DIFUSI-OSMOSIS DAN PENYERAPAN ZAT

CBVETBO VTBAXJAPM GJYJECEKJ XPMDPNBO „HJGPYJ ’ EYMEYJY HBO V@OZ@TBVBO \BX‚

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NBCBMBO V@OK@YBNBO VTBAXJAPM HJGPYJ HJGPYJ ’  ’ EYMEYJY HBO V@OZ@TBVBO \BX

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Xbohb Xbokbo

M`kb Ibnbzb Cjoxbok Xjmpt

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HJGPYJ ’ EYMEYJY HBO V@OZ@TBVBO \BX A`kjbxbo 2 „HBVBXABN BJT D@T-EYMEYJY D@T-EYMEYJY M@O@MDPY M@MDTBO Y@C LBTJOKBO XPMDPNBO‚

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Xplpbo Vtbaxjapm Y`x`cbn m`cbapabo v`tiedbbo hbvbx<

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2/

M`o`mpabo gbaxb m`ok`obj k`lbcb hjgpyj-eymeyjy/

4/

M`okbmbxj `g`a aeoy`oxtbyj cbtpxbo x`tnbhbv a`i`vbxbo hjgpyj/

9/

M`opolpaabo btbn k`tbabo bjt vbhb v`tjyxj{b hjgpyj-eymeyjy/

8/

M`oh`yatjvyjabo v`ok`txjbo hjgpyj hbo eymeyjy/

Abljbo Vpyxbab  Bjt

m`tpvbabo aemveo`o pxbmb hbcbm xpmdpnbo# hjmbob bjt 

m`ozpypo 76-:6% hbtj d`tbx hbpo/ Lpmcbn bjt zbok hjabohpok xjbv xbobmbo d`td`hb-d`hb# nbc joj d`tkboxpok vbhb nbdjxbx hbo l`ojy yv`yj`y xpmdpnbo x`ty`dpx/ Xpmdpnbo n`tdb c`djn dbozba m`okbohpok bjt hbtjvbhb xpmdpnbo v`thp/ Xpmdpnbo zbok d`thbpo x`dbc m`mvpozbj abhbt bjt boxbtb >0-:6 %# xpmdpnbo njhtegja >0-:> % hbo xpmdpnbo m`yegjc m`mvpozbj abhbt bjt boxbtb 266-966 %/ V`oxjokozb bjt y`dbkbj v`cbtpx hbcbm etkbojym` njhpv xbmvba bmbx  l`cby# mjybcozb vbhb vtey`y eymeyjy/ Hbcbm ypbxp hbpo# wecpm` y`c hjdbxbyj ec`n

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vtey`y zbok ybokbx aemvc`a# mpcbj hbtj v`okbmdjcbo bjt hbo mjo`tbc xbobn# v`obokabvbo ibnbzb mbxbnbtj# v`oz`tbvbo kby-kby# yjox`yjy kcpaeyb hbo `o`tkj# njokkb v`ok`hbtbo nbyjc gexeyjox`yjy/ Xpmdpnbo m`okbmdjc bjt hbo mjo`tbc xbobn hbcbm d`oxpa x`tcbtpx hbcbm bjt xbobn# poxpa m`oz`tbvozb# |bx|bx x`ty`dpx nbtpy m`o`mdpy hjohjok y`c`axjg v`tm`bd`c/ Hjohjok y`c x`dbc obmpo dbozba x`thbvbx vetj-vetj bxbp tpbok-tpbok hbo mphbn hjcbcpj cbtpxbo xbobn hbo kby-kby# y`njokkb xjhba m`ojmdpcabo mbybcbn poxpa v`oz`tbvbo/ Y`dbcjaozb# m`mdtbo y`c zbok cjve-vtex`jo# nbozb m`mjcjaj vetj zbok c`mdpx hbo d`tmpbxbo# y`njokkb xjhba y`xjbv |bx h`okbo mphbn m`c`{bxjozb/ V`tm`bdjcjxby m`mdtbo x`tnbhbv jeo-jeo bhbcbn vbcjok t`ohbn/ H`okbo abxb cbjo# jeo-jeo ypcjx m`o`mdpy m`mdtbo# mbab v`oz`tbvboozb vpo vbcjok ypcjx/ X`tabjx h`okbo v`oz`tbvbo |bx joj#

2/

Hjgpyj Hjgpyj bhbcbn v`tjyxj{b m`okbcjtozb bxbp d`tvjohbnozb ypbxp |bx hbcbm v`cbtpx hbtj dbkjbo d`taeoy`oxtbyj d`taeoy`oxtbyj xjokkj a` dbkjbo zbok d`taeoy`oxtbyj t`ohbn abt`ob `o`tkj ajo`xjaozb y`ohjtj ybmvbj x`tlbhj a`y`jmdbokbo hjobmjy/ Ieoxen zbok y`h`tnbob bhbcbn v`md`tjbo kpcb vbhb ibjtbo x`n xb{bt/ Cbmdbx cbpo ibjtbo m`olbhj mbojy/ Ieoxen cbjo bhbcbn pbv bjt hbtj bjt  hbtj i`t`a zbok d`thjgpyj hbcbm phbtb/Hjgpyj phbtb/Hjgpyj zbok vbcjok y`tjok x`tlbhj bhbcbn hjgpyj mec`apc`t/ Hjgpyj joj x`tlbhj ljab x`td`oxpa v`tvjohbnbo hbtj y`dpbn cbvjybo .cbz`t* mec`apc zbok hjbm hbtj yecjh bxbp gcpjhb/ Hjgpyj

m`cbcpj

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m`abojym`# zbjxp hjgpyj y`h`tnbob .yjmvc` hjgpyjeo*#hjgpyj m`cbcpj ybcptbo zbok x`td`oxpa ec`n vtex`jo xtboym`mdtbo .yjmvc` hjgpyjeo dz inbo`c getm`h*# hbo hjgpyj hjgbyjcjxbyj .gbyjcjbx`h .g byjcjbx`h hjgpyjeo*/ Hjgpyj m`cbcpj m`mdtbo` d`tcbokypok abt`ob mec`apc -mec`apc zbok d`tvjohbn bxbp d`tk`tba m`cbcpj m`mdtbo d`tyjgbx cbtpx hbcbm c`mba .cjvjh* y`njokkb hbvbx m`o`mdpy cjvjh djcbz`t vbhb m`mdtbo y`ibtb cbokypok/ cbokypok/ M`mdtbo y`c v`tm`bd`c v`tm`bd`c x`tnbhbv mec`apc cbtpx c`mba y`v`txj netmeo yx`tejh# wjxbmjo B# H# @# hbo A y`txb dbnbo-dbnbo etkboja zbok cbtpx hbcbm c`mba# Y`cbjo jxp# m`mdtbo y`c lpkb ybokbx v`tm`bd`c x`tnbhbv mec`apc boetkboja y`v`txj E#IE 4# NE# hbo N4E/

D`d`tbvb mec`apc a`ijc anpypy zbok x`tcbtpx hbcbm y`txb jeo-jeo x`tx`oxp# hbvbx m`o`mdpy m`mdtbo m`cbcpj ybcptbo bxbp inbo`c/ Ybcptbo joj x`td`oxpa hbtj vtex`jo xtboym`mdtbo# y`mbibm vetj h`okbo hjbm`x`t x`tx`oxp zbok m`mpokajoabo mec`apc h`okbo hjbm`x`t c`djn a`ijc hbtj hjbm`x`t vetj x`ty`dpx x `ty`dpx hbvbx m`cbcpjozb/ Y`m`oxbtb jxp# mec`apc  ’ mec`apc d`tpaptbo d`ybt y`v`txj bybm bmjoe# kcpaeyb# hbo d`d`tbvb kbtbm ’kbtbm  ’kbtbm mjo`tbc # xjhba hbvbx m`o`mdpy m`mdtbo` y`ibtb cbokypok# x`xbvj m`m`tcpabo vtex`jo v`mdb{b bxbp xtboyvetx`t poxpa hbvbx m`o`mdpy m`mdtbo`/ Vtey`y mbypaozb mec`apc d`ybt zbok m`cjdbxabo xtboygetx`t hjobmbabo hjgpyj hjgbyjcjxbyj# zbjxp v`cbcpbo |bx m`cbcpj to`mdtbo vcbytob zbok m`cjdbxabo vtex`jo v`mdb{b bxbp vtex`jo xtboygetx`t/ Vtex`jo xtboyvetx`t x`tkeceok vtex`jo xtboym`mdtbo zbok m`mcjaj x`mvbx v`tc`abxbo x`tnbhbv jeo bxbp mec`apc wbok babo hjxtboyg`t a` hbcbm y`c/ Y`xjbv mec`apc bxbp jeo m`mjcjaj vtex`jo xtboygetx`t zbok anpypy# mjybcozb poxpa v`cbcpbo ypbxp mec`apc kcpaeyb hjv`tcpabo vtex`jo xtboygetx`t zbok anpypy poxpa m`oxtboyg`t kcpaeyb a` hbcbm y`c/ 4/

Eymeyjy Eymeyjy bhbcbn vtey`y v`tvjohbnbo bxbp v`tk`tbabo mec`apc |bx v`cbtpx# hbtj cbtpxbo zbok aeoy`oxtbyj |bx v`cbtpxozb xjokkj m`oplp cbtpxbo zbok aeoy`oxtbyj |bx v`cbtpxzb t`ohbn m`cbcpj y`cbvpx bxbp m`mdtbo y`c`axjg v`tm`bd`c bxbp y`mj v`tm`bd`c/ Ljab hj hbcbm ypbxp d`lbob zbok hjvjybnabo ec`n y`cbvpx y`mjv`tmjbd`c# ljab hbcbm ypbxp d`lbob zbok hjvjybnabo ec`n y`cbvpx y`mjv`tmjbd`c hjx`mvbxabo hpb Jbtpxbo kcpaeyb zbok x`thjtj bxby bjt y`dbkbj v`cbtpx hbo kcpaeyb y`dbkbj |bx x`tcbtpx h`okbo aeoy`oxtbyj zbok d`td`hb hbo hjvjybnabo ec`n

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hjdbohjokabo h`okbo cbtpxbo hj hbcbm y`c hjabxbabo /y`dbkbj cbtpxbo njv`txeojy/ y`hbokabo cbtpxbo zbok aeoy`oxtbyjozb ybmb h`okbo cbtpxbo hj hbcbm y`c hjy`dpx cbtpxbo jyexeojy/ Ljab cbtpxbo zbok x`thbvbx hj cpbt y`c# aeoy`oxtbyj |bx x`tcbtpxozb c`djn t`ohbn hbtjvbhb hj hbcbm y`c hjabxbabo y`dbkbj cbtpxbo njvexeojy Hpb gbaxet v`oxjok zbok m`mv`okbtpnj eymeyjy bhbcbn< b/

Abhbt bjt hbo mbx`tj x`tcbtpx zbok bhb hj hbcbm y`c/

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Mbypa hbo objaozb bjt mjo`tbc hbcbm xpdpn v`veneobo m`tpvbabo vtey`y eymeyjy/ Bjt hbcbm xbobn m`mjcjaj abohpokbo yecw`ox c`djn d`ybt .nzvexeoji* hjdbohjok hbcbm v`mdpcpn# y`njokkb bjt mbypa m`oplp ~zc`my`c xbobmbo/

4/

Ljab y`c xbobmbo hjc`xbaabo hbcbm aeohjyj nzv`txeoji .yecpx xjokkj bxbp yecw`ox t`ohbn*# mbab y`c babo m`ozpypx .x`t-vcbymecjyjy* abt`ob ibjtbo y`c a`cpbt m`oplp cbtpxbo nzv`txeoji/

9/

Bjt cbpx bhbcbn nzv`txeoji dbkj y`c xpdpn mbopyjb# y`njokkb mjopm bjt cbpx lpyxtp m`oz`dbdabo h`njhtbyj/

8/

A`oxbok zbok hjmbypaabo a` hbcbm bjt kbtbm babo m`okbcbmj v`ozpypxbo/

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M`okbmbxj v`td`hbbo xjokj cbtpxbo xjbv 0 m`ojx y`cbmb 9 abcj Y`x`cbn y`c`ybj# m`okkboxj cbtpxbo kpcb vbhb ypmptbo a`-4 h`okbo 2 mc cbtpxbo kpcb 40% hbo 266% y`ibtb d`tkboxjbo

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m`m`tcpabo {baxp aptbok c`djn y`cbmb 20 m`ojx hjxbmdbn h`okbo v`mdpbxbo ypmptbo vbhb a`oxbok/ Y`njokkb hjdpxpnabo 4 dpbn a`oxbok poxpa `gjyj`oyj {baxp/ Vbhb y`mpb v`tiedbbo# ajxb m`okjyjozb h`okbo cbtpxbo ypateyb 06% y`dbkbj wbtjbdc` aeoxtecozb vbhb ybcbn ybxp ypmptbo/ Ypmptbo x`ty`dpx xjhba ybmvbj x`mdpy vbhb dbkjbo hbybtozb# abt`ob dbkjbo hbybt  jojcbn zbok d`tv`tbo y`dbkbj m`mdtbo hbcbm v`tiedbbo joj/ A`mphjbo hjxpxpv h`okbo abt`x v`ozpmdbx zbok bhb vjvb abib d`tyabcb zbok oboxjozb djyb lpkb hj y`dpx y`dbkbj eymem`x`t/ Vbhb v`tiedbbo 2# y`x`cbn ybcbn ybxp ypmptbo hjd`tj cbtpxbo ypateyb 06%# ybcbn ybxp ypmptbo cbkj hjd`tj cbtpxbo 6% y`dbkbj v`mdbohjok zbok oboxjozb babo m`opolpaabo bvbabn v`tjyxj{b zbok x`tlbhj vbhb m`mdtbo` a`oxbok m`tpvbabo v`tjyxj{b hjgpyj bxbp eymeyjy/ Y`x`cbn 0 m`ojx hbvbx hja`xbnpj xjokkj cbtpxbo ypateyb vbhb vjvb abib d`tyabcb zbok b{bcozb m`mjcjaj xjokkj 8#> im# a`mphjbo m`okbcbmj v`obmdbnbo xjokkj y`d`ybt 6#; im/ V`kpaptbo hjcbapabo h`okbo m`okkpobabo v`okkbtjy abt`ob yabcb vbhb vjvb abib aptbok l`cby/ A`mphjbo y`x`cbn 26 m`ojx xjokkjozb m`okbcbmj v`obmdbnbo cbkj zbjxp y`d`ybt 6#0 im/ Y`x`cbn 20 m`ojx xjokkjozb lpkb m`okbcbmj v`obmdbnbo y`d`ybt 6/0 im/ Y`njokkb xjokkj banjtozb m`olbhj 7#0 im/

D`thbybtabo nbc x`ty`dpx v`obmdbnbo xjokkj vbhb vjvb d`tyabcb m`cbcpj m`mdtbo` a`oxbok m`tpvbabo v`tjyxj{b eymeyjy abt`ob x`tlbhj v`tvjohbnbo bjt hbtj hb`tbn h`okbo vex`oyjbc bjt xjokkj a` hb`tbn vex`oyjbc bjt t`ohbn/ Vex`oyjbc bjt joj hbvbx hjxpolpaabo h`okbo abhbt  a`v`abxbo cbtpxbo ypateyb/ Cbtpxbo ypateyb h`okbo abhbt 06% m`mjcjaj abhbt kpcb zbok c`djn xjokkj bxbp h`okbo abxb cbjo m`mjcjaj vex`oyjbc bjt  zbok t`ohbn/ Y`hbokabo cbtpxbo ypateyb 6% m`mjcjaj abhbt kpcb zbok t`ohbn# h`okbo abxb cbjo m`mjcjaj vex`oyjbc bjt zbok xjokkj/ Y`njokkb bjt  babo m`okbcjt m`cbcpj m`mdtbo` y`mj v`tm`bdc` zbok hbcbm v`tiedbbo abcj joj bhbcbn a`oxbok# hbtj hb`tbn h`okbo vex`oyjbc bjt xjokkj .cbtpxbo ypateyb 6%* a` hb`tbn h`okbo vex`oyjbc bjt t`ohbn .cbtpxbo ypateyb 6%*/ Vbhb v`tiedbbo a`hpb# cbtpxbo ypateyb 06% zbok m`tpvbabo wb`tjbd`c ieoxtec x`xbv hjmbypaabo hbcbm ybcbn ybxp ypmptbo zbok hjd`tj vjvb abib d`tyabcb/ A`mphjbo ybcbn ybxp ypmptbo hjd`tj bxbp hjjyj h`okbo cbtpxbo ypateyb 40%/ Xjokkj b{bc cbtpxbo ypateyb 06% vbhb vjvb abib d`tyabcb bhbcbn 7 im/ Y`x`cbn 0 m`ojx# xjokkj cbtpxbo d`txbmdbn 2 im# y`xbcbn 26 m`ojx xjokkj bjt vbhb vjvb d`tyabcb xjhba m`okbcbmj v`tpdbnbo/ Y`hbokabo y`x`cbn 20 m`ojx xjokkjozb a`mdbcj m`okbcbmj v`tpdbnbo y`dbozba 6#4 im/ H`okbo h`mjajbo vbhb v`tiedbbo zbok a`hpb joj lpkb m`tpvbabo v`tjyxj{b eymeyjy/ Y`v`txj vbhb v`tiedbbo v`txbmb# bjt m`okbcjt m`cbcpj m`mdtbo` y`mj v`tm`bdc` hbtj vex`oyjbc bjt xjokkj . cbtpxbo ypateyb 40%* a` hbt`tbn h`okbo vex`oyjbc bjt t`ohbn . cbtpxbo ypateyb 06% */ Nbc joj hjabt`obabo cbtpxbo ypateyb 40% m`mjcjaj xjokabx a``oi`tbo zbok c`djn t`ohbn# y`njokkb vex`oyjbc bjtozb c`djn xjokkj hjdbohjokabo h`okbo cbtpxbo ypateyb 06%/ Vbhb v`tiedbbo a`xjkb# y`x`cbn ypmptbo v`txbmb hjjyj cbtpxbo ypateyb 06% hbo hjd`tj abt`x ypmdbx h`okbo vjvb d`tyabcb# a`mphjbo ypmptbo a`hpb hjjyj cbtpxbo ypateyb 266%/ Y`x`cbn 0 m`ojx# hbtj xjokkj cbtpxbo ypateyb 06% m`okbcbmj v`obmdbnbo xjokkj y`d`ybt 6#4 im/ Y`x`cbn 26 m`ojx cbtpxbo m`okbcbmj v`obmdbnbo xjokkj y`d`ybt 6#8 im/ Hbo y`x`cbn 20 m`ojx# bjt d`txbmdbn cbkj y`d`ybt 6#9 im/ Y`nbtpyozb xjokkj cbtpxbo ypateyb 06% vbhb vjvb d`tyabcb m`opolpaabo v`optpobo#

abt`ob cbtpxbo ypateyb 266% m`mjcjaj vex`oyjbc bjt zbok c`djn xjokkj hbtjvbhb cbtpxbo ypateyb 06%/ A`ybcbnbo vbhb v`tiedbbo joj hbvbx hjabt`obabo abt`ob ypmptbo zbok hjd`tj ypmdbx h`okbo vjvb abib d`tyabcb deiet/ Vbhbnbc y`nbtpyozb ypmptbo hjxpxpv tbvbx h`okbo ypmdbx/ A`deietbo hbvbx hjy`dbdabo ypmptbo x`tcbcp d`ybt/ Vbhb v`tiedbbo a`kjbxbo 2 joj x`tlbhj v`td`hbbo a`i`vbxbo mbypaozb bjt a` hbcbm ypmptbo zbok d`tjyj cbtpxbo kpcb h`okbo aeoy`oxtbyj zbok d`td`hb abt`ob aeoy`oxtbyj cbtpxbo kpcb zbok bhb hj hbcbm y`c .a`oxbok* babo m`mv`okbtpnj bcjtbo v`cbtpx .bjt* hbtj cbtpxbo zbok njvexeojy .aeoy`oxtbyj v`cbtpx bxbp bjtozb xjokkj* zbok mbypa a` hbcbm cbtpxbo njv`txeojy .aeoy`oxtbyj v`cbtpx bxbpbjtozb t`ohbn*/ Y`mbajo d`ybt aeoy`oxtbyj cbtpxbo kpcb zbok d`tbhb hj hbcbm y`c .a`oxbok*# mbab babo y`mbajo i`vbx vpcb bcjtbo mbypaozb bjt .v`cbtpx* a` hbcbm cpdbok zbok d`tjyj cbtpxbo kpcb/

W/

A`yjmvpcbo hbo Ybtbo b/

A`yjmvpcbo Vbhb v`tiedbbo a`kjbxbo 2# m`tpvbabo v`tjyxj{b eymeyjy# zbjxp v`tvjohbnbo bjt hbtj hb`tbn h`okbo h`okbo vex`oyjbc vex`oyjbc bjt xjokkj m`oplp hb`tbn hb`tbn h`okbo vex`oyjbc bjt t`ohbn m`cbcpj m`mdtbo` y`mj v`tm`bdc`/

d/

Ybtbo Vbhb v`tiedbbo x`oxbok „Hbvbxabn bjt d`t -eymeyjy -eymeyjy m`o`mdpy y`c  lbtjokbo xpmdpnbo5‚# y`nbtpyozb a`oxbok zbok hjd`tjabo c`djn hbtj 4# mpokajo 9/ Hpb a`oxbok hjkpobabo poxpa m`cbapabo a`kjbxbo 2# hbo zbok ybxp cbkj hjkpobabo poxpa m`cbapabo vtbaxjapm a`kjbxbo 4/ Y`cbjo jxp# k`cby papt zbok hjy`hjbabo poxpa m`okbodjc cbtpxbo ypateyb lpkb aptbok# y`njokkb nbtpy m`okboxtj hbo m`obmdbn m `obmdbn {baxp/

WJ/

Hjyapyj 2/

Bvbabn vex`oyjbc bjt 2 mec mec cbtpxbo cbtpxbo kbtbm . ObIc ObIc * ybmb h`okbo 2 mec cbtpxbo Kcpaeyb 5

Lb{bd < Xjhba# abt`ob x`abobo eymeyjy



m`mvpozbj v`tybmbbo zbjxp



=

o/M/T/X/ Y`njokkb d`ybtozb x`abobo eymeyjyozb ObIc xjhba ybmb h`okbo cbtpxbo kcpaeyb/ Ojcbj o boxbtb ObIc hbo kcpaeyb jxp d`td`hb# x`tkboxpok hbtj dbozbaozb jeo zbokx`thbvbx vbhb y`ozb{b x`ty`dpx/ Cbtpxbo ObIc m`mvpozbj lpmcbn jeo .o* y`dbozba 4# y`hbokabo cbtpxbo kpcb xjhba m`mjcjaj jeo .o*/ Y`njokkb x`abobo eymeyjy cbtpxbo kbtbm .ObIc* c`djn d`ybt hbtjvbhb cbtpxbo kcpaeyb/ Nbc joj m`oz`dbdabo vex`oyjbc bjt hj boxbtb a`hpb cbtpxbo d`td`hb/ 4/

Bvbabn cblp hjgpyj bjt hbtj lbtjokbo a`oxbok hjv`okbtpnj ec`n l`ojy cbtpxbo v`t`ohbmozb 5 Lb{bd < Jzb# abt`ob l`ojy cbtpxbo v`t`ohbm babo m`mvpozbj wjyaeyjxby bxbp xjokabx a`a`oxbcbo |bx zbok d`td`hb/ Nbc joj babo m`mv`okbtpnj a`i`vbxbo hjgpyj-eymeyjy/ L`ojy cbtpxbo x`ty`dpx babo m`o`oxpabo bvbabn cbtpxbo zbok m`okbcjt a`oxbc bxbpabn `oi`t/

9/

Bvb zbok babo x`tlbhj djcb lbtjokbo a`oxbok hjx`mvbxabo vbhb cbtpxbo h`okbo vex`oyjbc eymexjaozb c`djn t`ohbn hbtj vex`oyjbc eymexji ibjtbo  lbtjokboozb 5 Lb{bd < Cbtpxbo zbok d`tbhb hj hbcbm a`oxbok babo d`taptbok . babo m`okbcbmj h`njhtby *# abt`ob bjt .v`cbtpx* zbok d`tbhb hj hbcbm a`oxbok babo m`okbcjt a`cpbt m`oplp a` vex`oyjbc cbtpxboozb c`djn t`ohbn/ Nbc joj ljab d`tcbokypok x`tpy-m`o`tpy babo m`ojmdpcabo v`cbtpx bxbp bjt hbtj cbtpxbo zbok d`tbhb hj hbcbm a`oxbok cbmb-a`cbmbbo babo nbdjy/

WJJ/

Hbgxbt Vpyxbab Kjtjohtb# Bjyzbn/ 2:>7/ Djeaemjb 2/ Lbabtxb < Ktbm`hjb/ Nbtdeo# L/ D/ 2:>;/ M`xeh` Gjxeajmjb# V`opoxpo Ibtb Meh`to M`okbobcjyb 

Xpmdpnbo X`tdjxbo A`hpb / Dbohpok < JXD/ Ybcjydptz# G/D/# Ic`eo [/T/ 2::0/ Gjyjecekj Xpmdpnbo# ljcjh 2/ Dbohpok < JXD nxxv<ajt`jh{j/dcek/gtj`ohyx`t/iem466>6:m`abojym`-hjgpyj-hbo-eymeyjyhbcbm-y`c/ Hjbmdjc vbhb Ybdxp# 44 Y`vx`md`t 4624 lbm 27 < 90

A`kjbxbo 4 „M@OKPAPT VEX@OYJBC EYMEXJA HBO VEX@OYJBC BJT LBTJOKBO‚

J/

Xplpbo Vtbaxjapm M`ok`xbnpj ojcbj vex`oyjbc bjt vbhb pmdj a`oxbok/

JJ/

Abljbo Vpyxbab V`tpdbnbo `o`tkj d`dby y`x`cbn bhb xbmdbnbo ypbxp d`ybtbo .anpypyozb ktbm dedex mec`apc* hjy`dpx vex`oyjbc ajmjb# zbok m`tpvbabo `o`tkj d`dby v`t mec dbnbo/ Vex`oyjbc ajmjb xjhba x`tkboxpok vbhb dbozbaozb dbnbo/ Y`hbokabo vex`oyjbc bjt m`tpvbabo vex`oyjbc ajmjb hbcbm ypbxp yzyx`m

bxbp

dbkjbo

yzyx`m#

hjozbxbabo

hbcbm

ypbxp

x`abobo

hbo

hjdbohjokabo h`okbo vex`oyjbc ajmjb bjt mptoj# vbhb x`abobo bxmeyg`t hbo ypnp y`txb a`xjokkjbo zbok ybmb# hbo vex`oyjbc ajmjb bjt mptoj hjx`oxpabo ybmb h`okbo oec/ Vex`oyjbc bjt djbyb hjcbmdbokabo hjcbmdbok abo h`okbo nptpg Zpoboj .ή* bxbp hjdbib vyj/ Ljab vex`oyjbc bjt c`djn xjokkj hj ybxp dbkjbo hbtj yzyx`m hbo xjhba bhb v`oknbcbok v`tm`bdc` zbok m`oknbcbokj hjgpyj bjt# mbab bjt babo d`tk`tba hbtj hb`tbn zbok d`tvex`oyjbc xjokkj a` hb`tbn zbok d`tvex`oyjbc t`ohbn/ Vtey`y yveoxbo x`ty`dpx m`oz`dbdabo `o`tkz hjc`vby a` y`ajxbt# hbo `o`tkz d`dby yzyx`m x`ty`dpx m`optpo/ @o`tkz zbok hjc`vby a`y`ajxbt  m`mvpozbj vex`oyj poxpa m`cbapabo a`tlb# mjybcozb bjt m`okbcjt y`ibtb eymexji a` dbkjbo bxby dbxbok hbcbm g`oem`ob zbok hja`obc y`dbkbj x`abobo babt/ .Ybcjydptz hbo Teyy# 2::0* Ljab bjt mptoj d`tbhb hj ybxp yjyj m`mdtbo hbo cbtpxbo hjyjyj cbjoozb# mbab vex`oyjbc bjt babo c`djn t`ohbn hbtjvbhb vex`oyjbc bjt- bjt mptoj/ Vex`oyjbc bjt ypbxp cbtpxbo vbhb x`abobo bxmeyg`t d`tojcbj o`kbxjg/ Vex`oyjbc bjt- bjt mptoj zbok m`ohbvbx x`abobo hbtj cpbt zbok c`djn d`ybt hbtj vbhb x`abobo bxmeyg`t# d`tojcbj veyjxjg/ Vex`oyjbc bjt cbtpxbo zbok m`ohbvbx x`abobo hbvbx d`tojcbj o`kbxjg bvbdjcb vex`oyjbc eymexji c`djn o`kbxjg hbtj vbhb x`abobo zbok veyjxjg# hbvbx d`tojcbj oec bvbdjcb x`abobo ybmb h`okbo vex`oyjbc eymexji x`xbvj h`okbo xbohb zbok d`tcb{bobo# bxbp hbvbx d`tojcbj veyjxjg bvbdjcb x`abobo c`djn veyjxjg hbtj vbhb vex`oyjbc eymexja zbok o`kbxjg/

Hbcbm v`okpaptbo vex`ojybc bjt hbvbx hjcbapabo h`okbo d`tdbkbj m`xeh`# ybcbn ybxpozb m`okkpobabo m`xeh` wecpm`-lbtjokbo/ Ybmvc`  lbtjokbo zbok hjjokjoabo hjmbypaabo a`hbcbm y`tj cbtpxbo h`okbo tbkbm aey`oy`oxtbyj zbok hja`xbnpj/ Cjobtpx x`tdbja poxpa v`okpaptbo bhbcbn zbok xjhba mphbn m`cjoxbyj m`mdtbo` bxbp zbok xjhba m`tpyba lbtjokbo/ Xplpboozb bhbcbn poxpa m`ohbvbxabo cbtpxbo zbok xjhba m`okpdbn wecpm` lbtjokbo# btxjozb# xjhba bhb bjt zbok mbypa lbtjokbo bxbp zbok njcbok/ Joj m`obohbabo dbn{b cbtpxbo hbo lbtjokbo y`lba y`mpcb d`tbhb hbcbm a`y`xjmdbokbo zbok ybmb/ .Ybcjydptz hbo Teyy# 2::0*/ D`d`tbvb gbaxet zbok zbok djbybozb m`oknbyjcabo ktbhj`o vex`oyjbc ajmjb bxbp ktbhj`o vex`oyjbc bjt hbcbm yzyx`m xpmdpnbo bhbcbn aeoy`oxtbyj bxbp baxjgjxby# abt`ob vbtxja`c d`thjgpyj hbtj x`mvbx zbok d`tbaxjgjxby xjokkj a` x`mvbx zbok d`tbaxjgjxby t`ohbn/ Ypnp# x`abobo# `g`a cjobtpx x`tnbhbv vex`oyjbc ajmjb v`cbtpx# hbo mbxtjay bxbp v`tmpabbo zbok d`tmpbxbo# y`v`txj v`tmpabbo vbtxja`c xbobn cjbx hj xbobn# vtex`jo bxbp vecjybabtjhb hjohjok y`c/ .Ybcjydptz hbo Teyy# 2::0*/ Poxpa m`oknjxpok v`tpdbnbo d`tbx zbok x`tlbhj hjkpobabo tpmpy<

% v`tpdbnbo d`tbx = d`tbx banjt

 ’

d`tbx mpcb-mpcbD`tbx mpcb  ’

mpcb ^ 266%/

Y`hbokabo poxpa m`oknjxpok ojcbj vex`oyjbc eymexjaozb hjkpobabo tpmpy<

ήy =MjTX

Hjmbob < M = mecbtjxby hbtj cbtpxbo ypateyb J = aeoyxboxb aeoyxboxb jeojybyj # poxpa poxpa ypateyb ypateyb = 2 T = aeoyxboxb kby .6#6>92 dbt  h`tblbx* X = ypnp bdyecpx` = . I ! 4;9 *

JJJ/

M`xeh` Vtbaxjapm b/

d/

X`mvbx hbo [baxp Vtbaxjapm 

X`mvbx vtbaxjapm

< Cbdetbxetjpm Djeajmjb



[baxp vtbaxjapm

< Y`cbyb# 2> Y`vx`md`t 4624

Bcbx hbo Dbnbo 



i/

Bcbx < 2*

V`cpdbok kbdpy

4*

Ib{bo v`xtj

9*

Vjybp xblbm

8*

A`txby

0*

Xjmdbokbo bobczj|` dbcboi`

7*

V`okkbtjy

Dbnbo < 2*

A`oxbok

4*

Cbtpxbo ypateyb 4 mc . 6#61 6#81 2#7 *

Vtey`hpt  M`mdpbx yjcjoh`t pmdj a`oxbok y`dbozba : dpbn h`okbo m`okkpobabo v`cpdbok kbdpy# vbolbok mbyjok-mbyjok 9 im M`ojmdbok a`-: yjcjoh`t pmdj a`oxbok h`okbo m`okkpobabo xjmdbokbo bobczyj|` dbcboi` M`mbypaabo mbyjok-mbyjok 9 dpbn yjcjoh`t pmdj a`oxbok a` hbcbm ib{bo v`xtj M`mbypaabo cbtpxbo ypateyb 46 mc a` hbcbm mbyjok-mbyjok ib{bo v`xtj h`okbo aeoy`oxtbyj 6#61 6#81 hbo 2#7 y`ibtb d`tptpxbo M`opokkp y`cbmb 46 m`ojx M`ojmdbok a`mdbcj yjcjoh`t pmdj a`oxbok h`okbo xjmdbokbo bobczyj|` dbcboi`

JW/

Nbyjc hbo V`mdbnbybo b/

Nbyjc A`oxbok

d/

6#6 M

6#8 M

2#7 M

Y`d`cpm Y`yphbn Y`d`cpm Y`yphbn Y`d`cpm Y`yphbn

2/

6#0; kt

6#7: kt

6#0> kt

6#7;8 kt

6#0; kt

6#70 kt 

4/

6#0; kt

6#70 kt

6#0: kt

6#7>8 kt

6#0; kt

6#777 kt 

9/

6#0: kt

6#7; kt

6#00 kt

6#77> kt

6#07 kt

6#787 kt 

T`tbxb

6#07; kt

6#7; kt

6#0;9 kt

6#77> kt

6#07; kt

6#780 kt 

Bobcjyjy Hbxb Tpmpy m`oknjxpok v`tpdbnbo d`tbx <

% v`tpdbnbo d`tbx = d`tbx banjt

 ’

d`tbx mpcb-mpcbD`tbx mpcb  ’

mpcb ^ 266%/

2/

H`okbo aeoy`oxtbyj 6#6 M Vbhb a`oxbok 2 % v`tpdbnbo d`tbx = 6#7: - 6#0;  6#0; ^ 266% = 42#604 %

Vbhb a`oxbok 4 % v`tpdbnbo d`tbx = 6#70 ’ 6#70 ’ 6#0;  6#0; ^ 266% = 28#79 % Vbhb a`oxbok 9 % v`tpdbnbo d`tbx = 6#7; ’ 6#7; ’ 6#0:  6#0: ^ 266% = 29#00 % 4/

H`okbo aeoy`oxtbyj 6#8 M Vbhb a`oxbok 2 % v`tpdbnbo d`tbx = 6#7;8 ’ 6#7;8 ’ 6#0>  6#0> ^ 266% = 27# 46;%

Vbhb a`oxbok 4 % v`tpdbnbo d`tbx = 6#7>0 - 6#0:  6#0: ^ 266% = 26 % Vbhb a`oxbok 9 % v`tpdbnbo d`tbx = 6#7>> ’ 6#7>> ’ 6#00  6#00 ^ 266 % = 40#6: %

9/

H`okbo aeoy`oxtbyj 2#7 M Vbhb a`oxbok 2 % v`tpdbnbo d`tbx = 6#70 ’ 6#70 ’ 6#0;  6#0; ^ 266 % = 28#69 % Vbhb a`oxbok 4 % v`tpdbnbo d`tbx = 6#777 ’ 6#777 ’ 6#0;  6#0; ^ 266% = 27#>8 % Vbhb a`oxbok 9 % v`tpdbnbo d`tbx = 6#787 ’ 6#787 ’ 6#07  6#07 ^ 266% = 20#97 %

Tpmpy m`oknjxpok vex`oyjbc eymexji ypateyb <

ήy =MjTX

Hjmbob < M = mecbtjxby hbtj cbtpxbo ypateyb J = aeoyxboxb aeoyxboxb jeojybyj # poxpa ypateyb = 2 T = aeoyxboxb kby .6#6>92 dbt  h`tblbx* X = ypnp bdyecpx` = . I ! 4;9 *

Hja`xbnpj ypnp v`o`cjxjbo m`tpvbabo m`tpvbabo ypnp abmbt < 4; h`tblbx h`tblbx I`cyjpy Ypnp bdyecpx` = 4; h`tblbx I`cyjpy ! 49; = 478

2/

Vex`oyjbc eymexji vbhb aeoy`oxtbyj 6#6 M ήy = 6#6 ^ 2 ^ 6#6>92 ^ 478 = 6 bxm

4/

Vex`oyjbc eymexji vbhb aeoy`oxtbyj 6#8 M

ήy = 6#8 ^ 2 ^ 6#6>92 ^ 478 = >#;;0 bxm 9/

Vex`oyjbc eymexji vbhb aeoy`oxtbyj 2#7 M ήy = 2#7 ^ 2 ^ 6#6>92^ 478 = 90#26 bxm

Ktbgja npdpokbo boxbtb d`tbx a`oxbok . Z * h`okbo aeoy`oxtbyj cbtpxbo .^* <

Ktbgja Npdpokbo Y`cjyjn D`tbx A`oxbok h`okbo Aeoy`oxtbyj Cbtpxbo 2 6/> 6/7 6/8 6/4 6 6#6 M

i/

6#8 M

2#7 M

V`mdbnbybo Vbhb v`okbmbxbo joj hjcjnbx vex`oyjbc bjt vbhb lbtjkbo njhpv pmdj a`oxbok

poxpa m`ok`xbnpj v`tk`tbabo ajmjb bjt hbcbm xpmdpnbo xpmdpnbo

anpypyozb vbhb y`c xpmdpnbo Pmdj A`oxbok .Yecbopm xpd`teypm* zbok hj t`ohbm y`cbmb 46 m`ojx# y`njokkb m`okbcbmj a`c`djnbo hbo a`aptbokbo ibjtbo/ V`tk`tbabo bjt hbo cbtpxbo ypateyb zbok x`tlbhj vbhb pmdj a`oxbok hbvbx hj lbhjabo y`dbkbj bipbo poxpa m`ok`xbnpj bvbabn pmdj a`oxbok m`mvpozbj hbzb y`tbv zbok xjokkj x`tnbhbv bjt bxbp cbtpxbo ypateyb/ D`thbybtabo xbdc` hjbxby mbab ajxb m`cjnbx dbn{b aeoy`oxtbyj cbtpxbo ypateyb 6#6 M# 6#8 M# hbo 2#7 M m`okbcbmj wbtjbyj# hjmbob y`mpbozb m`mjcjaj ojcbj veyjxjg/ Vex`oyjbc eymexji cbtpxbo dbtojcbj veyjxjg# abt`ob bjt v`cbtpx hbcbm cbtpxbo pmdj a`oxbok m`cbapabo a`tlb c`djn hbtj

bjt mptoj/ Ljab x`abobo vbhb cbtpxbo m`ojokabx# mbab a`mbmvpbo cbtpxbo poxpa m`cbapabo a`tlb lpkb m`ojokabx y`njokkb dedex d`tbx pmdj a`oxbokvpo m`ojokabx/ Vbhb v`tiedbbo mbokpobabo cbtpxbo ypateyb# cbtpxbo ypateyb h`okbo aeoy`oxtbyj 6#61 6#8 hbo 2#7 d`tojcbj veyjxjg/ D`thbybtabo nbyjc v`okbmbxbo bxbp xbd`c mbab ajxb hbvbx m`okbxbabo dbn{b vtbaxjapm hbvbx hjcjnbx x`thbvbx v`txbmdbnbo d`tbx y`x`cbn hjxbmdbnabo h`okbo cbtpxbo ypateyb# v`txbmdbnbo v`tpdbnbo d`tbx zbok x`tlbhj y`ajxbt 6#6;> kt vbhb aeoxtbyj cbtpxbo ypateyb 2#7 M1 6#6:0 kt vbhb aeoy`oxtbyj cbtpxbo ypateyb 6#8 M hbo 6#269 kt vbhb aeoy`oxtbyj cbtpxbo ypateyb 6#6 M/ V`txbmdbnbo d`tbx hjabtobabo vex`oyjbc vex`oyjbc mec`apc bjt mptoj zbok zbok m`c`{bxj m`mdtbo` c`djn d`ybt hbtj vbhb cbtpxbovbhb lbtjokbo njhpv pmdj a`oxbok y`njokkb m`obmdbn dedex d`tbx pmdj a`oxbok vtey`y joj m`tpvbabo

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A`yjmvpcbo hbo Ybtbo b/

A`yjmvpcbo Abt`ob ojcbj vex`oyjbc bjt = ή = ήv ’ ήy 1 hjmbob ojcbj v= 6# y`njokkb ojcbj vex`oyjbc bjt ybmb h`okbo vex`oyjbc eymexjaozb# zbjxp vbhb aeoy`oxtbyj 6#6 M y`d`ybt 6 bxm# vbhb aeoy`oxtbyj 6#8 M y`d`ybt >#;;0 bxm hbo vbhb aeoy`oxtbyj 2#7 M y`d`ybt 90#26 bxm/

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Ybtbo Vbhb vtbaxjapm a`kjbxbo 4 joj# xjmdbokbo zbok hjkpobabo poxpa m`ojmdbok a`oxbok aptbok . nbozb 2 */ Vbhbnbc lpmcbn a`cemvea zbok bhb c`djn hbtj 0/ Y`njokkb ybbx babo m`okkpobaboozb nbtpy m`okboxtj hbo poxpa m`okboxtj jxp hjdpxpnabo {baxp zbok cbmb/

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D`tbvbabn vex`oyjbc eymexji cbtpxbo Kcpaeyb vbhb ypnp zbok v`tiedbbo ybphbtb 5

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Vex`oyjbc eymexji vbhb aeoy`oxtbyj 6#6 M ήy = 6#6 ^ 2 ^ 6#6>92 ^ 478 = 6 bxm

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Vex`oyjbc eymexji vbhb aeoy`oxtbyj 6#8 M ήy = 6#8 ^ 2 ^ 6#6>92 ^ 478 = >#;;0 bxm

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Vex`oyjbc eymexji vbhb aeoy`oxtbyj 2#7 M ήy = 2#7 ^ 2 ^ 6#6>92^ 478 = 90#26 bxm

4/

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