D
]hj hlr} l` SAR’ }hj Wllmwq Wllmwqigh}’ igh}’rr Rhls azidmr n `ll}/slwjqjm `ll}/s lwjqjm dn}hj nkm nk m eigrnw+ eigrnw+ Ay zrikg qjbybdjm dzoajq hj hjdsr }hj jkpiqlkojk}$ nmmr rloj ‘kjw’ j~zisojk} }l hir rhls nkm iosqjrrjr hir mnzgh}jq mnzgh}jq++
n}hj Dl`} `qqlo n `
} ndd ajgnk whjk I wjk} }l sibf zs oy mnzgh/ }jq Qnbhjdd n} }hj jkm l` hjq `qjrhonk yjnq n} blddjgj+ Wj hnm ezr} `ikirhjm dlnmikg hjq ajdlkgikgr whjk I rsl}}jm n sidj l` sikj = x =r nkm rzbh ik n kjnqay mzosr}jq+ mzosr}jq+ —Whn}’r ndd }hn} wllm<‟ I nrfjm hjq+ —]hjy’qj/ldm/dl`}r/`qlo/sjlsdj’r/mlqo/qllor$/ Mnm$/}hjy’qj/}qnrh/klw/ik/}hj/mzosr}jq/sdjnrj/ dj}’r/gl.‟ rhj rnim$ rikfikg n di}}dj ik hjq rjn}+ Hjq `qijkmr nkm bdnrron}jr wjqj ndd nqlzkm$ nkm I rzm/ mjkdy qjndiujm }hn} }hir wnr n sjq`jb} lsslq}zki}y }l mjolkr}qn}j oy blkbjqk `lq }hj jkpiqlkojk}+
I
Wlzdmk’} rhj aj sqlzm. —Dj}’r gl }nfj n dllf+ ]hjy jpjk hnpj n azkbh l` bnqqingj ald}r wi}h }hjo. I blzdm onfj n }qjn/ mdj dn}hj `qlo ndd }hir.‟ —I}’r/}qnrh/ik/n/mzosr}jq$/Mnm$/dj}’r/gl/klw —I}’r/}qnrh/ik/n/mzosr}jq $/Mnm$/dj}’r/gl/klw++ Sdjnrj.‟ rhj rnim$ szddikg n rwjn}rhiq} lpjq hjq `nbj nkm rikfikg jpjk dlwjq+ I gzjrr }hj rzk wnr al}h/ jqikg hjq+ —Bloj lk. Dj}’r rhlw jpjqylkj hlw wj mlk’} dj} wllm gl }l wnr}j.‟ I rnim nr I bdioajm zs ik}l }hj mzosr}jq nkm ajgnk szddikg ldm siuun alxjr l`` }hj }ioajqr+ Whn} n }qjnrzqj. Nkm ajr} l` ndd$
ay Qly Zkmjqhidd h r i q q n S d N y a l } l h S
Qly Zkmjqhidd ir }hj hlr} l` }hj }jdjpirilk rjqijr$ !]hj Wllmwqigh}'r Rhls$! klw bjdjaqn}ikg hir }wjk}ij}h yjnq l` rzapjqripj wllmwlqfikg lk szadib ]P+ ]P+ Hj ir }hj nz}hlq l` `ipj allfr lk }qnmi}ilknd wllmwlqfikg$ nkm `lq }jk yjnqr hj wnr onr}jq hlzrjwqigh} n} Bldlkind Widdinorazqg+ Hj }qnpjdr jx}jkripjdy$ }jnbhikg nkm r}zmyikg }hj }jbhkldlgy l` }hj sqj/ikmzr}qind jqn+
Rbhjmzdj l` On}jqindr ‡ @ll} Slwjqjm Dn}hj
Mqipj bjk}jq
Mjnm bjk}jq
Miojkrilkr ] W D On}jqind Djgr 2> ⁍ 1! x 2> ⁍ 1! x 23> ⁍ 1!% Sikj @ll} >> ⁍ 1! x 2> ⁍ 1! x 19> ⁍ 1! Sikj @jj} 2> ⁍ 1! x 2> ⁍ 1! x 19> ⁍ 1! Sikj R}qj}bhjqr >> ⁍ 1! x 2> ⁍ 1! x =3! Sikj Dn}hj ajm qnidr >> ⁍ 1! x 2> ⁍ 1! x =3! Sikj Aq A qnbjr >> ⁍ 1! x 2> ⁍ 1! x 2=> ⁍ 8!% Sikj Hjnmr}lbf qjnq >> ⁍ 1! x 2> ⁍ 1! x 20!% Sikj Hjnmr}lbf `qlk} >> ⁍ 1! x 2> ⁍ 1! x >>> ⁍ 1! Sikj Hjnmr}lbf szddjy 12 ⁍ 8! min+ x 2! Sikj ]nidr}lbf 2> ⁍ 1! x 2> ⁍ 1! x >1! Sikj 7 ⁍ > ]nidr}lbf wjmgj Sikj 8! x > ⁍ 8! x 0! 2 ⁍ 2 ]lld qjr} Sikj =! x 2 ⁍ 8! x 0! 2 ⁍ ]lld qjr} anrj Sikj =! x =! x 8! Gzimj adlbf 1> ⁍ 1! x 1> ⁍ 1! x 2> ⁍ =! Sikj 2 ⁍ > > Dlbfikg snkjd Sikj =! x 1 ⁍ 1! x : ⁍ 1! 2 ⁍ > ⁍ > @dywhjjd Sikj =! x 7 1! x 11 ⁍ 1! @dywhjjd >> ⁍ 1! x 7> ⁍ 1! x 11> ⁍ 1! Sikj 2 ⁍ > ]ij qlm Sikj =! x > ⁍ 1! x >2! 2 ⁍ > ]qjnmdj Sikj =! x 2 ⁍ 1! x 19! Blkkjb}ikg rsnbjq 2 ⁍ =! x >> ⁍ 1! x >> ⁍ 1! Sikj
Rhn`} dlbfr ik szddjy
Kl+ D} D }q+ I}jo
1 N > A 1 B 1 M 1 J 1 @ > G > H > I > E > F > D > O > K > L 0 S 2 ^ > Q > R > ] %Djkg}h ikbdzmjr }jklkr+ Eigrnw > Z > P > W > X 1 Y > U > NN > AA
]nadj @qlk} aqnbj Anbf aqnbj Al}}lo qnid Nqor Nqon}zqj dikf Ikmjx ad adlbf Dlbfikg snkjd
0! x >, =! ald}
D
E
O F L
K
G N
J 0! x 2,8! bnqqingj ald}
J ^ Rhn`} dlbfr lk rhn`}
] S
Sikj Sikj Sikj Sikj Lnf Sikj Sikj Sikj
Hnqmwnqj Dn}hj =/ > ⁍ 1! r}ls blddnqr =/ > ⁍ 1! }hqzr} ajnqikgr >/ > ⁍ 1! `jkmjq wnrhjq >/ > ⁍ 1! x 20! r}jjd qlm (nxdj$ mqipj & mjnm bjk}jq$ bjk}jq$ bqnkf) 0/ ">1 x =! wllm rbqjwr `lq n}}nbhikg r}qj}bhjqr }l `jj} =/ 0! x 2 ⁍ 8! bnqqingj ald}r$ kz}r nkm wnrhjqr wnrhjqr 1/ 2! x 2 ⁍ 8! bnqqingj ald}r blkkjb} }ij qlm$ whjjd nkm }qjnmdj >/ 2! !]! hikgj `lq }qjnmdj Eigrnw 1/ 2> ⁍ 1! x 2 ⁍ =! jyj min+ x 2 ⁍ >0 }hqjnm$ jyj ald}r >0! }hqjnm$jyj 2 ⁍ > ⁍ >/ >0 }hqjnm x 1 8! }zqkazbfdj >0! }hqjnm 1/ > ⁍ 1! aqlkuj rdjjpj ajnqikg (rnwk ik}l }wl > ⁍ 1! djkg}hr) 1/ >> ⁍ 1! djkg}hr l` > ⁍ 1! rhn`} 1/ Blsikg rnw jkmr >/ 0! x > ⁍ =! ald}$ wikg kz} nkm wnrhjqr `lq olzk}ikg rnw+ rnw+ >/ 2> ⁍ 1! ojkmikg sdn}j > > ⁍ 1! }hqzr} ajnqikg
Ajnqikgr ik hjnmr}lbf
H
N 2 ⁍ =! x 9! x 12! >> ⁍ 1! x 1! x >>> ⁍ 1! >> ⁍ 1! x 1> ⁍ =! x >8! >> ⁍ 1! x 2! x 11! > ⁍ 1! x 1! x 11! 2 ⁍ > > =! x > ⁍ =! x = ⁍ =! 2 ⁍ > ⁍ > =! x 1 1! x 1 ⁍ 1! 2 ⁍ > ⁍ > =! x 1 1! x : ⁍ 1!
I
S
S
@
R B
whjk I hnm `ikirhjm dlnm/ ikg }hj }ioajqr$ I dllfjm n} Qnbhjdd nkm rnw }hn} hjq sqimj ik hjq ldm onk hnm olpjm hjq }l }jnqr. Rloj}iojr jpjk I ml }hikgr qigh}+ ]hj @qnoj nkm }hj @dywhjjd ]hj rndpngjm }ioajq wnr sjq`jb} `lq oy kjw }qjnmdj dn}hj mjrigk+ ]hir kjw dn}hj wlzdm aj ozbh riosdjq }hnk oy ldm lkj$ zrikg nk —ikalnqm‟ `dywhjjd wi}h }hj blk/ kjb}ikg qlm n}}nbhjm }l i}r `nbj$ qn}hjq }hnk
]hj `qnoj ir }hj jnrijr} snq} l` }hj onbhikj+ Jrrjk}inddy }hj `qnoj ir }hqjj D/rhnsjm `qnojr$ }wl 1x= anrj sdn}jr nkm }wl 1x= aqnbjr+]hj }wl lz}rimj `qnojr nqj onmj `qlo }wl =x= slr}r$ nkm lkj 1x= wi}h }jklkr n} al}h al}h jkmr+]hj }ls l` }hj zsqigh} =x= ir qnaaj}jm lk al}h rimjr }l `lqo nk lsjk aqimdj elik} wi}h }hj }ls aqnbjr+ ]hj `dywhjjd `qnoj ir onmj l` 1x=r+
Rhn`}
^
Q
A !]!,r}qns hikgj
M
}l n bqnkfrhn`} }hn} wnr mi``ibzd} }l onfj nkm hnqm }l qjsniq+ I} wlzdm ndrl hnpj n eig/ rnw n}}nbhojk} nkm$ olr} ioslq}nk}$ wlzdm aj n wllmwlqfikg }lld }hn} fimr blzdm onfj `lq }hjorjdpjr+ Nr I wnr }l aj }hj sqionqy fim zrikg }hir dn}hj$ i} hnm }l bloj nsnq} nkm sn bf zs rondd jklzgh `lq jnry }qnpjd+ ]hj `qnoj l` oy dn}hj ir lkdy =3! dlkg `lq }wl qjn/ rlkr+ @iqr}$ }hjrj djkg}hr nqj jnrijq }l snbf whjk }qnpjdikg$ rjblkm$ }hj rbnpjkgjm 1 x =r wjqj 83! dlkg+ Ylz bnk bjq}nikdy onfj o nfj i} nr }ndd nkm nr dlkg nr ylz wnk}$ }hj lkdy jrrjk}ind ir n bdjnq sn}h `lq }hj mqipj ajd} aj}wjjk }hj `dywhjjd nkm }hj mqipjk szd/ djy+ I ndrl zrjm olq}irj/nkm/}jklk elik}r }l blkkjb} }hj }hqjj D/rhnsjm `qnojr nkm }hjiq aqnbjr rl I blzdm ~zibfdy fklbf }hjo nsnq}+ ]hjy blzdm ezr} nr jnridy aj blk/
m q n z } R o i E y a r k l i } n q } r z d d I
I }qioojm }hj bjk}jq l` }hj `dywhjjd rnkmwibh }l n bdlrj lb}nglk$ }hjk n}}nbhjm lkj rimj nkm blk}ikzjm }l rhnsj }hj }wl sijbjr+ I }hjk n}}nbhjm }hj l}hjq rimj nkm wlqfjm }hj whldj `dywhjjd }l i}r zd}ion}j qlzkm rhnsj+
Ajikg n `iqo ajdijpjq ajdijpjq ik hnkmy rbqnsr$ I wnr nadj }l zrj }wl `ndd/l`` sijbj }l hjds oj r~znqj zs }hj rhn`} }l }hj whjjd$}hjk whjjd$ }hjk onqf }hj ajnqikg dlbn}ilk lk }hj whjjd+
kjb}jm wi}h rbqjwr lq ald}r nkm n}}nbhjm sjqonkjk}dy+ Ik }hj snr}$ I hnpj onmj dn}hj `dywhjjdr
difj wnglk whjjdr$ wi}h hzar$ rslfjr$ `jd/ dlwr nkm rzbh+ Nd}hlzgh }hjy dllf kibj$ }hjy wlqf kl aj}}jq }hnk }hir rnkmwibhjm mirb onmj `qlo > x 8 nkm 1 x 8 sikj+ Rikbj n `ikirhjm —jigh}/ikbh‟ alnqm ir 7 > ⁍ 1! wimj$ }hqjj l` }hjo dnim rimj ay rimj widd gipj ylz n 11 11> ⁍ 1!/wimj }l}nd+ Ajbnzrj }hir ir nr wimj
Rzssdijr
Ajnqikg Mir}qiaz}lqr Ikb+ :>2/70>/3800 : ‡ Hjio rjndjm ajnqikgr$ ajnqikgr$ i}jo " Q@8/>8/>1SS$ -8+:3 jnbh+
]lld qjr}
Gqnikgjq www+Gqnikgjq www+ Gqnikgjq+blo$ +blo$ lq bhjbf shlkj allf `lq dlbnd aqnkbh =/ Rhn`} blddnqr$ blddnqr$ I}jo " 1X:08$ >+98,sfg+l` >+98,s fg+l` 2+
Ajnqikgr ikrj} ik}l al}h rimjr l` hjnmr}lbf
> >,1! >, =! 2!
R}ls blddnqr ikrj} ik}l szddjy
2, =!
}lld qjr} anrj `lq rjbzqikg wi}h > ald} nkm wikgkz} 1 ,1! 1 2, =! mjnm bjk}jq
=!
2 2,8!
2
: >,1!
BD =!
: >,1!
BD
0!
>,1!
0 >,1! > 1 >,1! ,1!
BD =!
> >,1!
Qlsj
1 >,1!
Ajnqikgr 7 ,8! ikrj} ik}l whjjd > >,8! x 7 ,8! hldj ik }nidr}lbf$ R}ls >,8! nalpj blddnq al}}lo jmgj l` qnidr+ ]nsjq }l >! lk l}hjq rimj
: >,1!
2, =!
> >,8!
2 >,1!
2!
BD
> >,1! BD =!
>, =!
2, =!
2, =!
R}ls blddnq
]nidr}lbf 2 2,8! 2, =!
2,8! x :! rdl} ik
>,1!x
0!
8! 7 >, =!
nr ylz bnk gj}$ }hn} gipjr ylz }hj minoj/ }jq l` }hj whjjd$ nkm }hj djkg}hr ylz’dd kjjm `lq }hj kikj alnqmr l` }hj rnkmwibh+ ]hj `dywhjjd hnr }l aj hjnpy rl i} widd r}lqj jkjqgy$ nkm andnkbjm rl i} wlk’} rhnfj }hj dn}hj nalz} nr i} rsikr+ N 2!/}hibf rldim mirb l` jpjk }hj digh}jr} sikj widd aj hjnpy jklzgh$ rl sz} ylzq jkjqgy ik}l gj }}ikg }hj whjjd andnkbjm+ I` ylz hnpj nky alnqmr }hn} nqj hjnpijq }hnk }hj l}hjqr$ }qy }l mir/ }qiaz}j }hjo ik }hj rnkmwibh }l bqjn}j nk jpjk andnkbj nqlzkm }hj bjk}jq+ Sny n}/ }jk}ilk n} }hir slik} nkm ylz wlk’} hnpj }l n}}nbh nky wjigh}r dn}jq lk+ R}nq} wi}h }hj }hqjj 1 x 8r }hn} widd aj }hj `iddikg l` ylzq alnqm rnkmwibh$ rnw/ ikg }hjo }l djkg}h nkm }hjk nrrjoadikg }hjo rimj ay rimj ik}l n 11> ⁍ 1! r~znqj+ @ikm }hj bjk}jq l` }hj r~znqj ay blkkjb}ikg ls/ slri}j blqkjqr wi}h ik}jqrjb}ikg minglknd dikjr nkm }hjk mqnw }hj dnqgjr} biqbdj ylz bnk `i} ik }hj r~znqj zrikg }qnoojd slik}r lq n r}ibf wi}h hldjr ik i}+ I zrjm n
: >,1! 1> >,1! min+ dnoikn}jm `qlo 2, =! x 7 >,1! nkm > >,1!x 7 >,1! alnqmr
12 >,1! 27 >,1!
12 >,1! 27 >,1!
> >,1! 2 >,1! > >,1!
2, =!
2 >,1! =!
Jdjpn}ilk
> >,1!
10! =3!
2 >,1!
2 >,1!
2, =!
2 >,1! > >,1! 2 >,1!
Sql`idj
11 >,1! 19 >,1!
2 >,1!
!]! hikgj rjbzqjr sjmnd
]hj blkkjb}ikg qlm ir n}}nbhjm }l }hj }qjnmdj ay n dng ald} rbqjwjm ik}l }hj }qjnmdj rimj+]hj lsslri}j jkm l` }hj blkkjb}ikg qlm qimjr lk n 2 ⁍ 8! dng ald} rbqjwjm }hqlzgh n rondd adlbf (}l nddlw bdjnqnkbj lpjq }hj r}ls blddnq) ik}l }hj `dywhjjd+
Eigrnw Bqnkfrhn`} Nssqlxion}jdy >>! dlkg eigrnw bqnkfrhn`} wi}h >! l``rj} }l qjsdnbj dn}hj mqipj bjk}jq >,1! >! BD Bnqpi kg }hj gqllpj ik }hj `dywhjjd `lq }hj qlsj }nfjr n di}}dj }ioj$ az} }hj bhnkgjr ik jkm/gqnik miqjb/ Bnqpikg }ilk onfjr bnqpikg jnrijq }hnk }zqkikg+
}hik/adnmjm }zqkikg rnw }l bz} }hj b iq/ bdj$ az} ylz bnk ndrl onfj n rjqijr l` bdlrj bz}r wi}h n qjgzdnq snkjd rnw nkm }hjk bhir/ jd nkm rhnpj mlwk }l }hj dikj+ Ajbnzrj jnbh l` }hj }hqjj dnyjqr ik }hj `dywhjjd widd aj l``rj} 03 mjgqjjr `qlo }hj l}hjqr$ }hj gqnik lk }hj jmgj l` }hj nr/ rjoadjm whjjd ir glikg }l aj hjnmjm jpjqy whibh wny nkm blosdibn}j roll}hikg wi}h sqlsjq jmgj }lldr+ ]hjqj`lqj$ I zqgj ylz }l aqikg }hj oimmdj dnyjq l` }hj rnkmwibh }qzj }l n biqbdj aj`lqj n}}nbhikg nk lz}jq dnyjq wi}h rdn}hjqr l` gdzj nkm `ikirhikg knidr+ Ylz bnk }hjk aqikg }hj lz}jq dnyjqr }qzj }l }hj ikkjq biqbdj wi}h n oikiozo l` bzqr/ ikg+
Olzk}i kg nkm Olzk}ikg n km ]qzikg Hnpikg }nfjk bnqj }l onfj n andnkbjm whjjd$ ylz kjjm klw }l hnkg i} }qzj lk }hj nxdj+ @ikm }hj bjk}jq bjk}j q l` }hj mirb ay qj/ sjn}jmdy rwikgikg nqbr `qlo }hj lz}rimj jmgj wi}h }hj }qnoojd lq l}hjq r}ibf ylz zrjm }l mqnw }hj lqigiknd minoj}jq+ minoj}jq+ ]hj bjk}jq l` }hjrj nqbr ir }hj bjk}jq l` ylzq whjjd+ I zrjm }wl bhjns }hqzr} andd ajnq/ ikgr ik }hj whjjd$ ndigkjm nr `lddlwr5 ‡ Rj} nk jxsnkripj ai} rl }hn} i} widd
alqj n rkzg hldj `lq }hj ajnqikg ylz ik/ }jkm }l zrj$ }jr}ikg i} lk n rbqns sijbj }l aj rzqj+ Alqj ik}l }hj bjk}jq onqf ezr} mjjs jklzgh }l ikrj} }hj ajnqikg+ ‡ Klw gj} n 9 ⁍ >0 >0 ! nzgjq nkm alqj }hj qjr} l` }hj wny }hqlzgh }hj whjjd+ whjj d+ (Nr nd/ wnyr$ i}’r n dl} jnrijq }l alqj }hj dnqgjq mi/ noj}jq hldj `iqr} nkm }hjk bjk}jq }hj rondd/ jq hldj wi}hik i} }hnk i} ir }l qjpjqrj }hj sqlbjrr+) ]hj laejb} klw ir }l ikrj} }hj rjblkm ajnqikg lk }hj lsslri}j `nbj rl }hn} }hj whjjd widd kl} wlaadj lk }hj rhn`}+ Jnry5 ‡ Ikrjq} }hj `iqr} ajnqikg ik i}r rlbfj} nkm rdimj n djkg}h l` }hj > ⁍ 1! rhn`}ikg }hqlzgh i}+ ‡ Dny }hj whjjd wi}h }hir `iqr} ajnqikg/ rimj mlwk+ Rdis }hj rjblkm ajnqikg lpjq }hj rhn`} rl i} rdimjr mlwk lk}l }hj zssjq `nbj+ ‡ Ajbnzrj }hj 9 ⁍ >0 >0 ! hldj jx}jkmikg }hqlzgh }hj whjjd ir dnqgjq }hnk }hj rhn`}$ ylz hnpj jklzgh sdny }l szrh }hj rhn`} ik}l n sqjbirjdy r~znqj qjdn}ilkrhis wi}h }hj `nbj l` }hj whjjd+ Bhjbf ndd nqlzkm }hj nxdj rhn`} wi}h rjpjqnd r~znqjr n} lkbj$ nkm whjk ylz hnpj i} ezr} qigh}$ bnqj`zddy }qnbj nqlzkm }hj rjblkm ajnqikg+
7 >,1!
1 >,1!
‡ Qjolpj }hj ajnqikg nkm }hj rhn`} nkm bnqpj lz} }hj rlbfj} `lq }hj ajnqikg wi}h glzgjr nkm bhirjdr+ Jpjk i` ylz `ikm ylz nqj n di}}dj lz} l` r~znqj$ ylz bnk blq/ qjb} }hj on}}jq wi}h rhior nkm rbqjwr nqlzkm }hj rimjr l` }hj ajnqikg+ Wi}h }hj whjjd klw qzkkikg lk i}r rhn`}$ ylz bnk `zq}hjq andnkbj nkm }qzj i} ay hldmikg }hj rhn`} ik n pirj nkm rsikkikg }hj whjjd+ I} mljrk’} kjjm }l rsik difj }hj whjjd lk n qnbikg aifj$ ezr} rl i} mljrk’} wlaadj nkm rhnfj olqj }hnk ylz ml+ I zrjm }hj }wl }jj}h l` n olq}irikg gnzgj }l dny lz} }hj 2 ⁍ 8! gqllpj `lq }hj mqipj blqm }hn} gljr ndd }hj wny nqlzkm }hj whjjd+ Ik }hj/ lqy$ ylz blzdm }zqk }hir gqllpj ik}l }hj sj/ sj / qishjqy l` }hj whjjd nr i} rsikr$ az} blk/ rimjqikg }hj gqnik bhnkgjr$ ylz’qj aj}}jq l`` bnqpikg+ ]hj `iknd `ikngdikg wi}h }hj whjjd ikpldpjr olzk}ikg i} r~znqjdy lk }hj anbf aqnbjr l` }hj dn}hj+ Ngnik$ }hj `nr}jr} wny }l gj} i} r~znqj ir }l alqj }hj `iqr} hldj }hqlzgh }hj ikkjqolr} aqnbj$ rj} }hj dlkg rhn`} ik}l }hir hldj$ olzk} }hj whjjd nkm }hjk szrh nkm szdd }hj rhn`} zk}id }hj whjjd ir hnkgikg wi}h j~znd bdjnqnkbj ndd nqlzkm+ Whjk }hj rhn`} ir ik }hj qigh} slri}ilk$
]hj }wl jkmr l` }hj qlsj ajd} nqj az}}/rsdibjm ay rjwikg anbf nkm `lq}h aj}wjjk }hj }wl sijbjr+ sijbjr+ I} lkdy }nfjr n oikz}j lq }wl wi}h nk zshldr}jqy kjjmdj+Wi}h }ioj nkm zrj }hj qlsj widd r}qj}bh nkm ylz’dd kjjm }l bz} nkm qj/rsdibj }hj qlsj+
ronbf }hj jkm wi}h n hnoojq }l djnpj n }hj bjk}jq l` lkj jkm nkm alqj n sqjbirj onqf lk }hj ikrimj `nbj l` }hj rjblkm$ lz}jq ikrj} `lq n r}ls blddnq ik}l }hj jkm gqnik+ aqnbj }l rhlw whjqj ylz kjjm kj jm }l alqj }hj Klw rj} n 9 ⁍ >0 >0! nzgjq ik }hj bjk}jq l` }hir rjblkm hldj+ @iknddy$ sz} n aig `jkmjq wnrh/ hldj nkm alqj }hqlzgh }l }hj l}hjq jkm$ jq aj}wjjk }hj whjjd nkm }hj `qnoj nkm n km r}lssikg ezr} nr }hj jkm l` }hj djnm rbqjw r}ls blddnqr lk }hj jkmr l` }hj rhn`}+ sjjfr lz}+ Zrikg }hir slik} }l bjk}jq }hj L` blzqrj }hj whjjd mljrk’} ml ozbh nzgjq$ alqj }hj ikrj} `lq }hj rjblkm r}ls wi}hlz} }hj }qjnmdj nkm blkkjb}ikg qlm+ blddnq ik}l }hj `nq jkm+ ]hj }qjnmdj riosdy n}}nbhjr }l }hj `qnoj ]hj szddjy ir r}idd ezr} n r~znqj adlbf n} wi}h n ]/hikgj ]/hikgj n} }hj anbf$ nkm }hj blk/ }hir slik} ” kl} ozbh gllm+ Sz} }hj }h j r}ls kjb}ikg qlm qimjr lk n dng ald} rj} ik}l i}r blddnqr ik sdnbj nkm olzk} }hj adlbf aj/ rimj$ wi}h }hj lsslri}j jkm n}}nbhjm n}}nbh jm }l }hj }wjjk }hj hjnmr}lbf ajnqikgr+ Hldm n sjk/ `dywhjjd+ Nmezr}ikg }hj n}}nbhojk} slik}r bid ik sdnbj lk }hj jkm gqnik }l mqnw n 12 ⁍ =!/ l` }hj }ij qlm }l }hj `dywhjjd nkm nk m }hj }qjn/ minoj}jq biqbdj lk jnbh jkm+ Yl Ylz z bnk }hjk mdj widd snq}inddy mj}jqoikj }hj —ojbhnk/ qjolpj }hj adlbf nkm bhirjd mlwk }l }hjrj ibnd nmpnk}ngj‟ (hlw high ylz hnpj }l di`} dikjr ” nrrzqjm }hn} ylz hnpj qlzghjm ik ylzq `ll}) l` }hj dn}hj+ N 0! ol}ilk n} }hj n szddjy sqjbirjdy blkbjk}qib }l }hj rhn`}+ jkm l` }hj }qjnmdj rjjor nalz} qigh} `lq (I}’r fikm l` difj rhll}ikg nqqlwr n} }hj rimj olr} wlqf+ l` }hj anqk nkm }hjk snik}ikg }hj }nqgj}r nqlzkm }hjo ” sjq`jb} jpjqy }ioj+) ]hj qlzghjm/ik szddjy ir nalz} }l aj/ Hjnmr}lbf nkm Mqipj Bjk}jq ]hj hjnmr}lbf blkrir}r l` }wl jx}jkrilkr bloj ylzq `iqr} }zqkikg ela+ L` blzqrj }hir l` }hj `qnoj hldmikg ajnqikgr+ ]hjrj ajnq/ ojnkr ylz kjjm n ajd} }l blkkjb} }hj `dy/ ikgr bnk aj aqlkuj lq andd$ az} n} djnr} whjjd }l }hj szddjy$ nkm rhlq} l` n sqlsjq }hj dj`} lkj ozr} aj n }hqzr} ajnqikg$ ojnk/ ai} l` qlzkm djn}hjq ajd}ikg (rzbh nr zrjm ikg i} ir mjrigkjm }l }nfj sqjrrzqj ndlkg }hj lk ldm rjwikg onbhikjr) ylz bnk gj} ay djkg}h l` }hj rhn`} nr wjdd nr jnrikg } hj wi}h > ⁍ =! bl}}lk blqm$ elikjm wi}h n r~znqj rhn`}’r ql}n}ilk+ Ylz `lddlw sqj}}y ozbh fkl} `lq }hj }ioj ajikg+ Riosdy wqns }hj }hj rnoj sqlbjmzqj zrjm }l ndigk }hj ajnq/ ikgr ik }hj `dywhjjd }l onfj rzqj }hj ajnq/ ikgr ik }hj hjnmr}lbf nqj sqlsjqdy dikjm zs+ Zkdifj }hj `dywhjjd$ }hj mqipjk szddjy kjjmr }l n}}nbh `iqody }l i}r rhn`}$ nr wjdd nr ajikg qjnmidy qjolpnadj+ ]hj r}ls bld/ dnqr ikrj} ik}l al}h jkmr l` }hj szddjy ojj} al}h l` }hjrj kjjmr6 }hjiq gqjn}jq minoj/ }jq onfjr n `iqo blkkjb}ilk }l }hj wllm l` }hj szddjy$ nkm }hjiq rj} rbqjwr (qjnbhjm }hqlzgh hldjr mqiddjm }hqlzgh }hj szddjy) nddlw ylz }l qjolpj nkm bhnkgj }hj rhn`} nr kjjmjm+ ]hj wllmjk snq} l` }hj mqipjk szddjy ajgikr nr n 2! rjb}ilk l` sikj = x =+ @ikm ]l rhnqsjk }hj mjnm bjk}jq `lq }hj }nid r}lbf$ I rdissjm }hj anq ik}l }hj mqipj szddjy nkm }igh}/ jkjm i} mlwk wi}h }hj r}ls blddnqr+]hjk i} wnr n riosdj on}}jq l` }zqkikg }hj dn}hj nkm zrikg n `idj }l `lqo }hj slik}+ Kl}j }hj bqlrrjm mqipj blqm lk }hj szddjy whibh ikbqjnrjr }hj blk}nb} lk }hj szddjy$fjjsikg i} `qlo rdissikg mzqikg zrj+
qlsj nqlzkm$ szdd i} rjoi/rkzg nkm }ij i} l``+ R}nq} }qjnmikg nkm }hj qlzghjm ik szd/ djy widd rsik rl }hn} ylz bnk }zqk i} mlwk }l }hj `ikirhjm riuj$ zrikg ylzq qjgzdnq }zqk/ ikg glzgjr nkm nk iosqlpirjm }lld qjr}+ Lkbj ylz gj} n roll}h sdnbj }zqkjm$ r}ls nkm olpj }hj qlsj ik}l }hn} rsl}$ qj}yikg }hj fkl} }igh}jq i` kjbjrrnqy+ kjbj rrnqy+ @iknddy$ }zqk n gqllpj ik }hj oimmdj l` }hj szddjy `lq }hj ajd} }l qimj ik+ Nr wi}h nky dn}hj$ }hj rondd/ jq }hj minoj}jq l` }hj mqipjk szddjy$ }hj highjq }hj rsjjm nkm }hj dlwjq }hj }lq~zj+ Ylz bnk$ l` blzqrj$ ezr} }qjnmdj `nr}jq lq rdlwjq$ nkm ylz bnk jnridy }zqk n} lpjq >$333 qso+ Lkj sjbzdinqi}y l` }hir mjrigk ir }hj bqlrrjm mqipj blqm whibh bqjn}jr }hj nm/ mi}ilknd sjbzdinqi}y l` }hj `dywhjjd glikg ik }hj lsslri}j miqjb}ilk nr }hj mqipjk szd/ djy+ ]hj slik} l` }hir bqlrrikg ir }l ikbqjnrj }hj blk}nb} rzq`nbj aj}wjjk }hj ajd} nkm n km }hj rondd szddjy+ Wi}hlz} }hj bqlrrjm ajd}$
]hj mqipj bjk}jq ir rhlwk hjqj ajikg `lqojm$ wi}h }hj eigrnw bqnkfrhn`} dyikg kjx} }l i}+N`}jq qlzgh rhnsikg$}hj bjk}jq ir `idjm nkm zd}ion}jdy }nfjr lk i}r rsnmj/ai} rhnsj+]hj bjk}jq ir }hjk olzk}jm ik }hj mqipj szddjy ay }igh}jkikg }hj r}ls blddnqr+
lq }hj nmmi}ilk l` nk imdjq szddjy$ }hj mqi/ pjk szddjy wlzdm aj blkr}nk}dy rdissikg+ Ylz bnk `zq}hjq qjmzbj rdissikg ay onf/ ikg }hj qlsj r}ibfy wi}h ezr} nalz} nky/ }hikg blk}nikikg rzgnq+ I zrj onsdj ryqzs wi}h gqjn} rzbbjrr+ Whjk }hj szddjy ir }zqkjm nr roll}h nr ylz kjjm$ `ikirh i} ay `iqr} mqiddikg }hj hldjr }hqlzgh i}r rimjr }l gipj nbbjrr }l }hj rj} rbqjwr ik }hj r}ls blddnqr+ N`}jq }hj hldjr nqj mlkj nkm }jr}jm$ qzk rloj gdzj nqlzkm }hj rjn}r `lq }hj r}ls blddnqr nkm$ wi}h }hj rhn`} ik sdnbj$ rj} }hj r}ls blddnqr anbf ik `lq }hj `iknd }ioj+ Ylz bnk blk/ }ikzj wi}h }hj fkl} ik }hj qlsj }l dj} i} r}qj}bh nkm zk}id ylz gj} nk imjn l` hlw ozbh }jkrilk i} kjjmr+ Jpjk}znddy Jpjk}znddy$$ }hlzgh$ ylz’dd wnk} }l az}}/rsdibj }hj qlsj+
]nidr}lbf nkm Mjnm Bjk}jq Klw `lq }hj rjblk r jblkm m sijbj l` }zqkikg }z qkikg ” }hj mjnm bjk}jq `lq }hj }nid r}lbf+ ]hj mjnm mjn m > ⁍ bjk}jq ir ezr} n rhlq} djkg}h l` }hj 1! rhn`}/ ikg wi}h }hj azrikjrr jkm rhnqsjkjm }l n sqjbirj blkibnd slik}+ ]hj nkgdj l` }hj blkj ir kl} bqi}ibnd$ az} i}r blkbjk}qibi}y ir+ I` }hj slik} ir }hj djnr} ai} dlsrimjm lq
qlzgh$ i} widd ~zibfdy jkdnqgj i}r blk}nb} slik} wi}h }hj wllm ajikg }zqkjm nkm widd aj n blkr}nk} rlzqbj l` }qlzadj+ Rl$ n d/ }hlzgh ylz bnk ~zibfdy qlzgh ik }hj slik} ay `qjjhnkm `idikg$ }hj `iknd rhnsikg kjjmr }l bloj `qlo olzk}ikg i} ik }hj mqipjk szddjy$ (aj`lqj ylz bz} i} ik}l }hj 2! djkg}h }hn} ylz kjjm)$ }igh}jkikg }hj r}ls bld/ dnqr nkm aqikgikg }hj jkm }qzj wi}h ylzq `idj hjdm ngnikr} }hj rsikkikg slik}+ N`}jq
}hir$ ylz’dd aj nadj }l }jdd `ldfr hlw ylzq }qjnmdj dn}hj wlqfr `lq }zqkikg oj}nd nr wjdd+ Wlzdm Wlzd m }hn} }hj mqipj bjk}jq wnr nr jnry+ ]hj mqipj bjk}jq kjjmr }l gqis }hj jkm l` }hj wllm ajikg }zqkjm$ nkm hnr rlojwhn} }hj rhnsj l` n rsnmj ai}+ Hnpikg nkpidr n kpidr nkm `lqgj nalz}$ i} wnr ~zibfjr} `lq oj }l rio/ sdy hjn}$ hnoojq nkm `idj }hj jkm l` }hj rhn`} ik}l rhnsj+ ]hir ony aj }hj olr} nwfwnqm snq} l` }hj dn}hj `lq ylz (fim lq kl}) }l onfj+ Nd}hlzgh ylz bnk bldm hno/ ojq }hj mqipj bjk}jq ik}l rhnsj$ ylz widd kjjm n gllm qjm hjn} }l onfj }hj rhnqsdy ajk} bqnkfrhn`} `lq }hj eigrnw n}}nbhojk}+ Oikionddy$ ylz bnk ml }hj ela ylzqrjd` wi}h n }lqbh$ n hnoojq$ n pirj nkm rloj}hikg }l zrj `lq nk nkpid+ ]hj sn}h l` wirmlo$ hlwjpjq$ ony aj }l rzsslq} ylzq dlbnd adnbfroi}h+ Wi}h }hj mqipj bjk}jq ik sdnbj$ ndd }hn} qjonikr ir }hj }lld qjr}$ whibh bnk aj n `zdd djkg}h anq qjr}ikg lk lz}qiggjqr n}}nbhjm }l }hj hjnm nkm }nid r}lbfr$ lq n ronddjq D/ rhnsjm blkr}qzb}ilk n}}nbhjm ay ald} nkm wikg kz}$ lq al}h+ ]hj }nidr}lbf ir n}}nbhjm wi}h n wjmgj+
]zqkikg Zrikg }hj dn}hj ir ezr} }hj rnoj nr wi}h nky l}hjq ndblhld/slwjqjm j~zisojk}+ Qlzgh ik }hj r}lbf }l nk lb}nglk aj`lqj olzk}/ ikg i} aj}wjjk }hj bjk}jqr$ ajikg rzqj }l qza rloj ajjrwnx ik }hj hldj `lq }hj mjnm
Eigrnw 1 >,=!
>7! BD
>! 2
Y
Z
>!
1!
P 0! 1!
2!
2, =!
2, =!
2!
1! >,1! > 2, =!
BD
2,8!
1
> >,1!
2, =!
U X BD AA >7 2, =! 11!
W
NN 1 2, =!
2, =!
>! >,1!
>!
1! >,1! > 2, =! >8!
1!
0!
0!
> >,1!
> >,1! 2, =!
9! minoj}jq bz} lk }nadj wi}h n 2! qj}zqk anbf }l }hj anbf aqnbj
>
>,1!
2, =!
2, =!
>! >,1!
>8!
]hj ajk} bqnkfrhn`} ir n}}nbhjm }l }hj eigrnw }hqlzgh n hnkgikg nqon}zqj dikf+]hj olzk} ir n}}nbhjm }l }hj eigrnw wi}h n sijbj l` r}jjd r}qnssikg rbqjwjm ik}l n rnw fjq` ik }hj olzk}$ nkm n}}nbhjm dllrjdy }l }hj dlwjq eigrnw nqo+
Nk D/rhnsjm D/rhnsjm }lld }lld qjr} ir rhlwk rhlwk hjqj hjqj n}}nbhjm n}}nbhjm ay ald} nkm wikg kz} }l }hj dn}hj `qnoj+]hj }nid/ r}lbf ir ajr} n}}nbhjm wi}h n wjmgj+]hir ir }hj `nr}jr} nkm }hj `iqojr} wny }l olpj nkm olzk} }hj }nidr}lbf+]hj wjmgj gipjr ezr} }hj qigh} —sikbh‟ }l }hj wllm ajikg }zqkjm i` ylz rdigh}dy blbf }hj al}}lo l` }hj }nidr}lbf }lwnqmr }hj bjk}jq aj`lqj }nssikg }hj wjmgj hloj+
bjk}jq+ I` ylzq ajnqikgr nqj }ll bhjns nkm ojk} nalz} —wndfikg nkm bhjwikg gzo n} hnpj rl ozbh sdny ik }hjo }hn} }hj wlqf }hj rnoj }ioj$‟ rl fjjs n `jw rsnqj ald}r bhn}}jqr whjk ylz’qj }zqkikg$ ylz bnk blo/ lk hnkm+ sjkrn}j n ai} ay nmezr}ikg ylzq bz}}ikg r}ydj }l sz} olqj l` n —szrh‟ `qlo qzaaikg }hj Eigrnw ajpjd+ Aqlkuj ajnqikgr ony hnpj djrr sdny Nr i` }hir }qjnmdj dn}hj wjqj kl} blld jklzgh$ }hnk bhjns andd ajnqikgr+ Ylz bnk jpjk klw ylz bnk onfj }hj eigrnw n}}nbhojk} }zqk }hj ajnqikgr rdigh}dy lz} l` r~znqj wi}h }hn} ri}r n}ls i}+ Bzqilzr Bzqilzrdy$ dy$ }hj eigrnw ir an/ }hj rhn`} }l }igh}jk }hjo zs+ ribnddy n wny }l blkpjq} }hj ql}nqy ol}ilk R}idd$ onbhikjr }jkm }l gipj ylz sqla/ l` }hj `dywhjjd nkm szddjy anbf ik}l qjb/ djor n} sdnbjr whjqj ol}ilk bhnkgjr mi/ isqlbn}ikg ol}ilk l` }hj adnmj+ ]hir blk/ qjb}ilk$ difj whjk bnq jkgikjr —}hqlw n pjqrilk qj~ziqjr }hn} ylz dllrjk }hj rj} qlm$‟ }hj blkpjqrilk l` }hj qjbisqlbnd ol/ rbqjwr ik }hj r}ls blddnqr l` }hj mqipjk szd/ }ilk l` ylzq `ll} lk }hj }qjnmdj ik}l }hj djy$ qjolpj }hj mqipj bjk}jq nkm qjsdnbj ql}nqy ol}ilk l` }hj `dywhjjd ir n sl}jk/ i} wi}h n bqnkfrhn`}+ Zkdjrr ylz nqj }ind }qlzadj rsl}+ Ezr} nr n bnq kjjmr nbbz/ Rzsjqonk$ ylz bnkkl} ajkm }hjrj rhnqs qn}j }ioikg$ rl }ll mljr }hj `ll} lsjqn}ikg nkgdjr ik bldm > ⁍ 1! r}jjd rhn`}ikg ” ylz’dd }hj dn}hj kjjm }ioikg$ nr n rzmmjk r}ls ik hnpj }l hjn} i} wi}h n }lqbh }lqb h nkm ajkm i} ik }hj `ll} widd ojj} wi}h blkrimjqnadj qj/ n pirj+ rir}nkbj `qlo }hj `dywhjjd$ rknssikg }hj ]hj `qnoj l` }hj eigrnw ir ~zi}j r}qnigh}/ blkkjb}ilk n} }hj jkm l` }hj }ij qlm+ Ylz `lqwnqm+ I zrjm aig mlpj}nidr `lq }hj `qlk} widd mjpjdls blkrimjqnadj jxsjq}irj wi}h nkm anbf slr}r nr }hj ajr} bloaikn}ilk bloaikn }ilk l` }hir dn}hj$ az} i} ir rl ikpi}ikg `lq l}hjqr }l r}qjkg}h nkm ~zibf mirnrrjoady+ ]hj nqor }qy }hn} ylz widd hnpj n dl} l` ikjxsjqi/ jkbjm `jj} lk i}$ }hjy widd rkns }hj ald}$ nkm jxbzrj }hjorjdpjr ay onfikg n blo/
Eigrnw ]nadj
2! 2, =!
> >,1! 9! 2, =!
9! min+
8 2, =!
>1!
1 >, =!
2!
12! ]hj }zqkazbfdj ir qigh} l`` }hj rhjd`$ wi}h }hj nmmi}ilk l` n dlbf kz} }l lkj l` i}r jyjald}r (lapilzrdy kl} }hj lkj wi}h }hj dj`} hnkm }hqjnmr)+Wi}hlz} }hqjnmr )+Wi}hlz} }hj dlbf kz}$ }hj }zqkazbfdj widd wlqf dllrj ik rjblkmr+ I ndrl ikrj} n aqlkuj > 1! djkg}h) ik}l jnbh l` }hj ajnqikg (rnwk ik}l n ⁍ nqor n} }hjiq sipl} slik}r+]hir ir kl} rl ozbh }l qjmzbj `qib}ilk ik lsjqn}ilk nr i} ir }l fjjs }hj wllm `qlo wjnqikg nkm ngnik dllrjkikg }hj }jkrilk lk }hj adnmj+
l` }hj eigrnw nqj }hj lkdy sijbjr }hn} nqjk’} rbqns sikj6 }hjy nqj rbqns lnf `lq r}qjkg}h+ ]hjy hnpj }l aj r}qlkg ajbnzrj }hj }zqk/ azbfdj n} }hj qjnq ozr} }jkrilk }hj bls/ ikg rnw adnmj n} }hj `qlk}+ I hnpj rjjk onky hlojonmj eigrnwr `qlo }hj snr} bjk}zqy$ nkm jpjqy lkj zrjm zrj m }hj adnmj hldmjqr hldmj qr `qlo nk ldm blsikg rnw rn w+ L`}jk }hj onfjq wlzdm ezr} hnbfrnw l`` }hj nqor l` }hj blsikg rnw nkm ald} }hjo lk}l }hj jkmr l` }hj eigrnw nqor+ ]hir hnr }hj nmpnk}ngj l` nddlwikg ylz }l }zqk }hj adnmj n} qigh} nkgdjr }l }hj nqor whjk kjb/ kj b/ jrrnqy `lq bdjnqnkbj+ I}’r ~zi}j n rsjb}nbdj whjk }hir whldj }hikg ir glikg+ ]hj `dywhjjd dllfr difj rloj}hikg l`` l` @qjm @dik}r}lkj’r @dik}r} lkj’r bnq$ }hj ajnqikgr nqj qn}}dikg$ }hj mqipj qlsj }wnkg/ ikg$ nkm }hj eigrnw ezosikg nr ylzq fkjj gljr zs nkm mlwk+ Az} }hjqj n} }hj azrikjrr jkm$ }hj rnw bz}r ndlkg ajnz}i`zddy$ }hj dn}hj }zqkr difj n }ls+ Wlk’} }hj fimr aj sqlzm. SW
