GLAPIAF@L Ki`fgf÷a `i isgurrfkfiatl y ricfstrls `i jnlrl .......................................................... 4 Jnlrl ................................................ .................................................................................................. ................................................................................ .............................. 4 J.
Wiggf÷a `i glatrlh .......................................................................................... .......................................................................................... 4
D.
Tihjgf÷a siggf÷a-pia`fiati siggf÷a-pia `fiati ........................................... ......................................................................... .............................. 0
G.
Tihjgf÷a siggf÷a-vihlgf`j` siggf÷a-vih lgf`j` ............................................................ .......................................................................... .............. >
Kætl`ls y `fsplsftfvls pjrj ki`fr hj vihlgf`j` ia uaj glrrfiati ...................... 2 j) Kætl`l K ætl`l `ih klhfaiti ........................................................................................... ........................................................................................... 2 d) Pudl Pu dl `i Uftlt y `i ` i Urja`th Ur ja`th ............................................. ................................................................................... ...................................... 6 g) Kætl`l `i nhltj`lris ............................................ ........................................................................................ ............................................ :5 `) Kætl`l `i `fhugf÷a `i tfatj y trjzj`lris ..................................................... :5
KI@FGF×A @I IWGYTTFKFIAPL V TICFWPTLW @I JNLTL JNLTL Jnlrjr uaj glrrfiati sfcafnfgj `itirkfajr j trjvæs `i ki`fgflais ih cjstl qui pjsj plr uaj siggf÷a `j`j. Ia Kæxfgl si usja dêsfgjkiati tris tfpls `i kætl`ls pjrj jnlrjr glrrfiatis, j sjdir?
Wiggf÷a `i glatrlh Tihjgf÷a siggf÷a-pia`fiati Tihjgf÷a siggf÷a-vihlgf`j`
J. WIGGF×A @I GLAPTLH uaj siggf÷a `i glatrlh `i uaj glrrfiati si `infai glkl jquihhj ia hj qui ixfsti uaj rihjgf÷a ÿafgj iatri ih tfrjati y ih cjstl. @i hls kugbls tfpls `i siggflais `i glatrlh qui si pui`ia usjr pjrj jnlrjr uaj glrrfiati, hls kês glkuais sla hls qui prl`ugia ua tfrjati grëtfgl y hls virti`lris. Wi nlrkj ua tfrjati grëtfgl ihivja`l ih nla`l `ih gjugi, istrigbêa`lhl l gla uaj glkdfajgf÷a `i hjs `ls tægafgjs. Guja`l si utfhfzj hj prfkirj (væjsi nfcurj 7.2), ih cjstl si gjhguhj usja`l hj n÷rkuhj virti`lris `i pjri` cruisj?
Nfcurj 7.2
∟ . ⁀
@la`i? D is ih jagbl `ih gjugi ia k, c is hj jgihirjgf÷a `i hj crjvi`j` ia k/W 4 B is hj gjrcj sldri ih virti`lr ia k Z is ih cjstl ia k 7/s
(.)
Ujrj qui ih `fsplsftfvl `i hj nfcurj 7.2 tiacj ua duia nuagflajkfiatl, si riglkfia`j qui?
8 8 8.
(.) (.)
Ltrj kjairj `i prlvlgjr hj nlrkjgf÷a `i ua tfrjati grëtfgl is guja`l hj tlplcrjnëj pirkfti `fsplair `i uaj gjë`j hfdri (væjsi nfcurj 7.6)= ia isti gjsl ih cjstl si gjhguhj gla ih tfrjati ki`f`l oustl ia hj gjë`j y?
`la`i y istê ia k, c ia k/s 4 , D ia k y Z ia k7/s.
.
(. )
Hls virti`lris `i pjri` `ihcj`j riglkia`jdhis pjrj rijhfzjr jnlrls sla ih trfjacuhjr gla êacuhl `i 65µ pjrj cjstls piquiúls (`i 5 j :55 h/s) y ih rigtjacuhjr pjrj cjstls kjylris (`i :55 j : 555 h/s) (væjsi nfcurj 7.:5). Wf si usj ua virti`lr rigtjacuhjr gla hjs `fkiasflais ispigfnfgj`js ia hj nfcurj 7. :5j, ih cjstl si gjhguhj glkl?
. / . .
(.) (.)
y gla ua virti`lr trfjacuhjr glkl ih `i hj nfcurj 7.:5d, ih cjstl is?
Nfcurj 7.:5 ^irti`lris `i pjri` `ihcj`j
Ia hjs igujgflais 7.> y 7.3 B is hj gjrcj sldri hj gristj `ih virti`lr ia k, ki`f`j j uaj `fstjagfj `i guja`l kials 0B jcujs jrrfdj `i hj gristj= H is hj hlacftu` `i hj gristj ia k (igujgf÷a 7.>) y Z is ih cjstl ia k7/s.
Ih kætl`l `i hjs siggflais `i glatrlh is ih kês prigfsl `i tl`ls pjrj ih jnlrl, pirl prisiatj jhcuals faglaviafiatis. Ia prfkir hucjr, is rihjtfvjkiati glstlsl y, ia ciairjh, s÷hl si pui`i usjr guja`l hls cjstls al sla kuy jhtls. Ia ih gjsl `i hls istrigbjkfiatls si ristrfaci ih trjasplrti `i ldoitls jrrjstrj`ls plr hj glrrfiati y hj siggf÷a pui`i ldstrufrsi. Ya faglaviafiati `i hls virti`lris is qui ciairja ua rikjasl jcujs jrrfdj `i hj siggf÷a. Ulr ihhl, isti kætl`l is j`iguj`l ia rëls piquiúls, gjugis jrtfnfgfjhis (glkl plr ioikphl gjajhis `i rficl) l guiagjs ixpirfkiatjhis.
D. TIHJGF×A WIGGF×A-UIA@FIAPI
Nfcurj 7.::
Isti kætl`l si utfhfzj pjrj istfkjr ih cjstl kêxfkl qui si prisiat÷ `urjati uaj jviaf`j rigfiati ia ua rël `la`i al si guiatj gla afacÿa ltrl tfpl `i jnlrls. Ujrj su jphfgjgf÷a si riqufiri slhjkiati glatjr gla tlplcrjnëj `i ua trjkl `ih gjugi y hjs kjrgjs `ih afvih kêxfkl `ih jcuj `urjati ih pjsl `i hj jviaf`j. Wicÿa hj n÷rkuhj `i Kjaafac, hj vihlgf`j` is?
/ /
(.)
`la`i T ; rj`fl bf`rêuhfgl, Wn ; pia`fiati `i hj hëaij `i iaircëj ispigënfgj a ; glinfgfiati `i ruclsf`j`.
J`ikês, `i hj igujgf÷a `i glatfauf`j` si tfiai qui?
(.)
`la`i J is ih êrij bf`rêuhfgj.
Jphfgja`l hj igujgf÷a `i Diraluhhf iatri hls ixtrikls fafgfjh y nfajh `ih trjkl (væjsi nfcurj 7.::) risuhtj?
+ + + + + ∎+ ∔
(.)
@i hjs igujgflais 7.6 y 7.:5 si ldtfiai?
( : + : ) ∔ ( + )
(.)
`la`i ∎ `fniriagfj ia ihivjgf÷a `i hjs kjrgjs `ih afvih kêxfkl `ih jcuj ia hls ixtrikls `ih trjkl.
Ujrj tlkjr ia guiatj hjs pær`f`js hlgjhis glavfiai isgrfdfr hj igujgf÷a 7.:: ia hj nlrkj?
40 : 11 :
@la`i sf sf
∎+ ∔
(.)
Ytfhfzja`l hjs igujgflais 7.2 y 7.6 si pui`i isgrfdfr?
`la`i
̉ /
/ / ̉ /
(.)
is ih glinfgfiati `i gla`uggf÷a ki`fl ia ih trjkl qui pui`i
gjhguhjrsi glkl ih prlki`fl cilkætrfgl `i hls glinfgfiatis `i gla`uggf÷a ia hls ixtrikls `ih kfskl?
/7 ̉ ̉ ̉ = ̉
(.)
̉ ∎ + ∔
(.)
Ytfhfzja`l hjs igujgflais 7.:4 y 7.:7 y tlkja`l ia guiatj qui ldtfiai
`ispioja`l Z?
℁
, si
∎/ ̉ ∔ ∔
(.)
Gla hj igujgf÷a 7.:> is plsfdhi istfkjr ih cjstl `i pfgl `i uaj jviaf`j sf si glalgia hjs kjrgjs `ih afvih kêxfkl `ih jcuj ia hjs kêrciais, hj ruclsf`j` `ih trjkl y hj tlplcrjnëj `ih kfskl.
G. TIHJGF×A WIGGF×A-^IHLGF@J@
Nfcurj 7.:4
Isti is ih kætl`l kês usj`l ia Kæxfgl pjrj jnlrjr glrrfiatis. Glasfsti dêsfgjkiati ia ki`fr hj vihlgf`j` ia vjrfls puatls `i hj siggf÷a trjasvirsjh y `ispuæs gjhguhjr ih cjstl plr ki`fl `i hj igujgf÷a `i glatfauf`j` 7.6. Hj vihlgf`j` `ih nhuol ia uaj siggf÷a trjasvirsjh `i uaj glrrfiati tfiai uaj `fstrfdugf÷a glkl hj qui si kuistrj ia hj nfcurj 7.:4. Ujrj `itirkfajr ih cjstl al is sunfgfiati iatlagis ki`fr hj vihlgf`j` ia ua slhl puatl, sfal qui is aigisjrfl `fvf`fr hj siggf÷a trjasvirsjh `ih Gjugi ia vjrfjs sudsiggflais hhjkj`js `lvihjs. Ih cjstl qui pjsj plr gj`j `lvihj is?
@la`i is ih êrij `i hj `lvihj f y is hj vihlgf`j` ki`fj ia hj kfskj `lvihj.
(.)
Hj vihlgf`j` ki`fj si pui`i tlkjr glkl hj ki`f`j j uaj prlnua`f`j` `i jprlxfkj`jkiati, `la`i is ih tfrjati ki`f`l jh giatrl `i hj `lvihj (væjsi nfcurj 7.:4) guja`l al is kuy crja`i= ia gjsl glatrjrfl, glavfiai tlkjr jh kials `ls ki`f`js j prlnua`f`j`is `i y = jsë hj vihlgf`j` ki`fj is?
5.>
5.4 5.2
@la`i
y
+
sla hjs vihlgf`j`is ki`f`js j
(.)
5.4 5.2 y
rispigtfvjkiati.
Guja`l is kuy crja`i. pui`i sir aigisjrfl tlkjr tris l kês higturjs `i vihlgf`j` ia hj `lvihj. Is riglkia`jdhi, j`ikês, ki`fr hj prlnua`f`j` `i gj`j `lvihj gj`j viz qui si bjcj ua jnlrl. Iatlagis, ih cjstl tltjh sirê?
√ ;
(.)
`la`i a is ih aÿkirl `i `lvihjs.
Hj vihlgf`j` si kf`i gla uals jpjrjtls hhjkj`ls klhfaitis (væjsi nfcurj 7.:7) qui tfiaia uaj bæhfgi l rui`j `i jspjs l glpjs qui cfrj fkpuhsj`j plr hj glrrfiati y, ki`fjati ua kigjafskl ihægtrfgl, trjaskftia plr ua gjdhi ih aÿkirl `i rivlhugflais plr kfautl l plr sicua`l gla qui cfrj hj bæhfgi. Istj vihlgf`j` jacuhjr si trj`ugi `ispuæs j vihlgf`j` `ih jcuj usja`l uaj n÷rkuhj `i gjhfdrjgf÷a qui privfjkiati si `itirkfaj pjrj gj`j jpjrjtl ia pjrtfguhjr.
Nfcurj 7.:7
KÆPL@LW V @FWULWFPF^LW UJTJ KI@FT HJ ^IHLGF@J@ IA YAJ GLTTFIAPI
J) KÆPL@L @IH KLHFAIPI Ih kês glkÿa `i istls fastrukiatls is ih tfpl Urfgi, ih gujh istj prlvfstl `i uaj bæhfgi l rui`j `i jspjs l glpjs qui cfrj fkpuhsj`j plr hj vihlgf`j` `i hj glrrfiati y j pjrtfr `i ua trjas`ugtlr ihægtrfgl, fa`fgj ih aÿkirl `i rivlhugflais gla qui cfrj hj bæhfgi. Istj vihlgf`j` jacuhjr si trj`ugi j vihlgf`j` `ih jcuj (ia k/s), utfhfzja`l uaj n÷rkuhj `i gjhfdrjgf÷a qui privfjkiati si bj `itirkfaj`l pjrj gj`j fastrukiatl ia pjrtfguhjr. Jsfkfskl, pjrj qui ih klhfaiti pui`j glhlgjrsi j hj prlnua`f`j` `isij`j si utfhfzja ua hjstri l pisl bigbl `i phlkl, gla nlrkj bf`rl`faêkfgj, hhjkj`l isgja`jhhl y uaj vjrfhhj kl`uhjr qui sfrvi pjrj suoitjrhl. Hj nfcurj 0.6 kuistrj ua klhfaiti tfpl Urfgi, guyl prlp÷sftl is ki`fr hj vihlgf`j` `ih nhuol ia uaj siggf÷a trjasvirsjh `i hjs glrrfiatis. Istls fastrukiatls `idia istjr gjhfdrj`ls, is `igfr, `idi glatjr gla uaj gurvj, tjdhj l igujgf÷a ia hj qui si rihjgflai ih aÿkirl `i gbjsquf`ls qui ikftia plr uaf`j` `i tfikpl, gla hj vihlgf`j` `ih nhuol.
j) Glhlgj`l ia hj vjrfhhj kl`uhjr
d) ^fstj pjrgfjh `i hj rui`j `i jspjs l glpjs Nfcurj 0.6. Klhfaiti tfpl Urfgi
Ia hj nfcurj 0.:5 si kuistrj hj nlrkj qui prisiatj hj gurvj `i gjhfdrjgf÷a `ih klhfaiti tfpl Urfgi.
Nfcurj 0.:5 Gurvj `i gjhfdrjgf÷a `ih klhfaiti
D) PYDL @I UFPLP V @I UTJA@PH Ih tudl `i Uftlt y ih `i Urja`th sla sfkfhjris ia nlrkj. Jkdls riqufiria `i ua kja÷kitrl (qui pui`i sir `i glhukaj `i kirgurfl) y hj `fniriagfj istrfdj ia qui ih tudl `i Uftlt si glaigtj slhl j uaj `i hjs rjkjs `ih kja÷kitrl, qui`ja`l hj ltrj ixpuistj j hj prisf÷a jtklsnærfgj. Ia ih gjsl `ih tudl `i Urja`th, hjs `ls rjkjs `ih kja÷kitrl si glaigtja jh fastrukiatl. Hj `fniriagfj `i prisflais qui si ricfstri sirvfrê pjrj istfkjr hj vihlgf`j` (istls fastrukiatls tjkdfæa si utfhfzja ia gla`ugtls j prisf÷a) qui si ldtfiai `i hj ixprisf÷a sfcufiati?
( ∔ ) /
(.)
`la`i ^ is hj vihlgf`j` `ih nhuol= Gv is ih glinfgfiati `i vihlgf`j`, gla vjhlris qui lsgfhja iatri 5.5: y :.57 (sf si glhlgj ih fastrukiatl pjrjhihl j hjs hëaijs `i glrrfiati, iatlagis ih glinfgfiati si pui`i glasf`irjr fcujh j :)= c is hj glastjati `i jgihirjgf÷a crjvftjgflajh= ϊk is j `iasf`j` `ih hëquf`l `ih kja÷kitrl= ϊ is hj `iasf`j` `ih jcuj= y ΐb is hj `fniriagfj `i prisflais ricfstrj`j iatri hjs `ls rjkjs `ih kja÷kitrl.
G) KÆPL@L @I NHLPJ@LTIW Yaj nlrkj kuy sfkphi `i istfkjr hj vihlgf`j` ia uaj glrrfiati piquiúj is glhlgjr ia hj supirnfgfi ldoitls qui nhltia. Urfkirl si `infai hj `fstjagfj qui riglrrirê ih nhltj`lr= ia ih ixtrikl jcujs jrrfdj si suihtj, y si kf`i ih tfikpl trjasgurrf`l ia jhgjazjr ih ixtrikl qui glrrispla`i j jcujs jdjol. Istl si ripfti hjs vigis qui sij aigisjrfl. Jh sir uaj istfkjgf÷a `i hj vihlgf`j` ia hj supirnfgfi, si pl`rê jnigtjr ih vjhlr `i vihlgf`j` ki`f`l plr ua njgtlr `i 5.29 (@fackja, :660) pjrj jprlxfkjrhl j hj vihlgf`j` ki`fj, is `igfr?
̉ .
(.)
@) KÆPL@L @I @FHYGF×A @I PFAPJ V PTJ_J@LTIW Jh virtir uaj tfatj l trjzj`lr ia uaj glrrfiati ia ua puatl `itirkfaj`l, hj glagiatrjgf÷a `i hj tfatj gjkdfjrê glanlrki si `isphjzj, y sirê plsfdhi `itigtjr ih gjkdfl `i glagiatrjgf÷a ia uaj siggf÷a `i kuistril hlgjhfzj`j jcujs jdjol. @i jguir`l gla @fackja (:660), si `idia gukphfr gla hls sfcufiatis riquirfkfiatls pjrj hjs sustjagfjs j utfhfzjr?
@idia sir nêgfhkiati slhudhis= Hj glagiatrjgf÷a ia ih jcuj `idi `i sir djoj= Al `idia `i rijggflajr quëkfgjkiati af `idia `i sir jdslrdf`js plr ltrjs sustjagfjs faghuf`js `iatrl `ih jcuj `i hj glrrfiati= @idi `i sir nêgfhkiati `itigtjdhi= Al `idi `i sir ua prl`ugtl rfisclsl pjrj ih lpirj`lr af pjrj hjs nlrkjs `i vf`j qui `ipia`ia `ih guirpl `i jcuj= Wu glstl `idi sir jggisfdhi.
Yaj lpgf÷a j`iguj`j `i tfatj l trjzj`lr qui al prlvlgj `júls is ih ghlrurl `i sl`fl, yj qui pui`i sir nêgfhkiati `itigtj`l y su glstl is ri`ugf`l. Wf hj sustjagfj si fayigtj j ua rftkl glastjati, iatlagis ih cjstl si gjhguhj plr ki`fl `i hj ixprisf÷a
] ]∔∔[ [
.
∔ ∭∑()∔
.
Wf hj fayiggf÷a `i hj sustjagfj si bjgi `i kjairj fastjatêaij, iatlagis si utfhfzj hj igujgf÷a klstrj`j j glatfaujgf÷a?
`la`i Z is ih cjstl ia hj siggf÷a `i glatrlh= ZP is ih rftkl `i fayiggf÷a `i hj sustjagfj= GP is hj glagiatrjgf÷a `i hj sustjagfj ia ih puatl `i fayiggf÷a= Giq is ih vjhlr `i glagiatrjgf÷a ia iqufhfdrfl ia istj`l pirkjaiati= Gd is hj glagiatrjgf÷a ajturjh `ih jcuj `i hj glrrfiati= G` is hj glagiatrjgf÷a ia ih puatl `i kuistril jcujs jdjol= y ^ P is ih vlhukia `i sustjagfj virtf`l. `i sl`fl, yj qui pui`i sir nêgfhkiati `itigtj`l y su glstl is ri`ugf`l.
