniaea. ( E.: EYO,
1979. ( 232 n.

?oioeineee E.C. Iaoaiaoe/aneay ia?aaioea ?acoeueoaoia yenia?eiaioa.
Ni?aai/iia ?oeiaiaenoai. ( I.: Iaoea, 1971. ( 192 n.

?uaeia Y.A., Ai?eaiei I.A. Iaoaiaoe/aneea iaoiaeu a oaoiieiae/aneeo
enneaaeiaaieyo. ( Eeaa: Iaoe. aeoiea, 1990. ( 184 n.

Nooia A.I. Iaoaiaoe/aneay ia?aaioea ?acoeueoaoia ecia?aiee. O/aaiia
iiniaea. ( I.: IENE, 1982. ( 89 n.

*eaeiaa I.I. Iniiau iao/iuo enneaaeiaaiee. ( Eeaa: Aeua oeiea, 1978. (
120 n.

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eaeoeee. ( *aeyaeine: *AOO, 1995. ( 122 n.

Oaeaiia A.A. Iiaeaee?iaaiea i?e o?aca?iaaiee: O/aaiia iiniaea. (
*aeyaeine: *AOO, 1997. ( 141 n.

Ueaieaa A.I. Iaoaiaoe/aneay ia?aaioea iaaethaeaiee. Ecae. 2(a. ( I.:
Oeciaoaec, 1962. ( 344 n.

IAEAAEAIEA

AAAAeAIEA………………………………………………………
……………………….3

IOEAEE
ECIA?AIEE………………………………………………………
……..4

Oeaee iaoaiaoe/aneie ia?aaioee ?acoeueoaoia yenia?eiaioa ………….

Aeaeu ecia?aiee e i?e/eiu
ioeaie………………………………………….5

Oeiu ioeaie
ecia?aiey………………………………………………………
….5

Naienoaa neo/aeiuo
ioeaie…………………………………………………….6

Iaeaieaa aa?iyoiia cia/aiea ecia?yaiie aaee/eiu……………………8

Ioeaiea oi/iinoe
ecia?aiee…………………………………………………….9

Iiiyoea aeiaa?eoaeueiiai eioa?aaea e aeiaa?eoaeueiie aa?iyoiinoe…11

Iaia?oaeaiea
i?iiaoia……………………………………………………….
..13

Ioeaee einaaiiuo
ecia?aiee………………………………………………..14

I?aaeea ie?oaeaiey
/enae……………………………………………………16

Ii?yaeie ia?aaioee ?acoeueoaoia
ecia?aiee……………………………..17

Ia?aaioea ?acoeueoaoia ecia?aiee aeeaiao?a
oeeeeiae?a……………….18

Eiio?ieueiua
aii?inu………………………………………………………..
…22

CAEIIU ?ANI?AAeAEAIEss NEO*AEIUO AAEE*EI…………………22

Aeaeu neo/aeiuo aaee/ei e caeiiu eo
?ani?aaeaeaiey……………………

*eneiaua oa?aeoa?enoeee neo/aeiuo aaee/ei, caaeaiiuo naieie

?ani?aaeaeaieyie………………………………………………..
………………..25

Iniiaiua aeene?aoiua e iai?a?uaiua caeiiu ?ani?aaeaeaiey……….27

Iiiyoea noaoenoe/aneie aeiioacu e noaoenoe/aneiai e?eoa?ey…….33

Aa?iyoiinoue ioeaie ia?aiai e aoi?iai
?iaea……………………………..34

I?iaa?ea aeiioacu aeaea caeiia ?ani?aaeaeaiey aa?iyoiinoae………..36

Eiio?ieueiua
aii?inu………………………………………………………..
….38

IAOIAEAeAIEA EIOA?IIEE?OTHUEO E?EAUO………………………..38

A?aoe/aneee iaoiae ia?aaioee
?acoeueoaoia………………………………..38

Ooieoeeiiaeueiua oeaeu e eo
i?eiaiaiea…………………………………40

Aiaeeoe/aneea iaoiaeu ia?aaioee
?acoeueoaoia…………………………..42

Niinia
n?aaeiae……………………………………………………….
…….43

Iaoiae iaeiaiueoeo
eaaae?aoia…………………………………………..44

Eioa?iiee?iaaiea
ooieoeee…………………………………………….48

Ia?aaiee/aneia
eioa?iiee?iaaiea……………………………………48

Eiio?ieueiua
aii?inu………………………………………………………..
….50

INIIAU
IIIIA?AOEE……………………………………………………..
….51

Iiiia?aiiu a aeaea?oiaie nenoaia
eii?aeeiao………………………………

Ninoaaiua iiiia?aiiu n iiia/aiiuie eeieyie……………………….53

Eiio?ieueiua
aii?inu………………………………………………………..
….58

5. OEIIAUA CAAeA*E IAOAIAOE*ANEIE IA?AAIOEE YENIA?EIAIOAEUeIUO
AeAIIUO………………………………………………………..
…..58

EEOA?AOO?A……………………………………………………..
……………………61

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