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_litm Glormliif (7662>06)
Qtfddl Dy`ml (
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EJ@VD GMDP_LQM Ijvfeofr
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EJ@VD GMDP_LQM Ijvfeofr
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EJ@VD GMDP_LQM Ijvfeofr ,? psmb.
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EJ@VD GMDP_LQM Ijvfeofr
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EJ@VD GMDP_LQM Ijvfeofr
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EJ@VD GMDP_LQM Ijvfeofr
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EJ@VD GMDP_LQM Ijvfeofr
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EJ@VD GMDP_LQM Ijvfeofr brle `fibli lmr
cmrlcmrl 7 D.
0. Efibl`ucsdurrytfrsfout sfalrl cjitmiu lblrcjisfitrlsmsdurrytftlp uimgjre.
^fibl`ucli `mdlcucli `m`ldle tlibcm
rfsfrvjlr `li pfibl`ucli `mdlcucli
sfalrl tfrusefifrus.
O. ^F_AJOLLIIj. ^rjsf`ur ^frajolli Cftfrlibli
,,? cb/ae1.
1. Efdftlccli feofr `m olwlh W-0 (gmdtrlt`fdmvfry vldvf).
Vituc efibucur gmdtrlt ylib `mhlsmdcli.
0. Efiklbl tlibcm rfsfrvjlr lblr tm`lc oftudoftud cjsjib `fibli alrl efiymrle `fibli
hltmhltm dlrutlisdurry`ldle tlibcm
rfsfrvjlr, `li uituc efylcmicli efeltmcli
pjepl sfofdue tlibcm oftudoftud cjsjib.
Dlrutlisdurrypl`l tlibcm rfsfrvjlr
sfolmciyl `moult `ldle kuedlh oliylc
sfhmibbl tm`lc pfrdu efdlcucli
pfileolhli dlbm.
6. Efibltur W-1 sfdlel pfrajolli uitucefi`lpltcli tfclili ylib cjistli. @li
efiutup W-? sfdlel pfrajolli.
Kmcl tfrkl`m pfruolhli tfclili elcl W-1
hlrus `mltur sf`femcmli rupl hmibbl
tfcliliiyl cfeoldm pl`l imdlm ylib
`mtfitucli.7. Efialtlt wlctu tfrtfitu sfdlel gmdtrlsm `fibli ^fialtltli imdlm Wg `mdlcucli pl`l sfdlib
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EJ@VD GMDP_LQM Ijvfeofr efimt.
2. Cftml pjepl `meltmcli, lcli tfr`lplt rlwdmqum`ylib tfrtmibbld `ldle pjepl, tlibcm
rfsfrvjlr `li pmpl. Almrli smsl tfrsfoutefruplcli sltu dmqum`ylib tm`lc tfrgmdtfr.
8. Efibudlibm pfrajolli `mltls pl`l tfcliliylib ofrof`l.
MMM.? Hlsmd ^frajolli
Plofd ,,?
cb/ae1
? 8> >
0
8 1 176
18> 066
7?6
?> 2 886
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EJ@VD GMDP_LQM Ijvfeofr ,< cb/ae?`li ^ 5
>,? cb/ae? ylib `mltur cjistli `fibli efibltur ldmrli gff` cf `ldle gmdtfr prfss ylib
`mbuilcli. Wjduef gmdtrlt (Wg) `m`lpltcli `fibli efdmhlt ofrlpl ofslr imdlm vjduefiyl
sftmlp mitfrvld wlctu ? efimt sleplm efimt cf ?> uituc elsmib-elsmib tfclili. @ltl ylib
`m`lpltcli l`ldlh sfolblm ofrmcut ;
Plofd ,,?
cb/ae1? 8> >
0
8 1 176
18> 066
7?6
?
>
2 886
L. ^frsleli _juth,^fralelli _juth `mbuilcli uituc efialrm imdlm cjistlitl h `li k.
^frslelli _juth ;
^frslelli `mltls cfeu`mli `mturuicli uituc efi`lpltcli pfrslelli dmiflr.
^fiuruiliiyl sfolblm ofrmcut ;
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EJ@VD GMDP_LQM Ijvfeofr ,? cb/ae1
Wg (ed) t/Wg
(sfa/ed)
Wg (ed) t/Wg
(sfa/ed)
? 8> > 2 8 886
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EJ@VD GMDP_LQM Ijvfeofr > 0>> 7>> 8>>
t/Wg
Wg
Brlgmc Wg tfrhl`lp t/Wg sllt ^ 5 >,< psm
Brlgmc Wg tfrhl`lp t/Wg
sllt ^ 5 >,< psm
Dmiflr (Brlgmc Wg tfrhl`lp
t/Wg sllt ^ 5 >,< psm)
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EJ@VD GMDP_LQM Ijvfeofr ,?cb/ae?
y 5 >,>>>?x + ,>>>?h 5
5
h 5 6>>>
a 5 5 =8,?6
@fibli `femcmli, cmtl `lplt efibhmtuibli h `li k rltl-rltl ituc efi`lpltcli imdlm
cjistlitl ylib sfsuibbuhiyl.
y 5 >.>>>?x + .201=
,? psm
Dmiflr (Brlgmc Wg
tfrhl`lp t/Wg sllt
^5>,? psm)
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EJ@VD GMDP_LQM Ijvfeofr >
k 5 k lvfrlbf 5 10?0,88
Qfhmibbl, pfrslelli _juth iyl efikl`m ;
O. ^frsleli Dfwms,
^frslelli Dfwms `mbuilcli uituc efialrm imdlm cjistlitl e `li i.
^frslelli Dfwms ;
^frslelli `mltls cfeu`mli `mturuicli uituc efi`lpltcli pfrslelli dmiflr.
^fiuruiliiyl sfolblm ofrmcut ;
y 5 e x + a`melil A 5
@lrm pfrslelli dmiflr `mltls, elcl cmtl `lplt efibftlhum imdlm sdjpf ltlu brl`mfi (e)
ylmtu e `li imdlm mitfrsfp (a) ylmtu djb A`fibli efepdjt brlgmc djb Wg tfrhl`lp djb t.
@fibli efibftlhum imdlm-imdlm tfrsfout, elcl imdlm cjistlitl `ldle pfrslelli Dfwms ylmtu e
`li A 5`lplt `mpfrjdfh. Ofrmcut efruplcli pfibjdlhli `ltl uituc efialrm imdlmcjistlitl pfrslelli Dfwms ofsfrtl brlgmciyl ;
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EJ@VD GMDP_LQM Ijvfeofr 06> ?,761? ?,21?1=0 ?,86211?
6?> ?,2>1 ?,=?0?2= 7?6 ?,2=688 ?,=?0?2=
6=6 ?,2206 > 2 ?,86
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EJ@VD GMDP_LQM Ijvfeofr ==2A 5 A 5 ,? psm l`ldlh sfolblm ofrmcut ;
Bleolr 2. Brlgmc djb Wg tfrhl`lp djb t sllt ^ 5 >,? cb/ae?
djb t 5 0=2 djb Wg - >,>,? psm
Brlgmc Djb Wg tfrhl`lp Djb t
sllt ^ 5 >,? psm
Dmiflr (Brlgmc Djb Wg
tfrhl`lp Djb t sllt ^ 5 >,?
psm)
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EJ@VD GMDP_LQM Ijvfeofr > ed, elcl ;
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EJ@VD GMDP_LQM Ijvfeofr ,>==2
djb t 5 0>1 djb(>>) - >,>==2
djb t 5 1,>?
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EJ@VD GMDP_LQM Ijvfeofr ,182 a 5 djb 5 ?,26>2
5 5 671,?6
Efifitucli imdlm C
5 C 5 5 L 5 duls pfileplib gmdtrlt
C 5 >,>
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EJ@VD GMDP_LQM Ijvfeofr
OLO W
LILDMQL & CFQME^VDLI
6.> brle sfolblm glsl pl`lt. Cldsmue clrojilt efi`fcltm smglt alcf ylib m`fld,
ylmtu ijiajeprfssmodf clrfil plrtmcfd tfpuib efemdmcm smglt cfrls `li ucurliiyl aucup
ofslr. [lt pl`lt ylib sliblt hldus `li rlplt ylib efeofituc alcf lcli sfbfrl tfrtlhli jdfh
ef`mue gmdtrlsm ylib efemdmcm pjrm-pjrm emcrj. _fsfrvjmr ylib `mbuilcli l`ldlh tlibcm ylib
`mdfibclpm `fibli pfibl`uc `fibli pjsmsm afitfr. ^fibl`uc `msmim ofrguibsm lblr cji`msm
sdurry sfdldu hjejbfi `li tm`lc l`l pl`ltli ylib efibfi`lp. Kmcl cjisfitrlsm tm`lc
hjejbfi `li sliblt ofslr pfrof`lliiyl elcl lcli tfrofituc alcf `m lwld prjsfs `li hld mim
tm`lc sfsulm `fibli lsuesm olhwl gdmtrlsm `meudlm `fibli pfilhlili ylib slel `fibli ijd
`li rueus pfrslelli ylib `mbuilcli tm`lc `lplt `mlpdmclsmcli. @lslr tlibcm efemdmcm afdlh
`m tfiblh ylib `mbuilcli sfolblm sldurli cfdulrlisdurry.
Qdurryylib tl`m `moult `fibli efialepurcli cldsmue clrojilt `li lmr `mldmrcli cf
`ldlegmdtfr prfss`fibli efibbuilcli pjepl, cfeu`mli pjepl efibldmrclisdurrysleplm
pl`l grlef `li pdltf. Grlef `li pdltf `ldle gmdtfr prfss mim `msusui sfalrl ofrsfdmibli.
@mlitlrlpdltf`ligrlef`mplslib ruoofr`ligmdtfr adjth. ^felslibli ruoofr`ligmdtfr adjth
hlrus tfplt clrfil sliblt efepfiblruhm dlku ldmr gmdtrlt `li prjsfs pfemslhli pl`l gmdtfr
prfss. @melil tjtld pfrldltli `ldle pfrajolli mim;
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EJ@VD GMDP_LQM Ijvfeofr ,,? cb/ae? `fibli cjisfitrlsm sdurry ylib `mbuilcli slel. Cjisfitrlsm ylib
slel mim `mbuilcli uituc efibukm pfrslelli _juth `li Dfwms `li efialrm cjistlitl
pfrslelli mtu elsmib-elsmib. @ltl ylib `mleomd sfkuedlh uituc elsmib-elsmib tlclili.
Qfelcmi dlel prjsfs gmdtrlsm elcl lcli sfelcmi sf`mcmt gmdtrlt ylib `mhlsmdcli. Hld mim
`msfolocli sfelcmi oliylciyl alcfylib tfrofituc `ldle ldlt sfhmibbl efibhleolt sdurry
ylib efdfwltmgmdtfr prfsssfhmibbl dlku ldmrsdurrylcli ofrcurlib. ^frmstmwl mim tfrouctm `lrm
pfibleltli ylib `mdlcucli. ^frof`lli tfclili sfhlrusiyl ofroli`mib durus `fibli
oliylciyl gdmtrlsm ylib `mhlsmdcli. Gfijefil mim `msfolocli jdfh l`liyl `rmvmib gjrafylmtu
pfrof`lli tfclili ylib efi`jrjib sdurry, sfhmibbl dlku ldmr sdurry lcli sfelcmi ofslr.
Lcli tftlpm, `ltl ylib `mpfrjdfh kustru sfoldmciyl. Hld mim euibcmi `msfolocli pfrof`lli
tfclili ylib `mofrmcli aucup cfamd, ylmtu sfofslr >,< cb/ae?, sf`libcli alcfylib tfrofituc
su`lh oliylc, sfhmibbl `leplc `rmvmib gjraf curlib tfrhl`lp cftfoldli alcf. Qfdlel prjsfs
ofrdlibsuib gff` vldvf tfrus `mltur uituc efi`lpltcli tfclili ylib cjistli. Pukuliiyl
hliyl uituc efeoult sltu vlrmlofd ylib efepfiblruhm kuedlh gdmtrlt, ylmtu wlctu.
^l`l pfrajolli vldvf W-? `m tutup clrfil uitu efiklbl dlku ldmr `li tfcliliiyl lblr
tm`lc tfrdldu dfelh, sf`libcli uituc efiklbl tfclili `m ltur vldvfW-1. Wldvf W-1 `m ltur
eliuld, clrfil dlku ldmr `lrm sdurry ylib elsuc cf `ldle gmdtfr prfss tm`lc stlomd. W-0
efruplcli vldvfylib `mbuilcli uituc efibfdulrcligmdtrlthlsmdgmdtrlsm, pfiblturli `lrm W-
0 sfi`mrm ylmtu cjistli `fibli efibltur ouclli lblr gmdtrltylib cfdulr tm`lc tfrdldu `frls,
hld mim `m clrfilcli uituc efiklbl tlibcm rfsfvjmr lblr tm`lc afplt hloms sdurryiyl.
6.? Lildmsl Hlsmd
^rlctmcli efdlcucli pfibleomdli `ltl ofrupl vjduef gmdtrlt (Wg) ylib cfdulr `lrm
gmdtrltf `fdmvfry vldvfpl`l mitfrvld wlctu tfrtfitu (t), `melil pl`l pfrajolli mim wlctu ylib
`mtfitucli ylmtu sfdlel ?> efimt uituc elsmib-elsmib tfclili. Qftmlp ? efimt vjduef gmdtrlt
`mucur sfalrl cjitmiyu sfhmibbl m`lpltcli `ltl sfoliylc cldm pl`l tmlp tfclili ylib
`mklbl cjistli pl`l prfssurf blubf (^ 5 >,< cb/ae?`li ^ 5 >,? cb/ae?) ltlu `m`lpltcli
?> `ltl sfalrl cfsfduruhli.
^fibleomdli `ltl `fibli wlctu `li tfclili ylib ofrvlrmlsm mim `melcsu`cli uituc
efibleltm pfruolhli kuedlh vjduef gmdtrlt ylib tfrofituc tmlp pfruolhli wlctu `li
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EJ@VD GMDP_LQM Ijvfeofr ,?
cb/ae1
? 8> >
0
8 1 176
18> 066 7?6
?> 2 886
Ofr`lslrcli `ltl hlsmd pfrajolli `m ltls, `lplt cmtl dmhlt l`liyl sultu pjdl `melil
cfilmcli vjduef gmdtrlt pfr uimt wlctu (Wg) hlsmd gmdtrlsm `lplt `mcltlcli afi`fruib
efiurui ltlu cjistli sfmrmib `fibli ofrtleolhiyl wlctu sfrtl dlku gmdtrlt ylib `mhlsmdcli
kubl sfelcmi ofslr sfmrmib `fibli l`liyl cfilmcli imdlm tfclili ylib `mofrmcli. Hld mim
`lplt `mouctmcli lplomdl cmtl efeoli`mibcli `ltl vjduef gmdtrlt pfr uimt wlctu pl`l wlctu
ylib slel uituc cf`ul tfclili.
Wjduef gmdtrlt pfr wlctu ltlu dlku ldmr gmdtrlt pl`l tfclili ylib dfomh tmibbm ylmtu pl`l
^ 5 >,? cb/ae?l lcli `mhlsmdcli dfomh oliylc ltlu afplt `moli`mibcli `fibli
efibbuilcli tfclili smstfe ^ 5 >,< cb/ae?. Hld mim `msfolocli sfelcmi ofrtleolhiyl
kuedlhgmtrlt alcfylib ofrupl ajeprfssmodf alcfylib tfrofituc sfmrmib pfrtleolhli wlctu
efiyfolocli vjduef `li dlku ylib `mhlsmdcli lcli efiurui ltlu ofrcurlib ltlupui
afi`fruib cjistli `fibli rfitlib wlctu ylib slel. @fibli cltl dlmi gmdtrlt ylib lcli
efdfwltm gmdtfr pl`l rfitlib wlctu lchmr lcli dfomh sf`mcmt clrfil tfdlh tfrhldlib jdfhgmdtrltf
alcfylib tfdlh tfrofituc sfmrmib pfrtleolhli gff` `li wlctu `moli`mibcli pl`l `ftmc-`ftmc
lwld pfrajolli clrfil pl`l sllt mtu alcf olru lcli eudlm tfrofituc.
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EJ@VD GMDP_LQM Ijvfeofr ,< cb/ae?uituc
pfrajolli pfrtlel `li ^ 5 >,? cb/ae?uituc pfrajolli cf `ul), tm`lc l`l cfojajrli pl`l
gmdtfr prfss, `li alcfylib `mhlsmdcli efruplcli iji-ajeprfsmodf alcf
L. ^F_QLELLI _JVPH^frslelli _juth sfalrl ueue efikfdlscli olhwl kmcl gmdtrlsm `mdlcucli pl`l ^
ylib cjistli elcl huouibli litlrl wlctu (t) `fibli vjduef gmdtrlt (W g) `lplt `mfcsprfsmcli
`ldle pfrslelli ofrmcut;
thWKW gg ..??
Cmtl `lplt efibuolh pfrslelli `fibli efeolbm tmlp ruls `fiblihWg
< sfhmibbl
pfrslelli `m ltls efikl`m ofituc pfrslelli olru sfpfrtm ofrmcut mim;
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EJ@VD GMDP_LQM Ijvfeofr .< psmb)
Bleolr 0.Brlgmc Wt tfrhl`lp
sllt ^ 5 >,< cb/ae?
y 5 >.>>>?x + >7_ 5 >.26 8>>
t/Wg
Wg
Brlgmc Wg tfrhl`lp t/Wg sllt ^ 5 >,< psm
Brlgmc Wg tfrhl`lp t/Wg
sllt ^ 5 >,< psmDmiflr (Brlgmc Wg tfrhl`lp
t/Wg sllt ^ 5 >,< psm)
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EJ@VD GMDP_LQM Ijvfeofr ,>>>?x + >7
@lrm pfrslelli ylib `m pfrjdfh elcl lcli `lplt efepfrjdfh `ltl sfpfrtm `molwlh mim.
h 5 6>>>
k 5 126,? psmb)
Bleolr 6. Brlgmc Wt tfrhl`lp sllt ^ 5 >,?cb/ae?
Ofituc dmiflrmslsm pfrslelli _juth ofr`lslrcli rfbrfsm `ltl ylib `mpfrjdfh jdfh
prlctmcli l`ldlhy 5>,>>>?x+ >>
k 5 1>=8,?6
y 5 >.>>>?x + .201=
,? psm
Dmiflr (Brlgmc Wg
tfrhl`lp t/Wg sllt
^5>,? psm)
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EJ@VD GMDP_LQM Ijvfeofr
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EJ@VD GMDP_LQM Ijvfeofr ,< psmb)
Bleolr 7. Brlgmc djb Wg tfrhl`lp djb t sllt ^ 5 >,< cb/ae?
Ofituc dmiflrmslsm pfrslelli Dfwms ofr`lslrcli brlgmc pdjttmib ylib tfdlh prlctmcli dlcucli
l`ldlhy 50>1x>,>==2
@li lcli efi`lpltcli `ltl sfpfrtm `m olwlh mim
e 5 0>1
A 5 1x + >.>==2
_ 5 >.===?
>
>.6
,< psm
Brlgmc Djb Wg tfrhl`lp Djb
t sllt ^ 5 >,< psm
Dmiflr (Brlgmc Djb Wg
tfrhl`lp Djb t sllt ^ 5 >,,? cb/ae?
Ofituc dmiflrmslsm pfrslelli Dfwms ofr`lslr pdjt brlgmcy 5 0=2x->,>
>.6
,? psm
Brlgmc Djb Wg tfrhl`lp Djb t
sllt ^ 5 >,? psm
Dmiflr (Brlgmc Djb Wg
tfrhl`lp Djb t sllt ^ 5 >,?
psm)
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EJ@VD GMDP_LQM Ijvfeofr > ae1. @li `m `lpltcli hlsmd sfpfrtm
tlofd ofrmcut.
Bleolr 8. Brlgmc djb `fdtl ^ tfrhl`lp djb t
Qftfdlh efi`lpltcli `ltl ^, djb t `li djb ^, elcl `ltl `m pdjt efikl`m brlgmc
`fibli efibhuouibcli litlrl djb ^ tfrhl`lp djb t, elcl lcli `m `lpltcli pfrslelli y 5 -
>,182x + ?,26>2
,26>2
y 5 e x + a
sfhmibbl lcli efi`lpltcli imdlm cjistlitl i `li
i 5 >,182
5 671,?6
y 5 ->.182x + ?.26>2
_ 5 ?
1.>0
1.>7
1.>8
1.,>
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EJ@VD GMDP_LQM Ijvfeofr