Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
Å@HGIF >. ZLXF@IGNY
9
>.>. Hfag`gigù` Hfag`gigù ` .................................................................................................................................................... 9 >.>.>. Fbfrigigls .............................................................................. ............... ............................................................................................................................. ........................................................................ ..........9
>.?. Zltf`igns Zltf`ig ns hf onsf >: ............................................................................................................................... 8 >.?.>. Fbfrigigl .......................................................... ........................................................................................................................... .............................................................................................. ............................. 6
>.9. Hfsileplsgigù` pldg`ùegin hf u` `òefrl f`tfrl ........................................................................... 6 >.9.>. Fbfrigigl .......................................................... ........................................................................................................................... .............................................................................................. ............................. 6
>.8. Iunhrnhls Iunhrnh ls pfrafitls p frafitls .............................................................................................................................. 6 >.8.>. Hfag`gigù` ........................................................ ......................................................................................................................... .............................................................................................. ............................. 6 >.8.?. Npdginigl`fs .................................................................................................................... ............................. 6
>.6. Iuols pfrafitls pfrafit ls ....................................................................................................................................... 6 >.6.>. Hfag`gigù` ........................................................ ......................................................................................................................... .............................................................................................. ............................. 6 >.6.?. Npdginigl`fs .................................................................................................................... ............................. 1
>.1. Ygk`l Yg k`l hf dns pltf`igns p ltf`igns ............................................................................................................................ 1 >.1.>. Onsf plsgtgvn ................................................................................................................................................ .................................................................................. .............................................................. 1 >.1.?. Onsf `fkntgvn...................................................................... `fkntgvn........ ............................................................................................................................. ......................................................................... ..........1 >.1.9. Xnodn-_fsuef` ......................................................... .......................................................................................................................... ................................................................................... .................. ; >.1.8. Fbfrigigls F bfrigigls ..................................................................................................................................................... ....................................................................................... .............................................................. ;
>.;. Zrlpgfhnhfs Zrlpgfh nhfs ............................................................................................................................................... = >.;.>. Xnodn ’ _fsuef` ....................................................... ........................................................................................................................ ................................................................................. ................ >? >.;.?. Fbfrigigls ................................................................................................................................ ................................................................. .................................................................................. ................... >9
>.=. Lpfrnigl`fs il` pltf`igns.................................................................................................................. >8 >.=.>. Yuen y _fstn ....................................................................................................... ...................................... ....................................................................................................... ...................................... >8 >.=.?. Eudtgpdginigù` ............................................................................................................................ ........................................................... ................................................................................. ................ >8 >.=.9. Hgvgsgù` ............................................................................................................................ ........................................................... ............................................................................................ ........................... >8 >.=.8. Zltf`ign ........................................................................................................................... .......................................................... ............................................................................................ ........................... >8
?. _NÅIFY
>6
?.>. Hfag`gigù` Hfag`gi gù` ................................................................................................................................................. >6 ?.?. Xgpls hf rnåifs fxnitns ...................................................................................................................... >6 ?.?.>. _nåz iunhrnhn ........................................................... ............................................................................................................................ ................................................................................. ................ >6 ?.?.?. _nåz iòogin ............................................................................................... ................................ ................................................................................................................ ................................................. >1 ?.?.9. Fbfrigigls....................................................... ........................................................................................................................ ............................................................................................ ........................... >;
?.9. Xgpls hf rnåifs r nåifs f`tfrns f`tfrn s....................................................................................................................... >= Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n > hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
?.9.>. _nåz iunhrnhn ........................................................... ............................................................................................................................ ................................................................................. ................ >= ?.9.?. _nåz iòogin ............................................................................................... ................................ ................................................................................................................ ................................................. >7
?.8. Ylduigl`fs sfkò` fd å`hgif hf dn rnåz y fd rnhgin`hl ................................................................... >7 ?.8.>. _nhgin`hl plsgtgvl p lsgtgvl .............................................................. ............................................................................................................................... ...................................................................... ..... >7 ?.8.?. _nhgin`hl `fkntgvl ....................................................................................................... ........................... >7 ?.8.9. Xnodn-_fsuef` ................................................................................................... ..................................... ?:
?.6. Iîdiudl hf dn rnåz iunhrnhn f`tfrn.................................................................................................. ?: ?.6.>. Iîdiudl hf h f alren nprlxgenhn ................................................................ ................................................................................................................ ................................................ ?: ?.6.?. Iîdiudl il` fd ndklrgtel ............................................................... .......................................................................................................................... ........................................................... ?> ?.6.?.>. Fbfrigigl ............................................................ ................................................................. ............... ?1
?.1. Lpfrnigl`fs il` rnåifs iunhrnhns fxnitns ................................................................................. ?; ?.1.>. Yuen y _fstn ............................................................ ............................................................................................................................. ................................................................................ ............... ?; ?.1.?. Eudtgpdginigù` ........................................................... ............................................................................................................................ ................................................................................ ............... ?; ?.1.9. Hgvgsgù` ........................................................... ............................................................................................................................ ........................................................................................... .......................... ?; ?.1.8. Zltf`ign hf u`n rnåz r nåz .......................................................... ........................................................................................................................ ..................................................................... ....... ?=
?.;. Dn rnåz ilel pltf`ign ......................................................................................................................... ?=
9. ZLXF@IGNY W _NÅIFY
?=
9.>. _filrhnr _filrh nr .................................................................................................................................................. ?=
8. LZF_NIGL@FY ILEOG@NHNY IL@ ZLXF@IGNY W _NÅIFY
?=
8.>. G`trlhuiigù` G`trl huiigù` ........................................................................................................................................... ?= 8.?. _fkdns _f kdns hf prglrghnh pr glrghnh .............................................................................................................................. ?= 8.9. Xgpls hf lpfrnigl`fs ileog`nhns ................................................................................................... ?7 8.9.>. Lpfrnigl`fs ileog`nhns il` pltf`igns y rnåifs iunhrnhns fxnitns ..... .......................................... ..................................... ?7 8.9.?. Lpfrnigl`fs ileog`nhns il` pltf`igns y rnåifs iòogins fxnitns ............................................... ?7 8.9.9. Lpfrnigl`fs ileog`nhns il` pltf`igns y rnåifs fxnitns f xnitns ....................................................... .............................................................. ....... ?7
8.8. Fbfrigigls Fbfrigi gls ................................................................................................................................................ ?7
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ? hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
>. ZLXF@IGNY >.>. Hfag`gigù` V`n pltf`ign fs u`n alren norfvgnhn hf fsirgogr u` prlhuitl alrenhl plr vnrgls anitlrfs gkundfs, fs hfigr, u`n eudtgpdginigù` hf anitlrfs gkundfs . Fstl fs, fs u`n eudtgpdginigù` f` dn quf fd egsel `òefrl sf eudtgpdgin vnrgns vfifs. Dn fxprfsgù` hf u`n pltf`ign fs dn onsf fdfvnhn n u` fxpl`f`tf . n` 5 n » n » n » n ... 5 `- vfifs —n― Onsf n` fxpl`f`tf ↟
↚
Hl`hf2 n fs dn onsf hf u`n pltf`ign quf fs fd `òefrl quf eudtgpdginels plr så egsel. Zlr tn`tl, dn onsf fs fd `òefrl quf sf rfpgtf . ` fd fxpl`f`tf hf u`n pltf`ign quf g`hgin fd `òefrl hf vfifs quf eudtgpdginels dn onsf. Zlr tn`tl, fd fxpl`f`tf g`hgin fd `òefrl hf vfifs quf sf rfpgtf dn onsf .
Nså pufs, u`n pltf`ign fstî alrenhn plr u`n onsf y u` fxpl`f`tf . Znrn rfsldvfr u`n pltf`ign sf eudtgpdgin dn onsf tn`tns vfifs ilel g`hgin fd fxpl`f`tf. F` dn indiudnhlrn igf`tåagin, sf usn dn tfidn x y . Fbfepdl >2
6 » 6 » 6 » 6 5 68 Dn onsf hf fstn pltf`ign fs 6 y fd fxpl`f`tf fs 8. Yf dff —6 fdfvnhl n 8― l —6 fdfvnhl n dn iunrtn―.
Fbfepdl ?2
(-7) » (-7) » (-7) » (-7) » (-7) ( -7) » (-7) 5 (-7) 1 Dn onsf hf fstn pltf`ign fs -7 y fd fxpl`f`tf fs 1. Yf dff —-7 fdfvnhl n 1 ― l —-7 fdfvnhl n dn sfxtn ―.
>.>.>. Fbfrigigls
>) Fsirgof f` alren hf prlhuitl y indiudn su vndlr2 n) (-1)? o) (-9)6 i) (+?)1 h) (+8)9
Ylduigù`2 (-1) » (-1) 5 +91 Ylduigù`2 (-9) » (-9) » (-9) » (-9) » (-9) 5 -?89 Ylduigù`2 (+?) » (+?) » (+?) » (+?) » (+?) » (+?) 5 +18 Ylduigù`2 (+8) » (+8) » (+8) 5 +18
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n 9 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
?) Ilepdftn dn tnodn2 Zrlhuitl
Zltf`ign
Onsf
Fxpl`f`tf
8 9 ?
? :
Yf dff
Qndlr l _fsudtnhl
?»?»? 7?
9? 8 fdfvnhl nd iuol fs gkund n 18
(’7) » (’7) » (’7) ’;
8
’?
(’6)1 ’> fdfvnhl n dn qug`tn
>.?. Zltf`igns hf onsf >: Il` pltf`ign hf onsf hgfz y fxpl`f`tf f`tfrl sf pufhf fsirgogr in`tghnhfs f`lrefs l euy pfqufþns. Fstl anigdgtn dls iîdiudls, nd `l tf`fr quf utgdgznr euimls hfigendfs. h figendfs. Fd iîdiudl hf dns pltf`igns hf onsf >: rfsudtn sf`igddl, pufs fd `òefrl hf ifrls ilg`ighf il` fd fxpl`f`tf hf dn pltf`ign . V`n pltf`ign hf onsf >: y fxpl`f`tf plsgtgvl fs gkund n dn u`ghnh sfkughn hf tn`tls ifrls ilel g`hgin fd fxpl`f`tf. Fbfepdl >2 >:9 5 >.::: Yl` 9 ifrls ilel g`hgin fd fxpl`f`tf hf dn pltf`ign. Fbfepdl ?2 >:; 5 >:.:::.::: Yl` ; ifrls ilel g`hgin fd fxpl`f`tf hf dn pltf`ign. Dns pltf`igns hf onsf >: y fxpl`f`tf `fkntgvl fqugvndf` n hgvghgr plr >:, >::, fti., plr dl quf vn` n rfprfsf`tnr in`tghnhfs ef`lrfs hf dn u`ghnh. Iun`tl enylr fs fd fxpl`f`tf f` vndlr nosldutl, ef`lr fs dn pltf`ign. Fbfepdl >2
>:’9 5
> >:
9
> >.:::
5 :,::>
Yl` 9 ifrls ilel g`hgin fd fxpl`f`tf hf dn pltf`ign. Fbfepdl ?2 >:’; 5
> >:
;
>
>:.:::.:::
5 :,::::::>
Yl` ; ifrls ilel g`hgin fd fxpl`f`tf hf dn pltf`ign.
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n 8 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
>.?.>. Fbfrigigl
>) Fxprfsn f` alren hf pltf`igns hf onsf >:. n) 6:.:::
Ylduigù`2 6 » >:8
o) 9.?::
Ylduigù`2 9? » >:? Ylduigù`2 9 » >:1
i) 9.:::.:::
>.9. Hfsileplsgigù` pldg`ùegin hf u` `òefrl f`tfrl V` `òefrl f`tfrl sf pufhf hfsilepl`fr utgdgzn`hl pltf`igns hf onsf >: . Fbfepdl >2 Fd `òefrl 9.16= plhfels hfsilepl`frdl hfd sgkugf`tf elhl2
9.16= 5 9.::: + 1:: + 6: + = 5 9 » >: 9 + 1 » >:? + 6 » >: > + = Fbfepdl ?2 Fd `òefrl >:=.:8; plhfels hfsilepl`frdl hfd sgkugf`tf elhl2 >:=.:8; 5 >::.::: + =.::: + 8: + ; 5 > » >: 6 + : » >:8 + = » >: 9 + : » >: ? + 8 » >:> + ; >.9.>. Fbfrigigl
>) Vtgdgzn`hl pltf`igns hf onsf >:, mnz dn hfsileplsgigù` pldg`ùegin hf fstls f stls `òefrls2 n) 9.?6; o) >:.?61 i) >?6.91=
Ylduigù`2 9.?6; 5 9 » >: 9 + ? » >: ? + 6 » >: + ; Ylduigù`2 >:.?61 5 > » >: 8 + : » >:9 + ? » >:? + 6 » >: + 1 Ylduigù`2 >?6.91= 5 > » >: 6 + ? » >: 8 + 6 » >: 9 + 9 » >: ? + 1 » >: + =
>.8. Iunhrnhls pfrafitls >.8.>. Hfag`gigù`
Dls iunhrnhls pfrafitls sl` dls vndlrfs hf dns pltf`igns hf fxpl`f`tf hls. Fbfepdl2 18 fs u` iunhrnhl pfrafitl, plrquf fs fd vndlr hf dn pltf`ign = ? 5 = » = Fbfepdl2 Dls iunhrnhls pfrafitls ef`lrfs hf >:: sl`2 > 8 7 >1 ?6 91 87 18 => Iunhrnhls pfrafitls2 ? ? ? ? ? ? ? ? Zltf`igns2 > ? 9 8 6 1 ; = 7? >.8.?. Npdginigl`fs
Dn npdginigù` hf dls iunhrnhls pfrafitls fs dn rfslduigù` hf rnåifs iunhrnhns fxnitns.
>.6. Iuols pfrafitls >.6.>. Hfag`gigù`
Dls iuols pfrafitls sl` dls vndlrfs hf dns pltf`igns hf fxpl`f`tf trfs. Fbfepdl2 = fs u` iuol pfrafitl, plrquf fs fd vndlr hf dn pltf`ign ? 9 5 ? » ? » ? Fbfepdl2 Dls iuols pfrafitls ef`lrfs hf ?:: sl`2 > = ?; 18 >?6 Iuols pfrafitls2 9 9 9 9 Zltf`igns2 > ? 9 8 69
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n 6 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
>.6.?. Npdginigl`fs
Dn npdginigù` hf dls iuols pfrafitls fs dn rfslduigù` hf rnåifs iòogins fxnitns.
>.1. Ygk`l hf dns pltf`igns >.1.>. Onsf plsgtgvn
>) Fxpl`f`tf pnr2 fd vndlr hf dn pltf`ign fs sgfeprf plsgtgvl.
Ygk`l plsgtgvl2
Fbfepdls2 ?
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Ygk`l `fkntgvl2
Fbfepdls2 ?
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Ygk`l plsgtgvl2
Fbfepdls2 6 ? ? ? ? ? ? 9?
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Ygk`l `fkntgvl2
Fbfepdls2 ?
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Ygk`l plsgtgvl2
Fbfepdls2
?? ? ? 8
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Ygk`l `fkntgvl2
Fbfepdls2
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Kfen Gsnofd Enrå` Inonddfrl
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Zîkg`n 1 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
?) Fxpl`f`tf gepnr2 fd vndlr hf dn pltf`ign fs sgfeprf `fkntgvl.
Ygk`l plsgtgvl2
Fbfepdls2
?9 ? ? ? = ?6 ? ? ? ? ? 9?
Ygk`l `fkntgvl2
Fbfepdls2
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Fxpl`f`tf
Ygk`l hfd rfsudtnhl hf dn pltf`ign
Znr Gepnr Znr Gepnr
+ + ’
_filrhnr2 Mny quf npdginr dn rfkdn hf sgk`ls. >.1.8. Fbfrigigls
>) Ilepdftn y pl` fbfepdls2 n) Dns pltf`igns hf onsf `fkntgvn y fxpl`f`tf pnr sl`2 …… o) Dns pltf`igns hf onsf `fkntgvn y fxpl`f`tf gepnr sl`2 ……
Ylduigù`2 n) Zlsgtgvns. Fbfepdl2 ?? ? ? 8 o) @fkntgvns. Fbfepdl2 ?9 ? ? ? = ?) Indiudn dns sgkugf`tfs lpfrnigl`fs2 n) (’?)9
Ylduigù`2 ’=
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Ylduigù`2 +7 Ylduigù`2 +87 Ylduigù`2 +?; Ylduigù`2 ’>
i) (’;)? h) 99 f) (’>)
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ; hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
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Fbfepdls2 98 98 >
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Ileprlonigù`2
99 » 96 5 9=
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Zîkg`n = hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls. ?
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Ileprlonigù`2
96 2 99 5 9? ?89 2 ?; 5 7
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Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n 7 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
1 1 : 8 6
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Ileprlonigù`2
>:9 » 69 5 6:9 >.::: » >?6 5 >?6.:::
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Fbfepdls2 ? 8 ? 8 = 9
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Kfen Gsnofd Enrå` Inonddfrl
(>: » >: » >:) 2 ( 6 » 6 » 6) 5 ? » ? » ? >.::: 2 >?6 5 =
Zîkg`n >: hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
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Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n >> hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
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Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
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Ylduigù`2 (-?)7 5 -6>? Ylduigù`2 (-?)9 » (-?)? » (-?): » (-?) 5 (-?) 1 5 18 Ylduigù`2 (-?)6 5 -9? Ylduigù`2 ?-> 5 >/? Ylduigù`2 ?-> 5 >/? Ylduigù`2 ?-6 5 (>/?)6 5 >/9? Ylduigù`2 ?6 5 9? Ylduigù`2 ? Ylduigù`2 (-?)-1 » (-?)9 » (-?)8 5 -? Ylduigù`2 S(-?)9U 9 » (-?) » (-?)-8 5 (-?)7 » (-?)-9 5 (-?)1 5 18 Zîkg`n >9 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
?) _fndgzn dns sgkugf`tfs lpfrnigl`fs il` pltf`igns hf `òefrls f`tfrls2 n) (-9)> » (-9)9 » (-9)8 o) (-?;) » (-9) » (-9) ? » (-9): i) (-9)? » (-9)9 » (-9)-8 h) 9-? » 9-8 » 98 f) 6? 2 69 a) 6-? 2 69 k) 6? 2 6-9 m) 6-? 2 6-9 g) (-9)> » S(-9)9 U? » (-9)-8 b) S(-9)1 2 (-9)9 U9 » (-9): » (-9)∟8
Ylduigù`2 (-9)= 5 1.61> Ylduigù`2 (-9)9 » (-9) » (-9) ? » (-9): 5 (-9)1 5 ;?7 Ylduigù`2 -9 Ylduigù`2 9-? 5 (>/9)? 5 >/7 Ylduigù`2 6-> 5 >/6 Ylduigù`2 6-6 5 (>/6)6 5 >/9.>?6 Ylduigù`2 66 5 9.>?6 Ylduigù`2 6 Ylduigù`2 (-9)> » (-9)1 » (-9)-8 5 (-9)9 Ylduigù`2 S(-9)9 U9 » (-9): » (-9)-8 5 (-9)7 » (-9)-8 5 (-9)6 5?89
>.=. Lpfrnigl`fs il` pltf`igns >.=.>. Yuen y _fstn
Znrn plhfr suenr y rfstnr il` `òefrls fxprfsnhls ilel pltf`igns , hfof` fstnr eudtgpdginhls plr dn egsen pltf`ign. Znrn pltf`igns hf onsf >: , sg `l fs nså, hfofels mnifr quf tf`kn` dn pltf`ign hf >: fd egsel fxpl`f`tf. Yf usn` f` dn `ltnigù` igf`tåagin. Fbfepdls2 9 » >:6 + = » >: 6 5 (9 + 6) » >: 6 5 >> » >: 6 ? » >:1 ’ ; » >:6 5 ?: » >: 6 ’ ; » >: 6 5 (?: ’ ;) » >: 6 5 >9 » >: 6 >.=.?. Eudtgpdginigù`
Znrn plhfr eudtgpdginr il` `òefrls fxprfsnhls ilel pltf`igns , sf npdgin` dns prlpgfhnhfs2 n) Zrlhuitl hf pltf`igns il` dn egsen onsf. o) Zrlhuitl hf pltf`igns il` fd egsel fxpl`f`tf. >.=.9. Hgvgsgù`
Znrn plhfr hgvghgr il` `òefrls fxprfsnhls ilel pltf`igns , sf npdgin` dns prlpgfhnhfs2 n) Iligf`tf hf pltf`igns il` dn egsen onsf. o) Iligf`tf hf pltf`igns il` fd egsel fxpl`f`tf. >.=.8. Zltf`ign
Znrn indiudnr pltf`igns, sf npdgin` dns prlpgfhnhfs2 n) Zltf`ign hf u`n pltf`ign. o) Zltf`ign hf u` prlhuitl. i) Zltf`ign hf u` iligf`tf.
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n >8 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
?. _NÅIFY ?.>. Hfag`gigù` Dn rnåz `-çsgen hf u` `òefrl n fs dn lpfrnigù` g`vfrsn hf dn pltf`ign , fs hfigr, fs u` `òefrl o tnd quf o ` n y sf rfprfsf`tn plr ` n o . `
n o o` n
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n sf ddnen fxprfsgù` hf u`n rnåz l rnhgind .
n fs fd rnhgin`hl.
` fs fd å`hgif hf dn rnåz .
o fs fd vndlr l rfsudtnhl hf dn rnåz .
Nså pufs, u`n rnåz fstî alrenhn plr u` rnhgin`hl y u` å`hgif . Yf dff —dn rnåz `-çsgen hf u` `òefrl n fs gkund n o― l — dn dn rnåz hf å`hgif ` hf u` `òefrl n fs gkund gku nd n o― .
@LXN2 F` dn indiudnhlrn igf`tåagin, sf usn dn tfidn y x .
?.?. Xgpls hf rnåifs fxnitns ?.?.>. _nåz iunhrnhn
Dn rnåz iunhrnhn fxnitn fs dn lpfrnigù` g`vfrsn hf fdfvnr nd iunhrnhl . n o n o?
Fstl fs, _nhgin`hl 5 (_nåz fxnitn) ?
Dn rnåz iunhrnhn fxnitn hf u` `òefrl n fs ltrl `òefrl o quf fdfvnhl nd iunhrnhl hn fd prgefrl, y tgf`f hf rfstl :. Yf dff —dn rnåz iunhrnhn fxnitn hf u` `òefrl n fs gkund n o― . @LXN2
@l sf pl`f ? f` fd å`hgif hf dn rnåz iun`hl dn rnåz fs iunhrnhn.
Yldnef`tf dls iunhrnhls pfrafitls tgf`f` rnåz iunhrnhn fxnitn .
F` dn indiudnhlrn igf`tåagin, sf usn dn tfidn x .
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Dns rnåifs iunhrnhns hf >1 sl` 8 y ’8 , yn quf2 8 » 8 5 >1 y (-8) » (-8) (-8 ) 5 >1 @LXN2 Dls `òefrls f`tfrls `fkntgvls `l tgf`f` rnåz iunhrnhn, yn quf tlhn pltf`ign hf fxpl`f`tf pnr fs sgfeprf plsgtgvn. Fbfepdl2 >1
Dn rnåz iunhrnhn hf ’>1 `l sf pufhf indiudnr.
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n >6 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
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Yf dff —dn rnåz iunhrnhn fxnitn hf 8 fs ¾ ?―.
?.?.?. _nåz iòogin
Dn rnåz iòogin fxnitn fs dn lpfrnigù` g`vfrsn hf fdfvnr nd iuol . n o n o9
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Yldnef`tf dls iuols pfrafitls tgf`f` rnåz iòogin fxnitn .
F` dn indiudnhlrn igf`tåagin, sf usn dn tfidn 9 x . Xlhl iuol pfrafitl tgf`f u`n rnåz iòogin, + . Fbfepdl2
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Dn rnåz iòogin hf ’?; fs 9 , yn quf2 (’9) » (’9) » (’9) 5 ’?; Fbfepdls2 _nhgin`hl + 9
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Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n >1 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
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Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
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?.9. Xgpls hf rnåifs f`tfrns ?.9.>. _nåz iunhrnhn
Dn rnåz iunhrnhn f`tfrn hf u` `òefrl n fs fd enylr `òefrl f`tfrl o iuyl iunhrnhl fs ef`lr quf fd prgefrl, y `l tgf`f hf rfstl :. n o n o ? rfstl
Fstl fs, _nhgin`hl 5 (_nåz f`tfrn) ? + _fstl
@LXN2
Yg u` `òefrl `l fs iunhrnhl pfrafitl, su rnåz fs f`tfrn. Fd rfstl hf dn rnåz iunhrnhn f`tfrn hfof sfr ef`lr quf fd hlodf hf dn rnåz eîs >. _fstl 4 ? » _nåz + > Ileprlonigù`2 V`n rnåz iunhrnhn fstî ogf` indiudnhn sg iuepdf fstns hls il`hgigl`fs2 >) (_nåz)? + _fstl 5 _nhgin`hl ?) _fstl 4 ? » _nåz + > Fbfepdls2
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Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n >= hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
?.9.?. _nåz iòogin
Dn rnåz iòogin f`tfrn hf u` `òefrl n fs fd enylr `òefrl f`tfrl o iuyl iuol fs ef`lr quf fd prgefrl, y `l tgf`f hf rfstl :. n o n o 9 rfstl
Fstl fs, _nhgin`hl 5 (_nåz f`tfrn) 9 + _fstl
@LXN2 Yg u` `òefrl `l fs iuol pfrafitl, su rnåz fs f`tfrn. Ileprlonigù`2 V`n rnåz iòogin fstî ogf` indiudnhn sg iuepdf dn sgkugf`tf il`hgigù`2
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Yg fd rnhgin`hl fs plsgtgvl, fxgstf sgfeprf fd vndlr hf dn rnåz. >) Å`hgif hf dn rnåz pnr. Xgf`f sgfeprf hls slduigl`fs2 u`n plsgtgvn y ltrn `fkntgvn . Fbfepdls2 8 ? ? 8 , ?
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Kfen Gsnofd Enrå` Inonddfrl
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Zîkg`n >7 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
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?.6. Iîdiudl hf dn rnåz iunhrnhn f`tfrn Hls alrens hf indiudnr dn rnåz iunhrnhn f`tfrn2 n) Iîdiudl hf alren nprlxgenhn. o) Iîdiudl il` fd ndklrgtel. ?.6.>. Iîdiudl hf alren nprlxgenhn
Dn rnåz iunhrnhn f`tfrn hf u` `òefrl fs fd enylr f`tfrl iuyl iunhrnhl fs ef`lr quf hgiml `òefrl . Fd rfstl hf dn rnåz iunhrnhn hf u` `òefrl iunhrnhl hf su rnåz .
Fbfepdl >2
fs gkund n dn hgafrf`ign f`trf fd `òefrl y fd
89
Fd `òefrl 89 `l fs u` iunhrnhl pfrafitl, plr dl tn`tl `l tgf`f rnåz iunhrnhn fxnitn. Yg losfrvnels 1 ? 5 91 4 89 4 87 5 ; ? Dufkl, 1 fs fd enylr f`tfrl iuyl iunhrnhl fs ef`lr quf 89. Yf hgif quf 1 fs rnåz iunhrnhn f`tfrn hf 89 y sf fsirgof2 89 1
Ilel 89 - 1 ? 5 89 ’ 91 5 ;, fd rfstl hf dn rnåz iunhrnhn f`tfrn fs ;. Ylduigù`2 89
89 1 y rfstl 5 ;
1 89 1 ? ;
Yf dff —dn rnåz
iunhrnhn f`tfrn hf 89 fs 1 y su rfstl ; ―.
Ileprlonigù`2 >) 1? + ; 5 91 + ; 5 89 ?) ; 4 ? » 1 + > 5 >9
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?: hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
Fbfepdl ?2
?1
>² Ousinels hls iunhrnhls pfrafitls ifrin`ls n ?1, quf sl`2 6? 5 ?6 4 ?1 1? 5 91 0 ?1 ?² Fdfkgels fd iunhrnhl pfrafitl quf eîs sf nprlxgen plr hfonbl hf ?1, quf fs ?6. 9² Hfspuçs, indiudnels fd rfstl, quf fs dn hgafrf`ign f`trf fd `òefrl hnhl n y fd iunhrnhl hf dn rnåz f`tfrn o. ?1 ’ ?6 5 > 8² Zrlonels quf fd rfsudtnhl hf dn rnåz iunhrnhn sfn ilrrfitl, pnrn fddl, sf tgf`f quf iuepdgr quf _nhgin`hl 5 (_nåz f`tfrn) ? + _fstl. ?1 5 ?6? + > ?1 6 y rfstl 5 >
Ylduigù`2
?1
6 ?1 6 ? >
Yf dff —dn rnåz
iunhrnhn f`tfrn hf ?1 fs 6 y su rfstl > ―.
Ileprlonigù`2 >) 6? + > 5 ?6 + > 5 ?1 ?) 6 4 ? » 6 + > 5 >> ?.6.?. Iîdiudl il` fd ndklrgtel
Fbfepdl >2
>87
>² Yg fd rnhgin`hl tgf`f eîs hf hls igarns , sfpnrnels dns igarns f` krupls hf hls fepfzn`hl plr dn hfrfimn . ?² Indiudnels dn rnåz iunhrnhn (f`tfrn l fxnitn) hfd prgefr krupl hf igarns plr dn gzqugfrhn . ¼^uç `òefrl fdfvnhl nd iunhrnhl hn >< > fs u` iunhrnhl pfrafitl plrquf (> ? 5 >). Dn prgefrn igarn hf dn rnåz r nåz iunhrnhn fs > y dn ildlinels f` dn insgddn ilrrfspl`hgf`tf. ilrrfsp l`hgf`tf.
9² Fd iunhrnhl hf dn rnåz lotf`ghn sf rfstn nd prgefr krupl hf igarns quf npnrfif` f` fd rnhgin`hl.
Fd iunhrnhl hf dn rnåz > fs >, sf dl rfstnels n > y lotf`fels :.
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?> hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
8² Hftrîs hfd rfstl ildlinels fd sgkugf`tf krupl hf igarns hfd rnhgin`hl y sfpnrnels hfd `òefrl alrenhl su òdtgen igarn.
Onbnels 87, sgf`hl dn in`tghnh lpfrnodf hfd rnhgin`hl :87. 6² Hfonbl hf dn rnåz mnddnhn fsirgogels su hlodf y hgvghgels dl quf rfstn plr fd hlodf hf dn rnåz n`tfrglr . Fd iligf`tf lotf`ghl sf pl`f n dn hfrfimn hfd hlodf hf dn rnåz y fd `òefrl alrenhl sf eudtgpdgin plr fstf iligf`tf.
:8 2 ? 5 ? 4 7 Xlenels ilel rfsudtnhl ?, yn quf fs u`n ò`gin ò `gin igarn quf vn hfd : nd 7. 1² Ileprlonels quf fd `òefrl alrenhl fs g`afrglr n dn in`tghnh lpfrnodf hfd rnhgin`hl . Zufs sg muogçsfels lotf`ghl u` vndlr supfrglr n dn in`tghnh lpfrnodf hfd rnhgin`hl, mnorånels prlonhl plr dn n`tfrglr in`tghnh lpfrnodf y nså suifsgvnef`tf mnstn f`il`trnr u` vndlr g`afrglr. ?? » ? 5 88 4 87 ;² Fd iligf`tf lotf`ghl sf nþnhf n dn hfrfimn hf dn rnåz . Yuogels fd ? n dn rnåz. =² Hfspuçs, rfstnels n dn in`tghnh lpfrnodf hfd rnhgin`hl fd `òefrl mnddnhl hfonbl hf dn rnåz.
87 ’ 88 5 6 7² Zrlonels quf fd rfsudtnhl hf dn rnåz iunhrnhn sfn ilrrfitl, pnrn fddl, sf tgf`f quf iuepdgr quf _nhgin`hl 5 (_nåz f`tfrn) ? + _fstl. >87 5 >?? + 6 Ylduigù`2
>87 >87
>? y rfstl 5 6
>? >87 >? ? 6
Yf dff —dn rnåz
iunhrnhn f`tfrn hf >87 fs >? y su rfstl 6 ―.
Ileprlonigù`2 >) >?? + 6 5 >88 + 6 5 >87 ?) >? 4 ? » >? + 6 5 ?7
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?? hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
Fbfepdl ?2
=7??6
>² Yg fd rnhgin`hl tgf`f eîs hf hls igarns , sfpnrnels dns igarns f` krupls hf hls fepfzn`hl plr dn hfrfimn . ?² Indiudnels dn rnåz iunhrnhn (f`tfrn l fxnitn) hfd prgefr krupl hf igarns plr dn gzqugfrhn . ¼^uç `òefrl fdfvnhl nd iunhrnhl hn =< = `l fs u` iunhrnhl pfrafitl, pfrl fstî ileprf`hghl f`trf hls iunhrnhls pfrafitls2 8 y 7. (?? 5
Xlenels dn rnåz iunhrnhn hfd iunhrnhl pfrafitl quf sf nifrquf eîs n =, quf fs2 ? 8). Dn prgefrn igarn hf dn rnåz r nåz iunhrnhn fs ? y dn ildlinels f` dn insgddn ilrrfspl`hgf`tf.
9² Fd iunhrnhl hf dn rnåz lotf`ghn sf rfstn nd prgefr krupl hf igarns quf npnrfif` f` fd rnhgin`hl.
Fd iunhrnhl hf dn rnåz ? fs 8, 8 , sf dl rfstnels n = y lotf`fels 8. 8² Hftrîs hfd rfstl ildlinels fd sgkugf`tf krupl hf igarns hfd rnhgin`hl y sfpnrnels hfd `òefrl alrenhl su òdtgen igarn.
Onbnels 7?, sgf`hl dn in`tghnh lpfrnodf hfd rnhgin`hl 87?. 6² Hfonbl hf dn rnåz mnddnhn fsirgogels su hlodf y hgvghgels dl quf rfstn plr fd hlodf hf dn rnåz n`tfrglr . Fd iligf`tf lotf`ghl sf pl`f n dn hfrfimn hfd hlodf hf dn rnåz y fd `òefrl alrenhl sf eudtgpdgin plr fstf iligf`tf.
87 2 8 5 >?,?6 0 7 Xlenels ilel rfsudtnhl 7, yn quf sùdl pufhf sfr u`n ò`gin igarn quf vnyn hfd : nd 7. 1² Ileprlonels quf fd `òefrl alrenhl fs g`afrglr n dn in`tghnh lpfrnodf hfd rnhgin`hl . Zufs sg muogçsfels lotf`ghl u` vndlr supfrglr n dn in`tghnh lpfrnodf hfd rnhgin`hl, mnorånels prlonhl plr dn n`tfrglr in`tghnh lpfrnodf (=, ;, …) y nså suifsgvnef`tf mnstn
f`il`trnr u` vndlr g`afrglr. 87 » 7 5 8>> 4 87> ;² Fd iligf`tf lotf`ghl sf nþnhf n dn hfrfimn hf dn rnåz . Yuogels fd 7 n dn rnåz. Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?9 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
=² Hfspuçs, rfstnels n dn in`tghnh lpfrnodf hfd rnhgin`hl fd `òefrl mnddnhl hfonbl hf dn rnåz.
87? ’ 88> 5 6> 7² Onbnels fd sgkugf`tf pnr hf igarns .
Onbnels ?6, sgf`hl dn in`tghnh lpfrnodf hfd rnhgin`hl :6>?6. >:² _fpftgels dls pnsls n`tfrglrfs. 6>? 2 6= 5 =,= 0 =, prlonels plr 7.
Ilel 6=7 » 7 5 6.9:> 0 6.>?6, prlonels pr lonels plr =. Ilel 6== » = 5 8.;:8 4 6.>?6, suogels fd = n dn rnåz.
_fstnels n dn in`tghnh lpfrnodf hfd rnhgin`hl 6.>?6 fd `òefrl mnddnhl hfonbl hf dn rnåz 8.;:8.
>>² Zrlonels quf fd rfsudtnhl hf dn rnåz iunhrnhn sfn ilrrfitl, pnrn fddl, sf tgf`f quf iuepdgr quf _nhgin`hl 5 (_nåz f`tfrn) ? + _fstl. =7.??6 5 ?7=? + 8?>
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?8 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls. =7.??6 ?7= y rfstl 5 8?>
Ylduigù`2
=7.??6
?7= =7.??6 ?7=? 8?>
Yf dff —dn rnåz
iunhrnhn f`tfrn hf =7.??6 fs ?7= y su rfstl 8?>―.
Ileprlonigù`2 >) ?7=? + 8?> 5 ==.=:8 + 8?> 5 =7.??6 ?) ?7= 4 ? » ?7= + 8?> 5 >.:>; Fbfepdl 92
189
Znrn fd iîdiudl hf dn rnåz iunhrnhn hf 189, sfkugels fstls pnsls2 >² Hgvghgr fd rnhgin`hl f` krupls hf hls igarns, fepfzn`hl plr dn hfrfimn . Fd `òefrl hf krupls fs gkund nd `òefrl hf igarns hf dn rnåz iunhrnhn. 1 ?² Indiudnr dn rnåz iunhrnhn hfd prgefr krupl hf dn gzqugfrhn . Dufkl ? fs fd `òefrl hf hfif`ns hf dn rnåz 9² _fstnr hfd prgefr krupl fd iunhrnhl hf su rnåz f`tfrn . Nþnhgr n dn hgafrf`ign dns hls igarns sgkugf`tfs hfd rnhgin`hl. ?<
1 -8 ? 89
8² Eudtgpdginr plr hls dn prgefrn igarn hf dn rnåz (? » ? 5 8). Indiudnr fd ef`lr f`tfrl h tnd quf 8 h » h sf pufhf rfstnr hfd rnhgin`hl3 h sfrî dn sfku`hn igarn hf dn rnåz. 8? » ? 5 =8 3 89 » 9 5 >?7 , 88 » 8 5 >;1, 86 » 6 5 ??6 81 » 1 5 ?;1 0 ?89 1
?<
-8
86 » 6 5 ??6 ? 89
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?6 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
6² _fstnr hf dn hgafrf`ign n`tfrglr 86 » 6. Fd rfstl hf dn rnåz fs dn `ufvn hgafrf`ign. 1
?6
-8
86 » 6 5 ??6 ? 89 -? ?6 >=
Ylduigù`2
189 ?6 y rfstl 5 >= 189 ?6 189 ?6
?
Yf dff —dn rnåz
>=
iunhrnhn f`tfrn hf 189 fs ?6 y su rfstl >= ―.
Ileprlonigù`2 >) (?6) ? + >= 5 1?6 + >= 5 189 ?) >= 4 ? » ?6 + > 56> ?.6.?.>. Fbfrigigl
>) Indiudn dns sgkugf`tfs rnåifs il` fd ndklrgtel2 n)
?18
Ylduigù`2
o)
1.?61
Ylduigù`2
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?1 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
i)
;?.1;6
Ylduigù`2
?.1. Lpfrnigl`fs il` rnåifs iunhrnhns fxnitns ?.1.>. Yuen y _fstn
Znrn suenr y rfstnr rnåifs , hfof` tf`fr fd egsel å`hgif hf dn rnåz y il`tf`fr fd egsel rnhgind. Yg fs nså, sf suen` dls `òefrls quf fstî` aufrn hf fddls (ilfagigf`tfs) y fd rnhgind sf hfbn gkund. Fbfepdls2 9 ? 6 ?
? 9 6 >
89 ; ?9 ; 9 ; 8 ? >
? ; ? 9
; 9
9
;
?.1.?. Eudtgpdginigù`
Fd prlhuitl hf hls l eîs rnåifs iunhrnhns fxnitns 2 n) Fs u`n rnåz iunhrnhn fxnitn. o) Yu rnhgin`hl fs gkund nd prlhuitl hf dls rnhgin`hl hf dls anitlrfs. Fbfepdls2 91 => 1 7 68
91 =>
?6 87 6 ; 96
?6 87
91 =>
1 7 1 7 68 ?
?
?6 87 6 ; 6 ; 87 ?
?
?.1.9. Hgvgsgù`
Fd iligf`tf hf hls l eîs rnåifs iunhrnhns fxnitns 2 n) Fs u`n rnåz iunhrnhn fxnitn. o) Yu rnhgin`hl fs gkund nd iligf`tf hf dls rnhgin`hl hf dls anitlrfs. Fbfepdls2 91 2 7 1 2 9 ? 91 2 7 18 2 >1 = 2 8 ?
Kfen Gsnofd Enrå` Inonddfrl
91 2 7
18 2 >1
1 29 129 ? ?
?
? ? 18 2 >1 = 2 8 = 2 8 ?
Zîkg`n ?; hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
?.1.8. Zltf`ign hf u`n rnåz
Dn pltf`ign hf onsf u`n rnåz iunhrnhn fxnitn 2 n) Fs u`n rnåz iunhrnhn fxnitn. o) Yu rnhgin`hl fs gkund nd rnhgin`hl hf pnrtghn fdfvnhl nd fxpl`f`tf hf dn pltf`ign. Fbfepdls2 8
?68 ?6 ?6 ?6 ?6 ?6 ?6 8
1
=>1 => => => => => => => =>1
?6 =>
8
1
?.;. Dn rnåz ilel pltf`ign Dn rnåz hf u`n pltf`ign fs gkund nd rnhgin`hl fdfvnhl nd rfsudtnhl hf hgvghgr su fxpl`f`tf plr fd å`hgif hf dn rnåz. e `
=
Fbfepdls2
6 =
?
6 6 =
?
x
e
x `
>: 9
?
>:
?9
9. ZLXF@IGNY W _NÅIFY 9.>. _filrhnr n) Hfsilepl`fr dls `òefrls f` anitlrfs prgels. o) Ygepdgaginr dls `òefrls npdgin`hl dns prlpgfhnhfs ilrrfspl`hgf`tfs. i) V`n vfz lotf`ghls dls `òefrls sgepdgaginhls, usnh dn indiudnhlrn pnrn indiudnr fd `òefrl rfsudtn`tf.
8. LZF_NIGL@FY ILEOG@NHNY IL@ ZLXF@IGNY W _NÅIFY 8.>. G`trlhuiigù` Nd rfsldvfr fxprfsgl`fs il` lpfrnigl`fs ileog`nhns, hfofels tf`fr f` iuf`tn dns `lrens hfd df`kunbf entfeîtgil . Fstns `lrens nsfkurn` quf inhn fxprfsgù` tf`kn u` sgk`gaginhl y u`n slduigù` ò`gils.
8.?. _fkdns hf prglrghnh Dns rfkdns pnrn rfndgznr dns lpfrnigl`fs hf `òefrls `nturndfs l prglrghnh hf dns lpfrnigl`fs sl` dns sgkugf`tfs2 >) Fafitunels dns lpfrnigl`fs f`trf pnrç`tfsgs, ilrimftfs y ddnvfs. ?) Indiudnels dns pltf`igns y rnåifs. 9) Fafitunels dls prlhuitls (eudtgpdginigl`fs) y iligf`tfs (hgvgsgl`fs) hf gzqugfrhn n hfrfimn. 8) _fndgznels dns suens y rfstns. @LXN2 Fs geplrtn`tf rfspftnr fd lrhf` hf dns lpfrnigl`fs pnrn lotf`fr fd rfsudtnhl ilrrfitl.
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?= hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
8.9. Xgpls hf lpfrnigl`fs ileog`nhns 8.9.>. Lpfrnigl`fs ileog`nhns il` pltf`igns y rnåifs iunhrnhns fxnitns
Znrn rfsldvfrdns, prgefrl fafitunrfels dns pltf`igns y dns rnåifs iunhrnhns, il` dl iund `ls qufhnrfels il` lpfrnigl`fs ileog`nhns hf `òefrls f`tfrls y sfkugels fd lrhf` hf dns egsens. @LXN2 F` dns rnåifs iunhrnhns, iunhr nhns, mny hls slduigl`fs, u`n + y ltrn ’ . Yùdl usnrfels dn + . Fbfepdls2 n) (-9)62 (-9)9 +
>88 » 6? 5 7 + >? » ?6 5 7 + 9:: 5
(-9)6 2 (-9)9 5 (-9)? 5 7 1?6 » ( 6 ’ 99 ) + 8: +
o)
1?6
>88
6? 5 ?6
5 >?
>?> 5 ?6 » (-??) + > +
6 ’ 99 5 6 ’ ?; 5 -??
5 ?6
9:7
>> 5 -66: + > + >> 5 -69=
8: 5 >
>?> 5 >>
8.9.?. Lpfrnigl`fs ileog`nhns il` pltf`igns y rnåifs iòogins fxnitns
Znrn rfsldvfrdns, prgefrl fafitunrfels dns pltf`igns y dns rnåifs iòogins, il` dl iund `ls qufhnrfels il` lpfrnigl`fs ileog`nhns hf `òefrls f`tfrls y sfkugels fd lrhf` hf dns egsens. @LXN2 F` dn rnåifs iòogins, mny u`n slduigù` + ù - . Fbfepdls2 n)
9
989 » ( >: ? ’ =? ) + 9
989
9
= 2 8: 5 ; » 91 + (-?) 2 > 5 ?6? - ? 5 ?6:
>:? ’ =? 5 >:: ’ 18 5 91
5;
8: 5 >
9
= 5 -?
o) >:9 + ;? + 9 ?; 2 (’1): 5 >.::: + 87 + ( ’9) 2 > 5 >.:87 ’ 9 5 >.:81 9
?; 5 ’9
(’1): 5 >
8.9.9. Lpfrnigl`fs ileog`nhns il` pltf`igns y rnåifs fxnitns
Fbfepdls2 n)
>:.::: ’
9
;?7 » ?9 2 9 +
9
>?6 » 6-> 5 >:: ’ 7 » = 2 9 + ( ’6) 2 6 5 >:: ’ ;? 2 9 ’ > 5
5 >:: ’ ?8 ’ > 5 ;6 >:.::: 5 >::
o) =9 ’
18 2 ?? + 18 5 =
9
9
;?7 5 7
9
>?6 5 -6
18 2 8-> 5 6>? ’ = 2 8 + 8 » 8 5 6>? ’ ? + >1 5 9
6?1
18 5 8
8.8. Fbfrigigls >) _fndgzn dns sgkugf`tfs lpfrnigl`fs ileog`nhns tf`gf`hl f` iuf`tn su prglrghnh2 n) ? + 6 » (? » 9)¹
Ylduigù`2 ? + 6 » (1)¹ 5 ? + 6 » ?>1 5 ? + >.:=: 5 >.:=?
o) ; » 9 + S1 + ? » (? 9 2 8 + 9 » ?) ’ ; »
8U+729
Ylduigù`2 ?> + S1 + ? » (? 9 2 ?? + 1) ’ >8U + 9 5 5 ?> + S1 + ? » (? + 1) ’ >8U + 9 5 ?> + (1 + ? » = ’ >8) + 9 5 5 ?> + (1 + >1 ’ >8) + 9 5 ?> + = + 9 5 9? Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n ?7 hf 9:
Xfen 82 Zltf`igns y rnåifs hf `òefrls f`tfrls.
?) _fndgzn dns sgkugf`tfs lpfrnigl`fs il` `òefrls f`tfrls2 n) (9 - =) + S6 - (-?)U o) i) h) f)
Ylduigù`2 -6 + S6 + ?U 5 -6 + ;5 ? 6 - S1 - ? - (> - =) - 9 + 1U + 6 Ylduigù`2 6 - S1 - ? - (-;) - 9 + 1U + 6 5 5 6 - S1 - ? + ; - 9 + 1U + 6 5 6 - >8 + 6 5 ∟8 7 2 S1 2 (- ?)U Ylduigù`2 7 2 (-9) 5 -9 S(-?)6 - (-9)9U? Ylduigù`2 S-9? - (-?;)U 5 S-9? + ?;U? 5 (-6)? 5 ?6 (6 + 9 » ? 2 1 - 8 ) » (8 2 ? - 9 + 1) 2 (; - = 2 ? - ?) ? Ylduigù`2 (6 + 1 2 1 - 8 ) » (8 2 ? - 9 + 1) 2 (; - = 2 ? - ?) ? 5
5 (6 + > - 8 ) » (? - 9 + 1) 2 (; - 8 - ?) ? 5 5 ? » 6 2 > ? 5 ? » 6 2 > 5 >: 2 > 5 >: a) S(>; - >6)9 + (; - >?)?U 2 S(1 - ;) » (>? - ?9)U Ylduigù`2 S(?) 9 + (-6)?U 2 S(->) » (->>)U 5 5 (= + ?6) 2 S(->) » (->>)U 5 (= + ?6) 2 >> 5 99 2 >> 5 9 9) _fndgzn dns sgkugf`tfs lpfrnigl`fs il` `òefrls f`tfrls2 n) (; - ? + 8) - (? - 6) Ylduigù`2 7 - (-9) 5 7 + 9 5 >? o) > - (6 - 9 + ?) - S6 - (1 - 9 + >) - ?U
Ylduigù`2 > - 8 - S6 - 8 - ?U 5 > - 8 ’ (->) 5 > ’ 8 + > 5 -?
i) ->? » 9 + >= 2 (->? 2 1 + =)
Ylduigù`2 -91 + >= 2 (-? + =) 5 -91 + >= 2 1 5 -91 + 9 5 -99 h) S(-?)6 » (-9)?U 2 (-?)? Ylduigù`2 (-9? » 7) 2 8 5 -?== 2 8 5 -;? f) 1 + {8 - (>; - (8 » 8)U + 9} - 6 Ylduigù`2 1 + {8 - S>; - >1U + 9} - 6 5 1 + {8 - > + 9} - 6 5 51+1-65; a) ?9 + >: 2 ? + 6 » 9 + 8 - 6 » ? - = + 8 » ? ? - >1 2 8 Ylduigù`2 = + >: 2 ? + 6 » 9 + 8 - 6 » ? - = + 8 » 8 - >1 2 8 5 5 = + 6 + >6 + 8 - >: - = + >1 - 8 5 ?1
Kfen Gsnofd Enrå` Inonddfrl
Zîkg`n 9: hf 9:
