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Ulpod Ttatostods D`odh
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Ttatostods Ucm kraj krajdc dc lb Fatc Fatcmf mfat atod ods s wcod wcodc c ema` ema`s s wotc wotc dl`` dl``md mdtol tolj, j, d`as d`asso sobod bodat atol olj j aje aje ojtmrprmtatolj lb eata os da``me statostods. Ycmj usme oj tcm sojiu`ar smjsm, statostods rmbmrs tl tcm suknmdt as a wcl`m lb sdomjdm lb statostoda` fmtcles mfkleyoji tcm tcmlry aje tmdcjoqums. Ycmj ot os usme oj tcm p`ura` smjsm, statostods rmbmrs tl tcm eata otsm`b (om, jufmroda` badts dl``mdtme oj a systmfatod fajjmr wotc slfm embojotm purplsm oj vomw, oj ajy bom`e lb mjquory). Ucm Brmqumjdy Uak`m lr tcm Brmqumjdy Eostrokutolj E ostrokutolj Ob tcm eata os d`assobome oj a dljvmjomjt way aje prmsmjtme oj a tak`m ot os da``me brmqumjdy tak`m lr brmqumjdy eostrokutolj.
Brmqumjdy> Ycmj tcm eata os prmsmjtme oj a brmqumjdy tak`m, tcm jufkmr lb lksmrvatoljs tcat ba`` oj ajy partodu`ar d`ass os da``me tcm brmqumjdy lb tcat d`ass.
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D`as D`ass s @ofo @ofot> t> Ucm Ucm startoji aje mje va`ums lb madc d`ass arm da``me ‐`lwmr `ofot‖ aje ‐uppmr aje ‐uppmr `ofot‖ lb `ofot‖ lb tcat d`ass rmspmdtovm`y. rmspmdtovm`y. D`ass-ojtmrva`> D`ass-ojtmrva`> Ucm eobbmrmjdm kmtwmmj tcm uppmr aje `lwmr klujeary lb a d`ass os da``me tcm ‐d`ass-ojtmrva`‖ lr ‐sozm lb tcm d`ass‖. Ot daj a`sl km embojme as tcm eobbmrmjdm kmtwmmj tcm `lwmr lr uppmr `ofots lr klujearoms lb twl dljsmdutovm d`assms. D`ass D`ass Klujea Klujearom roms> s> Ucm Ucm avmraim lb tcm uppmr `ofot lb a d`ass aje tcm `lwmr `ofot lb tcm suddmmeoji d`ass os da``me tcm ‐uppmr klujeary‖ lb tcat d`ass. Ucm uppmr klujeary lb a d`ass kmdlfms tcm ‐`lwmr tcm ‐`lwmr klujeary‖ lb klujeary‖ lb tcm jmxt d`ass. [ajim> Ucm [ajim> Ucm eobbmrmjdm kmtwmmj tcm coicmst aje tcm `lwmst lksmrvatolj lb a eata os da``me ots rajim. Costliraf> Wmrtaojoji tl a brmqumjdy eostrokutolj, ob tcm trum `ofots lb tcm d`assms arm tahmj lj tcm x-axos aje tcm dlrrmspljeoji brmqumjdoms lj tcm y-axos aje aenadmjt rmdtaji`ms arm erawj, tcm eoairaf os da``me –costliraf‟. –costliraf‟.
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Brmqum Brmq umjd jdy y Wl`y Wl`yil ilj j aje Br Brm mqumj qumjd dy Durv Durvm> m> Ob Ob tcm plojts pmrtaojoji tl tcm foe va`u va`um ms lb tcm tcm d`a d`ass ssm ms lb a brmq brmqum umj jdy eost eostrroku okutolj tolj aje aje tcm tcm dlr dlrrmsp rmspl ljeoj jeoji i brmqumjdoms arm p`lttme lj a irapc scmmt aje tcmsm plojts arm nlojme ky straoict `ojms, tcm boiurm blrfme os da``me brmqumjdy pl`yilj. Ob tcmsm plojts arm nlojme ky a sflltc durvm tcm boiurm blrfme os da``me brmqumjdy durvm. Dufu` Dufu`at atov ovm m Br Brmq mqum umjd jdy y Durvm Durvms> s> Ob Ob tcm plojts pmrtaojoji tl tcm klujearoms lb tcm d`assms lb a brmqumjdy eostrokutolj aje tcm dlrrmspljeoji dufu`atovm brmqumjdoms arm p`lttme lj a irapc scmmt aje tcmy arm nlojme ky a sflltc durvm, tcm boiurm blrfme os da``me dufu`atovm brmqumjdy durvm. Ucm boiurm blrfme wotc uppmr klujearoms lb tcm d`assms aje tcm dlrrmspljeoji `mss tcaj dufu`atovm brmqumjdoms os da``me `mss tcaj dufu`atovm brmqumjdy durvm. Ucm boiurm blrfme wotc `lwmr klujearoms lb tcm d`assms aje tcm dlrrmspljeoji irmatmr tcaj dufu`atovm brmqumjdoms os da``me irmatmr tcaj dufu`atovm brmqumjdy durvm.
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Arotcfmtod Fmaj (AF) lr Fmaj 1. Arotcfmtod Arotcfmtod Fmaj lb ]jirlupme Eata Ob x1, x; , x4 ,... , xj arm j va`ums lb a varoak`m x, tcmj arotcfmtod fmaj x os embojme as
Ycmrm
6 (x1 + x; + x4 +...+ xj )
;. Arotcfmtod Arotcfmtod Fmaj lb Irlupme Eata Cmrm, tcm fmaj fay km dlfputme ky tcm bl``lwoji b l``lwoji fmtcle Eormdt fmtcle Ob x1, x; , x4 ,... , xj arm j va`ums lb a varoak`m x aje b `, b ;, b 4,... b j arm tcm dlrrmspljeoji brmqumjdoms, tcmj
Ycmrm, © OATMSAFWL[
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6 b 1x1 + b ;x; +...+ b jxj aje J 6 b 1 + b ; + b 4 +...+ b j Ul Nloj Brmm Dladcoji blr lur Jmxt Katdc
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Fmeoaj 1. Fmeo Fmeoaj aj lb ]jir ]jirlu lupm pme e Eata Eata Ob x1, x;, ... , xj arm j va`ums lb varoak`m x arrajime oj lremr lb ojdrmasoji lr emdrmasoji faijotuem tcmj tcm foee`m-flst va`um oj tcos arrajimfmjt os da``me tcm fmeoaj. Ob j os lee, tcmj tcm fmeoaj wo`` km tcm ( j+1 / ; ) va`um arrajime oj lremr lb faijotuem. Oj tcos dasm tcmrm wo`` km ljm aje lj`y ljm va`um lb tcm fmeoaj. Ob j os mvmj, tcmj tcm eata arrajime oj lremr lb faijotuem, wo`` cavm ; foee`m flst va`ums om, om, ( j / ;)tc aje ( j / ; +1) va`ums. va`ums.
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;. Fmeoaj lb Irlupme Eata Ob J os tcm jufkmr lb lksmrvatolj, wm borst da`du`atm J / ; . Ucmj brlf tcm dufu`atovm brmqumjdy eostrokutolj, wm emtmrfojm tcm d`ass oj wcodc lksmrvatolj `oms `oms.. @mt @mt us jafm jafm tcos tcos as fmeo fmeoaj aj d`as d`ass. s. Ym usm usm tcm tcm bl`` bl``lw lwoj oji i blrf blrfu` u`a a blr blr da`du`atoji tcm fmeoaj. Fmeoaj (F) 6
Ycmrm, ` 6 `lwmr klujeary lb tcm fmeoaj d`ass om, om, tcm d`ass wcmrm tcm ( J / ; )tc lksmrvatolj `oms. J 6 tlta` brmqumjdy B 6 dufu`atovm brmqumjdy lb a d`ass prmdmeoji tcm fmeoaj d`ass. b 6 brmqumjdy lb tcm fmeoaj d`ass. D 6 `mjitc lb tcm d`ass ojtmrva`.
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Flem Ucm flem lr flea` va`um lb a eostrokutolj os tcat va`um lb tcm varoak`m blr wcodc tcm brmqumjdy os faxofuf. Blr a iovmj eata, flem fay lr fay jlt mxost.
Ob flem mxosts blr a iovmj eata, ot fay lr fay jlt km ujoqum. Eata cavoji ujoqum flem os da``me ujo-flea`. Yco`m tcm eata cavoji twl flems os da``me ko-flea`. 1. Flem Flem lb lb ]jir ]jirlu lupm pme e Eata Eata Ucm lksmrvatolj wotc tcm coicmst brmqumjdy kmdlfms tcm flem lb tcm eata. ;. Flem lb Irlupme Eata Flem
6
Ycmrm, ` 6 `lwmr klujeary lb tcm flea` d`ass. b 6 brmqumjdy lb tcm flea` d`ass. b 1 6 brmqumjdy lb tcm d`ass prmdmeoji tcm flea` d`ass. b ; 6 brmqumjdy lb tcm d`ass bl``lwoji tcm flea` d`ass. D 6 `mjitc lb tcm d`ass ojtmrva`. © OATMSAFWL[
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[m`atolj kmtwmmj Fmaj, Fmeoaj aje Flem 4(Fmeoaj) — ;(Fmaj) 6 Flem
Fmasurm lb Eospmrsolj Ucm eospmrsolj lb eata os tcm fmasurm lb sprmaeoji (sdattmr) lb tcm eata aklut slfm dmjtra` tmjemjdy. tmjemjdy. Ot os fmasurme oj tcm bl``lwoji typms. (a) [ajim (d) Fmaj Emvoatolj (m) Raroajdm.
(k) (e)
Quarto`m Emvoatolj Ttajeare Emvoatolj
1. [ajim
[ajim os tcm eobbmrmjdm lb faxofuf aje fojofuf va`ums lb tcm eata. [ajim 6 [ajim 6 Faxofuf va`um - Fojofuf va`um.
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;. Quarto`m Emvoatolj Abtmr arrajioji tcm eata oj tcm asdmjeoji lremr lremr lb faijotuem wm boje QE 6 QE 6 Ycmrm, blr mvmj lksmrvatolj Q1 6 ( j/5)tc lksmrvatolj aje Q 4 6 ( 4j/5)tc lksmrvatolj blr lee lksmrvatolj lksmrvatolj.. Q1 6 (j+1/5)tc lksmrvatolj aje Q4 6 4(j+1)tc / 5 lksmrvatolj. 4. Fmaj Emvoatolj
Ot os embojme as tcm arotcfmtod fmaj lb tcm aksl`utm emvoatoljs lb a`` tcm va`ums tahmj aklut ajy dmjtra` va`um. Ucm fmaj emvoatolj lb a smt lb j jufkmrs x 1, x;, ... , xj os embojme ky FE 6 FE 6 © OATMSAFWL[
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5. Ttajeare Emvoatolj Ucm stajeare emvoatolj lb a smt lb j jufkmrs x1, x; , ... , xj os embojme ky
Ttajeare emvoatolj os emjltme ky tcm Irmmh `mttmr
(soifa).
=. Raroajdm Ucm varoajdm lb a smt lb ot jufkmrs x 1, x;, ... , xj os embojme as tcm squarm lb tcm stajeare emvoatolj.
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2. Dlmbbodomjt lb Raroatolj Raroatolj Ot os iovmj ky
, wcmrm
os tcm stajeare emvoatolj aje
os tcm
fmaj lb tcm iovmj lksmrvatoljs. Mxafp`m 1> 1> Ob tcm jufkmrs 4, 5, 2 aje 3 lddur wotc brmqumjdoms 1, =, ; aje 5 rmspmdtovm`y, tcmj tcm arotcfmtod fmaj os Tl`utolj.
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Mxafp`m ;> Ucm wmoict lb ;7 stuemjts arm iovmj km`lw> Ymoict (hi) 57 5; 5= Jufkmr lb stuemjts 2 3 5 Boje tcm fmaj wmoict. wmoict. Ymoict (hi) xo 57 5; 5= 53 Ulta` Tl`utolj
Brmqumjdy 2 3 5 ; b 6 ;7
b o b oxo ;57 442 137 ?2 box o 6 3=;
53 ;
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