Practica 3
August 5, 2022 | Author: Anonymous | Category: N/A
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Mhcgkakñg mh S`rk`ndhs @dh`terk`s Mhcgkr ug` v`rk`ndh `dh`terk` hg ug hxphrklhgte `dh`terke aegsksth hg `seak`r ug v` v`de derr gul gulërk ërkae ` a`m` sua suahse hse hdhl hdhlhg hgtt`d mhd hx hxph phrrklhg klhgtte. Kg Kgth thrh rhs` s` ugm`lhgt`dlhgth `skig`r pren`nkdkm`mhs ` mkafes v`derhs gulërkaes. Cerl`dlhgth, m`mes ug hxphrklhgte `dh`terke θ, ug hsp`ake luhstr`d Ϋ, ug` `lkdk` mh suahses hg Ϋ, aeg ug` pren`nkdkm`m R, mkrhles quh ug` ugakñg? V? Ϋ↞ ^, hs ug` v`rk`ndh `dh`terk` sk V-0(-, x\ < {ϋ ∆ Ϋ? V (ϋ) ≭ x} hs ug suahse
Hst` mhcgkakñg `shiur` quh sh` peskndh rh`dkz`r aàdaudes mh pren`nkdkm`mhs senrh suahses mhcgkmes hg ^ ` p`rr mh v`derhs mh d`s v`rk`ndhs `dh`terk`s. Hg ea`skeghs des suahses hdhlhgt`dhs mh ug hxphrklhgte `dh`terke seg gÿlhres, hg hst` sktu`akñg hses gÿlhres aekgakmhg aeg hd v`der mh ug` v`rk`ndh `dh`terk`.
Hohlpde 0 θ < sh hdkih ug kgmkvkmue `d `z`r mh ug` pend`akñg y sh rhikstr` au`gtes `ðes aelpdhtñ mh d` hsauhd` shaugm`rk` Ϋ < {2,0,>,1,=,8} Quahses < au`dqukhr sunaegougte mh Ϋ V? Ϋ↞ ^ d` ugakñg kmhgm`m S`derhs peskndhs mh V < {2, 0,>,1,=,8} < ^V µHg quë a`ses hs r`zeg`ndh `skig`r hqukpren`nkdkm`m ` des v`derhs peskndhs mh d` v`rk`ndh `dh`terk` V5
Luaf`s vhahs des suahses hdhlhgt`dhs mh ug hxphrklhgte `dh`terke seg vhaterhs, hg hst` sktu`akñg pemhles mhcgkr ug` e làs v`rk`ndhs `dh`terk`s hg mkafe hxphrklhgte y `skig`r pren`nkdkm`mhs ` sus v`derhs.
Hohlpde > θ < sh hdkihg `d `z`r y aeg rhpeskakñg 1 `raudes mh ug deth quh aeghgh 8% mh `raudes mhhatueses. Ϋ < {ϋ / ϋ Ѝ (MMM, NMM, MNM, MMN, NNM, NMN, MNN, NNN)} Quahses < au`dqukhr sunaegougte sunaegougte mh Ϋ V? Ϋ↞ ^ V (ϋ) < a`gm`m mh mhhatueses hg ϋ S`derhs peskndhs mh V < {2,0,>,1} < ^V R(V } < R(NMM, R(NMM, MNM, MNM, MMN)< 1 (2.;8)0 (2.28)> R(V µAuàd hs d` pren`nkdkm`m mh enthghr ` de sule ug mhhatuese5 R (V ≭ 0) < R(V `raudes mhhatueses5 R (V ≭ >) < 0- R (V
S`rk`ndhs `dh`terk`s Mksarht`s Xg` v`rk`ndh `dh`terk` sh mkrà mksarht` sk hd aegougte mh v`derhs quh tel` hs ug aegougte gulhr`ndh, hs mhakr, quh sede puhmh tel`r uges v`derhs aegarhtes. Mkafe aegougte de mhget`rhles per? {x0, x>, x1,…, xj}. ]em` v`rk`ndh `dh`terk` mksarht` hgh `seak`m` ug` ugakñg mh pren`nkdkm`m, quh, ` a`m` v`der, dh l`ra` d` pren`nkdkm`m mh quh d` v`rk`ndh telh mkafe v`der. Hst` pren`nkdkm`m vkhgh ` oui`r hd lksle p`phd quh d` rhauhgak` rhd`v`.
Mkstrknuakñg mh S`rk`ndhs mksarht`s Xg` mkstrknuakñg mksarht` mhsarknh d` pren`nkdkm`m mh eaurrhgak` mh a`m` v`der mh ug` v`rk`ndh `dh`terk` mksarht`. Xg` v`rk`ndh `dh`terk` mksarht` hs ug` v`rk`ndh `dh`terk` quh hgh v`derhs aegt`ndhs, t`dhs aele ug` dkst` mh hgthres ge ghi`ves. Aeg ug` mkstrknuakñg mh pren`nkdkm`m mksarht`, a`m` v`der peskndh mh d` v`rk`ndh `dh`terk` mksarht` puhmh hst`r `seak`me aeg ug` pren`nkdkm`m mksgt` mh ahre. Rer de t`gte, ug` mkstrknuakñg mh pren`nkdkm`m mksarht` suhdh rhprhshgt`rsh hg erl` t`nud`r.
Hohlpde mhd gÿlhre mh quho`s mh adkhgths
Aeg ug` mkstrknuakñg mksarht`, ` mkhrhgak` mh ug` mkstrknuakñg aeggu`, usthm puhmh a`daud`r d` pren`nkdkm`m mh quh V sh` hx`at`lhgth kiu`d ` `diÿg v`der. Rer hohlpde, puhmh udkz`r d` mkstrknuakñg mksarht` mh Reksseg p`r` mhsarknkr hd gÿlhre mh quho`s mh adkhgths hg ug mì`. Qupegi`les quh hd gÿlhre prelhmke mh quho`s per mì` hs 02 y usthm mhsh` s`nhr d` pren`nkdkm`m mh rhaknkr 8, 02 y 08 quho`s mh adkhgths hg ug mì`.
x
R (V < x)
8
2.219611
02
2.0>800
08
2.21=906
Xsthm t`lnkëg puhmh vksu`dkz`r ug` mkstrknuakñg mksarht` hg ug` iràca` mh mkstrknuakñg p`r` vhr d`s pren`nkdkm`mhs hgtrh des r`gies.
Iràca` mh mkstrknuakñg mhd gÿlhre mh quho`s mh adkhgths
D`s n`rr`s selnrh`m`s hg hsth hohlpde rhprhshgt`g hd gÿlhre mh eaurrhgak`s au`gme d`s quho`s mk`rk`s mh des adkhgths seg 08 e làs. D` `dtur` mh d`s n`rr`s sul` 2.261=3: per de t`gte, d` pren`nkdkm`m mh quh hd gÿlhre mh dd`l`m`s per mì` sh` 08 e làs hs 6.18%.
µPuë hs ug` mkstrknuakñg mh pren`nkdkm`m Mksarht`5 Xg` mkstrknuakñg mh pren`nkdkm`mhs p`r` ug` v`rk`ndh `dh`terk` mksarht` hs ug dkst`me lutu`lhgth hxaduyhgth mh temes des rhsudt`mes gulërkaes peskndhs p`r` hs` v`rk`ndh `dh`terk` t`d quh ug` pren`nkdkm`m hsphaìca` mh eaurrhgak` sh `seak` aeg a`m` rhsudt`me. Hd v`der hsphr`me mh ug` v`rk`ndh `dh`terk` mksarht` hs ug prelhmke pegmhr`me mh temes des peskndhs rhsudt`mes, megmh d`s pegmhr`akeghs seg d`s pren`nkdkm`mhs `seak`m`s aeg a`m` uge mh des rhsudt`mes.
Mñgmh? Vk < k-ëskle rhsudt`me mh V, d` v`rk`ndh mksarht` mh kgthrës. R(Vk) < pren`nkdkm`m mh eaurrhgak` mhd k-ëskle rhsudt`me mh V D` v`rk`gz` mh ug` v`rk`ndh `dh`terk` mksarht` (s >) sh mhcgh aele hd prelhmke pegmhr`me mh des au`mres mh d`s mkhrhgak`s hgtrh a`m` rhsudt`me peskndh y su lhmk` (des phses seg d`s pren`nkdkm`mhs mh des rhsudt`mes peskndhs).
Mñgmh?
Vk < k-ëskle rhsudt`me mh V, d` v`rk`ndh mksarht` mh kgthrës. R(Vk) < pren`nkdkm`m mh eaurrhgak` mhd k-ëskle rhsudt`me mh V
Mkstrknuakñg pren`nkdìsa` Nkgelk`d d` mkstrknuakñg nkgelk`d hs ug` mkstrknuakñg mh pren`nkdkm`m mksarht` quh kgmka` hd gÿlhre mh ëxktes `d rh`dkz`r ug` shauhgak` mh g hgs`yes h gs`yes kgmhphgmkhgths hgtrh sì, aeg ug` pren`nkdkm`m co` (p) mh eaurrhgak` mhd ëxkte hgtrh hses hgs`yes. Xg` v`rk`ndh mksarht` hs `quhdd` quh sede puhmh tel`r ug gÿlhre cgkte mh v`derhs hgtrh mes v`derhs au`dhsqukhr` mh ug` a`r`athrìsa`. D` ugakñg mh pren`nkdkm`m mh d` mkstrknuakñg nkgelk`d, t`lnkëg mhgelkg`m` ugakñg mh d` mkstrknuakñg mh Nhrgeuddk, sh hxprhs` aeg d` ñrlud`?
Megmh? g hs hd gÿlhre mh pruhn`s e hgs`yes. x hs hd gÿlhre hsphr`me mh ëxktes. p hs d` pren`nkdkm`m perahgtu`d mh ëxkte. q hs d` pren`nkdkm`m perahgtu`d mh r`a`se, quh sh enhgh skhlprh f`akhgme 0 ‑ p. Get`? F`y quh enshrv`r quh d`s pren`nkdkm`mhs mh ëxkte y r`a`se seg aelpdhlhgt`rk`s:: hs mhakr, q < 0 ‑ p y p < 0 ‑ q, per de aelpdhlhgt`rk`s d e quh n`st` s`nhr ug` mh hdd`s p`r` a`daud`r d` etr`. Hd aehcakhgth nkgelk`d
, t`lnkëg dd`l`me gÿlhre aelnkg`terke, sh puhmh hxprhs`r aele gAx. Hd aàdaude mhd aehcakhgth nkgelk`d sh enhgh aeg d` ñrlud`
@d kgadukr g! kgaerper`les hd aegahpte mh ugakñg ugakñg `aterk`d, hd quh sh puhmh vhr hg C`aterk`d e Cugakñg `aterk`d. @fer`, vh`les `diuges hohlpdes e hohrakakes quh ges phrlkràg hgthgmhr lhoer hst` ephr`terk` l`thlàa` dd`l`m` mkstrknuakñg nkgelk`d.
Hohlpde Hd 62 % mh ug ugkvhrse pethgak`d f` vkste ug hxktese preir`l` mh thdhvkskñg. @d ougt`rsh = `lki`s `cakeg`m`s `d thl`? µAuàd hs d` pren`nkdkm`m mh quh > `lki`s mhd irupe f`y`g vkste hd preir`l`5
M`tes quh thghles? g < = (tet`d mh d` luhstr`) p < 2,6 (perahgt`oh ugkt`rke mh ëxkte) sh enhgh ` p`rr mhd 62% aegeakme q < 2,> (perahgt`oh ugkt`rke mh r`a`se) (sh enhgh f`akhgme 0 ‑ 2,6 < 2,> x < > (`lki`s quh f`y`g vkste hd preir`l`) @pdkquhles guhstr` ñrlud` aegeakm` y pegi`les des m`tes quh thghles?
A`daudhles hd aehcakhgth nkgelk`d?
[ f`ahles hd aàdaude?
De quh hxprhs`me aele perahgt`oh ges mkah quh f`y 08,13 % mh pesknkdkm`mhs mh quh, hgtrh d`s = `lki`s, > f`y`g vkste hd preir`l`. Kl`ikghles quh ug 62% mh phrseg`s hg hd lugme f`g vkste hd p`rme mh d` cg`d mhd ÿdle ÿd le lug lugmk` mk`dd mh utned utned.. ]r`s ]r`s hd hvhgte hvhgte,, = `lkies `lkies sh rhÿghg rhÿghg ` aegvhr aegvhrs`r s`r,, µAuàd µAuàd hs d` pren`nkdkm`m mh quh 1 mh hddes f`y`g vkste5 Mhcg`les d`s v`rk`ndhs mhd hxphrklhgte? g
< = (hs h hdd tet`d mh d` luhstr` quh thghles)
x < gÿlhre mh ëxktes, quh hg hsth a`se a`se hs kiu`d ` 1, m`me quh nusa`les d` pren`nkdkm`m pren`nkdkm`m mh quh 1 mh des = `lkies de f`y`g vkste. p
< pren`nkdkm`m mh ëxkte (2,6)
q
< pren`nkdkm`m pren`nkdkm`m mh r`a`se (2,>). Hsth rhsudt`me rhsudt`me sh enhgh `d rhst`r 0-p.
]r`s mhcgkr tem`s guhstr`s v`rk`ndhs, sklpdhlhgth sustukles hg d` erlud`.
Hd gulhr`mer mh d` `aterk`d sh enthgmrì` mh ludpdka`r =*1*>*0 < >= y hg hd mhgelkg`mer thgmrì`les 1*>*0*0 < 3. Rer de t`gte, hd rhsudt`me mh d` `aterk`d shrì` >=/3 (m`me quh =-1 < 0 y au`dqukhr gÿlhre hdhv`me ` 0 hs hd lksle). Rer t`gte, guhstre rhsudt`me cg`d shrì`? =*2,80>*2,> < 2,=2;3. Qk ludpdka`les per 022 thghles quh f`y ug` pren`nkdkm`m mhd =2,;3% mh quh 1 mh des = `lkies f`y`g vkste hd p`rme mh d` cg`d mhd lugmk`d.
Aele hd`ner`r ug` mkstrknuakñg hst`mìsa` nkgelk`d Aegskmhrhles rhphakeghs kgmhphgmkhgths mh ug hxphrklhgte `dh`terke aeg mes peskndhs rhsudt`mes rhsudt`mes ` des au`dhs ges rhhrkrhle rhhrkrhless ihgërka`l ihgërka`lhgth hgth aele —ëxkte“ y —cr`a`se“ . Hd ëxkte eaur eaurrh rh aeg ug` pren`nk pren`nkdkm dkm`m `m p y hd r`a`se, per t`gte, aeg ug`
pren`nkdkm`m q < 0-p. Hg hsth aegthxte, kgthrhs` hstumk`r hd gÿlhre mh ëxktes hg hst`s rhphakeghs mhd hxphrklhgte `dh`terke y, p`r` hdde, sh mhcgh d` skiukhgth v`rk`ndh `dh`terk`, V < —Gÿlhre mh ëxktes hg g hgs`yes kgmhphgmkhgths aeg pren`nkdkm`m mh ëxkte aegst`gth p“. p“.
Hgtegahs mhakles quh V skiuh ug` mkstrknuakñg nkgelk`d mh p`ràlhtres g y p, y de rhprhshgt`les aele V ↞N ↞N (g, p) p). D` mkstrknuakñg nkgelk`d hs ug` mkstrknuakñg mh pren`nkdkm`m mksarht`, lkmh hd gÿlh gÿ lhre re mh ëx ëxkt ktes es hg ug` ug` shau shauhg hgak ak` ` mh g hgs hgs`ye `yess kgmhph kgmhphgmk gmkhgt hgths, hs, aeg ug` pren`nkdkm`m co` p mh eaurrhgak` mh ëxktes hgtrh des hgs`yes. Hs hvkmhgth quh des peskndhs v`derhs quh puhmh tel`r d` v`rk`ndh `dh`terk` (e, de quh hs de lksle, hd gÿlhre mh hgs`yes hxkteses mh des quh sh rh`dkz`g) seg des v`derhs aelprhgmkmes hgtrh 2 y g. @ aeggu`akñg, v`les ` mhcgkr y a`daud`r? 0.
D` pr pren`nkdkm`m mh mh qu quh d` d` v` v`rk`ndh `d `dh`terk` V telh a`m` v`der aegarhte e, hqukv`dhgthlhgth, hd v`der mh d` cugakñg l`s` mh pren`nkdkm`m hg hg a`m` uge mh hstes pugtes
>.
D` pren pren` `nkdk nkdkm` m`m m quh quh `aulu ulud` a` a`m` m` uge mh de dess v` v`de derh rhss mh mh d` d` v` v`rk` rk`ndh ndh `dh `dh` `te terk rk` ` V , hs mhakr, hd v`der mh d` cugakñg mh mkstrknuakñg mkstrknuakñg hg a`m` pugte mh d` v`rk`ndh
1.
Au`gdhs mh d` mkstrknuakñg nkgelk`d
=.
S`derhs ` `ddh`terkes mh mh d` d` mk mkstrknuakñg nk nkgelk`d.
Rrepkhm`mhs mh d` mkstrknuakñg nkgelk`d R`r` quh ug` v`rk`ndh `dh`terk` sh aegskmhrh quh skiuh ug` mkstrknuakñg nkgelk`d, hgh quh aulpdkr d`s skiukhgths prepkhm`mhs?
Hg a`m` hgs`ye, hxphrklhgte e pruhn` sede seg peskndhs mes rhsudt`mes (ëxkte e r`a`se) D` pren`nkdkm`m mh ëxkte f` mh shr aegst`gth. Hst` sh rhprhshgt` lhmk`gth d` dhtr` R. D` pren`nkdkm`m mh quh s`di` a`r` `d d`gz`r ug` leghm` hs mh 2.8 y hst` hs ae aegs gst` t`gt gth h m` m`me me quh quh d` legh leghm` m` ge a` a`ln lnk` k` hg a`m` a`m` hx hxph phrk rklh lhgt gte e y d`s d`s pren`nkdkm`mhs mh s`a`r a`r` hs aegst`gth D` pren`n pren`nkdk kdkm`m m`m mh r`a`s r`a`se e f` mh shr t` t`lnk lnkëg ëg aegst aegst`gt `gth. h. Hst` Hst` sh rhprhs rhprhshgt hgt` ` lhmk`g lhm k`gth th d` dhtr` dhtr` q f` mh eaurrkr. Qk ge sh hs felnrh sh hs luohr D` v`rk`ndh `dh`terk` quh skiuh ug` mkstrknuakñg nkgelk`d sh suhdh rhprhshgt`r aele V~ (G, R). G rhprhshgt` hd gÿlhre mh hgs`yes e hxphrklhgtes y p d` pren`nkdkm`m mh ëxkte.
Lhmk` e v`der hsphr`me y mhsvk`akñg hstàgm`r mh ug` mkstrknuakñg Nkgelk`d D` lhmk` mh d` mkstrk mkstrknuakñ nuakñg g nkge nkgelk`d lk`d hs ¸< gp sñde p`r` mkstrk mkstrknuakñ nuakñg g nkge nkgelk`d. lk`d. > D` v`rk`gz` mh d` mkstrknuakñg nkgelk`d hs ` < gpq y d` mhsvk`akñg hstàgm`r ρ <
D`s lhmkm`s mh v`rk`akñg làs aelughs seg d` v`rk`gz` y su r`ìz au`mr`m` e sh`, d` mhsvk`akñg hstàgm`r, d` au`d lkmh d` v`rk`nkdkm`m prelhmke mh d`s v`rk`akeghs au`mràtka`s mh d` lhmk`.
Hohlpde @) 322 phrseg` kgvkt`m` ` ug` chst` aeg pren`nkdkm`m më `sksr mhd 2.12 ¸ < 322(2.12) < 062 ρ > < 322(2.12) (2.92) 3 ρ > N) @raudes mhhatueses mhhatueses hg ug` luhstr` mh g < 322 p`rths më l`qukg`rk` aeg pren`nkdkm`m mh mhhate mh 2.2= ¸ < 322(2.2=) < >= ρ > < 322(2-2=) (2.;3) < >1.2= ρ < =.6 A) 622 hstumk`gths quh ge dhs iust` d` aelkm` quh skrvhg hg d` a`hthrì` mh d` ugkvhrskm`m aeg hd 2.38 mh pren`nkdkm`m mh ge iust`rdhs. ¸ < 622(2.38) < 8>2 ρ > < 622(2.38) (2.18) < 06> ρ < 01.=;
Mkstrknuakñg mh Reksseg Hst` mkstrknuakñ mkstrknuakñg g hs ug` mh d`s làs klpert`gt klpert`gths hs mkstrknuak mkstrknuakeghs eghs mh v`rk`ndh v`rk`ndh mksarht`. Qus prkgakp`dhs `pdka`akeghs f`ahg rhhrhgak` ` d` lemhdkz`akñg mh sktu`akeghs hg d`s quh ges kgthrhs` mhthrlkg`r hd gÿlhre mh fhafes mh akhrte pe quh sh puhmhg premuakr hg ug kgthrv`de mh hlpe e mh hsp`ake, n`oe prhsupuhstes mh `dh`terkhm`m y akhrt`s akraugst`gak`s rhstrkav`s. Etre mh sus uses rhauhgths hs d` aegskmhr`akñg dìlkth mh preahses mkaetñlkaes rhkthr`mes ug ir`g gÿlhre mh vhahs sk d` pren`nkdkm`m mh enthghr ug ëxkte hs luy phquhð`. Rreahse hxphrklhgt`d mhd quh sh puhmh f`ahr mhrkv`r Hst` Hst ` mkstr mkstrknu knuakñ akñg g sh puhmh puhmh f`ahr f`ahr mhrkv` mhrkv`rr mh ug preahs preahse e hxphrk hxphrklhg lhgt` t`dd mh enshrv`akñg hg hd quh thgi`les d`s skiukhgths a`r`athrìsa`s?
Qh enshrv` d` rh`dkz`akñg mh fhafes mh akhrte pe mur`gth ug akhrte phrkeme mh hlpe e ` de d`rie mh ug hsp`ake mh enshrv`akñg
Des fhafes ` enshrv`r enshrv`r hghg g`tur`dhz g`tur`dhz` ` `dh`terk`: `dh`terk`: puhmhg premuakrsh premuakrsh e ge mh ug` l`ghr` ge mhthrlkgìsa`. D` pren`nkdkm`m mh quh sh premuza`g ug gÿlhre x mh ëxktes hg ug kgthrv`de mh `lpdktum t ge mhphgmh mhd erkihg mhd kgthrv`de (@ugquh, sì mh su `lpdktum) D` pren pren`n `nkdk kdkm` m`m m mh quh quh eaur eaurr` r` ug fhaf fhafe e hg ug kgth kgthrv rv`d `de e kgcg kgcgkt ktës ëskl kle e hs pràaa`lhgth preperakeg`d ` d` `lpdktum mhd kgthrv`de. D` pr pren en`n `nkd kdkm km`m `m mh quh quh sh pr prem emuz uza` a`g g > e làs làs fh fhaf afes es hg ug kgth kgthrv rv`d `de e kgcgktëskle hs ug kgcgktëskle mh ermhg suphrker ` mes. Hg aegshauhgak`, hg ug kgthrv`de kgcgktëskle pemràg premuakrsh E e 0 fhafe, phre guga` làs mh uge ¹ Qk hg hst`s akraugst`gak`s `dh`terkz`mes mh erl` quh d` v`rk`ndh `dh`terk` V skigkcquh e mhskigh hd "gÿlhre mh fhafes quh sh premuahg hg ug kgthrv`de mh hlp h lpe e e mh hsp` hsp`ak ake" e",, d` v` v`rk rk`n `ndh dh V sh mkst mkstrk rknu nuyh yh aeg aeg ug` ug` mkst mkstrk rknu nuak akñg ñg mh
p`ràlhtre d. @sì ?
Hd p`ràlhtre mh d` mkstrknuakñg hs, hg prkgakpke, hd `ater mh preperakeg`dkm`m p`r` d` pren`nkdkm`m mh ug fhafe hg ug kgthrv`de kgcgktëskle. Qh dh suhdh mhskig`r aele p`ràl p`r àlhtr htre e mh kgthgs kgthgskm` km`m, m, `ugquh `ugquh làs t`rmh vhrhle vhrhless quh sh aerrhs aerrhspeg pegmh mh aeg hd gÿlhre lhmke mh fhafes quh a`nh hsphr`r quh sh premuza`g hg ug kgthrv`de ugkt`rke (lhmk` mh d` mkstrknuakñg): y quh t`lnkëg aekgakmh aeg d` v`rk`gz` mh d` mkstrknuakñg. Rer etre etre d`me hs hvkmhgt hvkmhgth h quh sh tr`t` tr`t` mh ug lemhde lemhde mksar mksarhte hte y quh hd a`lpe a`lpe mh v`rk`akñg mh d` v`rk`ndh shrà hd aegougte mh des gÿlhre g`tur`dhs, kgadukme hd ahre? .
Cerlud` mh Reksseg
]herhl` mh `mkakñg.
D` mkstrknuakñg mh Reksseg vhrkcka` hd therhl` mh `mkakñg p`r` hd p`ràlhtre
.
D` v` v`rk rk`n `ndh dh su sul` l` mh me mess e làs làs v` v`rk rk`n `ndh dhss kg kgmh mhph phgm gmkh khgt gths hs qu quhh thgi` thgi`g g ug ug`` mkstrknuakñ mkstrk nuakñg g mh Reksseg Reksseg mh mkstkgtes mkstkgtes p`ràlhtres p`ràlhtres (mh mkstkgt`s lhmk`s) sh mkstrknukrà, t`lnkëg t`lnk ëg aeg ug` mkstrknuakñ mkstrknuakñg g mh Reksseg aeg p`ràlhtre p`ràlhtre d` sul` mh des p`ràlhtres (aeg lhmk`, d` sul` mh d`s lhmk`s)? Hg hchate? Qh`g x h y mes v`rk`ndhs `dh`terk`s quh sh mkstrknuyhg aeg mes mkstrknuakeghs mh Reksseg mh mkstkgtes p`ràlhtres skhgme `mhlàs x h y kgmhphgmkhgths
@sì
h Mhnhles pren`r quh d` v`rk`ndh _< x+y shiukrà ug` Reksseg aeg p`ràlhtre kiu`d `
d` sul` mh des mh `ln`s?
Hg n`sh ` d`s C.I.L p`r` V
R`r` [
Mh l`ghr` quh d` cugakñg ihghr`trkz mh lelhgtes mh _ shrà hd premuate mh `ln`s y` quh seg kgmhphgmkhgths ?
Qkhgme
d`
C.I.L
mh
ug`
Reksseg
Hohlpdes mh d` utkdkm`m
D` ddhi`m` mh ug adkhgth `d ghieake mur`gth ug` fer` D`s dd`l`m`s thdhñgka`s quh sh rhaknhg hg ug mì` Des mhhates hl l`gu`atur` mh p`phd per a`m` lhtre premuakme Des hgv`shs ddhg`mes uhr` mh des dklkths per a`m` 022 i`deghs mh premuate thrlkg`me Gÿlhre mh `dd`s hg d` suphrcakh mh ug` ahràlka` rhat`giud`r rhat`giud`r Gÿlhre mh n`athrk`s hg ug vedulhg mh `iu` Gÿlhre mh `aakmhgths mh tr`n`oe quh eaurrhg hg ug` ànrka` mur`gth ug` shl`g`
Lhmk` e v`der hsphr`me y mhsvk`akñg hstàgm`r mh d` mkstrknuakñg mh Reksseg
Hohlpdes? 0. Qk ug n`gae rhaknh hg prelhmke 3 afhquhs skg egme per mì`, µauàdhs seg d`s pren`nkdkm`mhs mh quh rhakn`, `) au`tre afhquhs skg egme hg ug mì` m`me, n) 02 afhquhs skg egmes hg au`dqukhr` mh mes mì`s aegshauves5 Qeduakñg? `) x < v`rk`ndh quh ges mhcgh hd gÿlhre gÿlhre mh afhquhs skg skg egme quh ddhi`g `d n`gae hg ug mì` au`dqukhr` < 2, 0, >, 1, …, hta., hta. d < 3 afhquhs skg egme per mì` h < >.906
n) x< v`rk`ndh quh ges mhcgh hd gÿlhre mh afhquhs skg egme egme quh ddhi`g `d n`gae hg mes mì`s aegshauves < 2, 0, >, 1, ......, hta., hta. d < 3 x > < 0> afhquhs skg egme hg prelhmke quh ddhi`g `d n`gae hg mes mì`s aegshauves Get`? d skhlprh mhnh mh hst`r hg ugakñg mh x skhlprh e, mkafe mh etr` erl`, mhnh —f`nd`r“ mh de lksle quh x.
>. Hg d` kgsphaakñg kgsphaakñg mh feo`d`t` feo`d`t` premuakm` premuakm` per ug preahse preahse hdhatredì hdhatredìae ae aeggue, aeggue, sh kmhg kmhgc ca` a`g g 2. 2.> > klph klphr rha haak akeg eghs hs hg pr prel elhm hmke ke per per lkgu lkgute te.. Mhth Mhthrl rlkg kgh h d` d`ss pren`nkdkm`mhs mh kmhgca`r `) ug` klphrhaakñg hg 1 lkgutes, n) `d lhges mes klphrhaakeghs hg 8 lkgutes, a) au`gme làs ug` klphrhaakñg hg 08 lkgutes. Qeduakñg? `) x < v`rk`ndh quh quh ges mhcgh hd gÿlhre gÿlhre mh klphrhaakeghs hg d` feo`d`t` per a`m` 1 lkgutes < 2, 0, >, 1, hta. d < 2.> x 1 , 1,...., hta., hta. d < 2.> x 8 , 1,..., hta., hta. d < 2.> x 08 < 1 klphrhaakeghs hg prelhmke per a`m` 08 lkgutes hg d` feo`d`t`
< 2.2=;62>3 + 2.0=;=26 < 2.0;;>023
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