Tarea 2

 

Ubckj`ólocj Kfcojkf` eb Aïxocj Cfapus Vubrïtfrj   ^rbsbktf(k)9 Kjamrb

Kuabrj eb Cjktrj`

Cubvfs Ajrf`bs Eoblj Lfb`

6?656>=<

  Bstueofktb(s) eb `f cfrrbrf(s)9

Oklbkobráf okeustrof` Okscrotj bk9 Aftbrof

Lrupj

Feaokostrfcoók eb jpbrfcojkbs OO

5F

Ejcbktb9   Ejcbktb9

]fdfb` Sækchbz Frcokoblf Urfmfij9   Urfmfij9

Ufrbf = Dbchf eb bktrblf9

Sfktoflj eb Vubrïtfrj f =2 eb dbmrbrj eb` =>==

6

 

62.8 - @js prjkóstocjs eb ebafkef eb uk b`babktj dokf` pfrf `fs próxoafs 6> sbafkfs sjk9 3>, =>, 32, 2>, =2, =2, >, 5>, > y 2> ukoefebs. B` okvbktfroj eospjkom`b fctuf` bs eb 8> ukoefebs. @f pj`átocf eb pbreoejs bs prjeucor bk `jtbs eb 6>>. @js pbeoejs eb c`obktbs rblostrfejs pfrf b` b`babktj, f pfrtor eb `f sbafkf 6, sjk9 ==, 3>, 62, ?, >, > , 2, 3, < y > ukoefebs. Fctuf`abktb kj hfy cfktoefebs bk b` A^S pfrf bstb b`babktj. B` tobapj eb bspbrf bs eb ejs sbafkfs. Ebsfrrj``b bk A^S pfrf bstb b`babktj dokf`.

^roabrj fsolkfajs `fs cfktoefebs eb prjkóstocj y `fs cfktoefebs eb pbeoejs eb `js c`obktbs. ^frf cf`cu`fr b` okvbktfroj prjybctfej f `f afkj uto`ozfajs `f soluobktb dórau`f9 Okvbktfroj prjybctfej 1 Okvbktfroj sbafkf` fktbrojr + A^S - ]bqubroaobktj aæxoaj ^frf cf`cu`fr b` okvbktfroj eospjkom`b pfrf prjabsf p rjabsf uto`ozfajs `f soluobktb dórau`f9 FU^ 1 Cfktoefe eospjkom`b bk `f sbafkf fktbrojr + A^S - ^beoejs rblostrfejs hfstf b` soluobktb A^S.

Bs oapjrtfktb sböf`fr qub so `f cfktoefe bk afkj bs sudocobktb pfrf cumror b` proabr j `js soluobktbs pbrojejs, kj kbcbsotfajs fsolkfr ukoefebs bk `f do`f eb cfktoefe eb A^S. B`babkj F Cfk bk afkj 8> ^rjkóstcj Jrebkbs eb c`obkb Okvbkfroj prjy. bk afkj Cfktefe A^S Okocoj A^S Okvbkfroj eospjkom`b pfrf p rjabsf (FU^)

6>> ukoefsebs = sbaf kf s

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B` okocoj eb` A^S sb ``bvfræ f cfmj ejs sbafkfs fktbs eb` rbqubroaobktj eb cfktoefe eb A^S. Bstj sb vb rbd`bifej bk `f tfm`f.

=

6>

6>>

 

62.? - @f dolurf 62.3> aubstrf uk rblostrj eb` A^S, pfrcof`abktb ``bkj, pfrf `f prjeuccoók eb cjiokbtbs eb mj`fs. f) Ebsfrrj``b b` A^S pfrf `js cjiokbtbs eb mj`fs. m) Sb hfk rbcomoej cuftrj pbeoejs eb `js c`obktbs bk `f soluobktb sbcubkcof.

Supjklf qub tobkb qub cjaprjabtbrsb f ftbkebr `js pbeoejs eb fcubrej cjk `f sbcubkcof eb ``blfef y qub kj pubeb cfamofr `fs dbchfs eb bamfrqub ebsbfefs ko b` A^S. ºVuï pbeoejs ebmb fcbptfr:

f) Okvbktfroj prjybctfej 1 Okvbktfroj sbafkf` fktbrojr + A^S - ]bqubroaobktj aæxoaj FU^ 1 Cfktoefe eospjkom`b bk `f sbafkf fktbrojr + A^S - ^beoejs rblostrfejs hfstf b` soluobktb A^S. 3

 

Bs oapjrtfktb sböf`fr qub so `f cfktoefe bk afkj bs sudocobktb pfrf cumror b` proabr j `js soluobktbs pbrojejs, kj kbcbsotfajs fsolkfr ukoefebs bk `f do`f eb cfktoefe eb A^S.

Cjiokbtbs eb mj`fs B`babkj Cfk bk afkj 5>> 6 = ^rjkóstcj 22> 3>> Jrebkbs eb c`obkb 3>> 32> 32> > Okvbkfroj prjy. bk afkj C fktefe A^S 2>> Okocoj A^S 2>> Okvbkfroj eospjkom`b pfrf =2> prjabsf (FU^)

3

5

2

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52 >

^j`átcf eb pbeoejs

2>> ukoefebs

Uobapj eb bkrblf 8 ?

6 sbafkf

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B` okocoj eb` A^S sb sb ``bvfræ f cfmj ukf sbafkf fktbs eb` rbqubroaobktj rbqubroaobktj eb cfktoefe eb A^S. Bstj sb vb rbd`bifej bk `f tfm`f.  m) Ujafkej bk cubktf qub9   

Sb ebmb cuap`or cjk `js pbeoejs bk b` jrebk bk qub ``blfrjk  Kj sb pubeb cfamofr `f dbchf eb bamfrqub ko b` A^S ^frf cf`cu`fr b` okvbktfroj prjybctfej sj`j sb vf f tjafr bk cubktf `fs jrebkbs eb` c`obktb

Sb tobkb qub9 ^beoej 6 B`babkj Cfk bk afkj ^rjkóstcj

Sb fcbpf b` pbeoej Cjiokbtbs eb mj`fs

5>>

Jrebkbs eb c`obkb Okvbkfroj prjy. bk afkj C fktefe A^S Okocoj A^S Okvbkfroj eospjkom`b pfrf prjabsf (FU^)

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^j`átcf eb pbeoejs Uobapj eb bkrblf 8 ?

2>> ukoefebs 6 sbafkf

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Sb cjktkuf cjk ^beoej =

Sb fcbpf b` pbeoej

Cjiokbtbs eb mj`fs B`babkj Cfk bk afkj 5>> 6 = 22> 3>> ^rjkóstcj 3>> 32 3 2> Jrebkbs eb c`obkb 4>> =2> Okvbkfroj prjy. bk afkj

C fktefe A^S Okocoj A^S Okvbkfroj eospjkom`b pfrf prjabsf (FU^) Sb cjktkuf cjk ^beoej 3

2>>

^j`átcf eb pbeoejs Uobapj eb bkrblf 8 ?

2>> ukoefebs 6 sbafkf

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Sb rbchfzf b` pbeoej, ebmoej f qub hfmræ df`f eb ukoefebs bk `fs sbafkfs =, 5, 2 y 4

B`babkj Cjiokbtbs eb mj`fs Cfk bk afkj 5>> 6 = ^rjkóstcj 22> 3>> 32> Jrebkbs eb c`obkb 4>> Okvbkfroj prjy. bk afkj 3>> - 2> C fktefe A^S 2>> Okocoj A^S 2>> Okvbkfroj eospjkom`b pfrf - 2>

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prjabsf (FU^) Sb cjktkuf cjk ^beoej 5

Sb fcbpf b` pbeoej

Cjiokbtbs eb mj`fs B`babkj Cfk bk afkj 5>> 6 = 22> 3>> ^rjkóstcj 3>> 32> Jrebkbs eb c`obkb 4>> =2> Okvbkfroj prjy. bk afkj C fktefe A^S 2>> 2>> Okocoj A^S Okvbkfroj eospjkom`b pfrf =2> prjabsf (FU^)

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Sb fcbptfk `js pbeoejs 6,= y 5.

2

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^j`átcf eb pbeoejs Uobapj eb bkrblf 8 ?

6 sbafkf

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62.6> - Ajrrosjk B`bctrjkocs hf prjkjstocfej, pfrf ukj eb sus prjeuctjs, bstfs codrfs eb ebafkef pfrf `fs próxoafs jchj sbafkfs9 , , 42, 4>, 22, 82, , 4>, 22, 5>, 32, >, > y > ukoefebs. B` okvbktfroj eospjkom`b fctuf` bs eb 6>> ukoefebs, `f cfktoefe eb pbeoej bs eb 62> ukoefebs y b` tobapj eb bspbrf bs eb 6 sbafkf. f) Ebsfrrj``b uk A^S pfrf bstb prjeuctj.

Sb usfk `fs soluobktbs dórau`fs9 Okvbktfroj prjybctfej 1 Okvbktfroj sbafkf` fktbrojr + A^S - ]bqubroaobktj aæxoaj FU^ 1 Cfktoefe eospjkom`b bk `f sbafkf fktbrojr + A^S - ^beoejs rblostrfejs hfstf b` soluobktb A^S.

Bs oapjrtfktb sböf`fr qub so `f cfktoefe bk afkj bs sudocobktb pfrf cumror b` proabr j `js soluobktbs pbrojejs, kj kbcbsotfajs fsolkfr ukoefebs bk `f do`f eb cfktoefe eb A^S.

B`babkj

^j`átcf eb pbeoejs Uobapj eb bkrblf

Cjiokbtbs eb mj`fs

C fk bk afkj 6>> ^rjkóstcj Jrebkbs eb c `obkb Okvbkfroj prjy. bk afkj Cfktefe A^S Okocoj A^S Okvbkfroj eospjkom`b pfrf prjabsf (FU^)

62> ukoefebs 6 sbafkf

6

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8





42

4>

22

82



4>

22

5>

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632

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652



632

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62>

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62> 32

62> 62>

62>

B` okocoj eb` A^S sb sb ``bvfræ f cfmj ukf sbafkf fktbs eb` rbqubroaobktj rbqubroaobktj eb cfktoefe eb A^S. Bstj sb vb rbd`bifej bk `f tfm`f. m) B` ebpfrtfabktj ebpfrtfabktj eb afrgbtokl afrgbtokl eb Ajrrosjk Ajrrosjk hf rbvosfej rbvosfej sus prjkóstocjs prjkóstocjs.. F pfrtor eb `f sbaf sbafkf kfbkej 6, `js s kubvj kub prjkó prj ocjs js^Ssjk9 sjk9 ,us , , >, 6>>,`f6>> yb 66 66> > ukoe uk s. Su Supj pjko kobk ej `j qub qu b b`vjsspr prj jmfm` mfkóst m`bbstoc A qub qub ustb tbe e, > 6 = ^rjkóstcj Jrebkbs eb c `obkb 2> 4> Okvbkfroj prjy. bk afkj 3> 66> Cfktefe A^S 62> Okocoj A^S 62> Okvbkfroj eospjkom`b pfrf 2> 32 prjabsf (FU^)

3

5 5> 662 62>



^j`átcf eb pbeoejs Uobapj eb bkrblf 4 < 6>> 6>> > > ?2 -2 62> 62> 62>

62> ukoefebs 6 sbafkf

8 66> > 32 62>

62>

 

Ajrrosjk sb bkdrbktf bkdrbktf f `f sotufcoók eb qub hfmræ ukf df`tf eb 2 ukoefebs bk `f sbafkf > 6 = ^rjkóstcj 2> 4> Jrebkbs eb c `obkb Okvbkfroj prjy. bk afkj 3> 66> Cfktefe A^S 62> 62> Okocoj A^S Okvbkfroj eospjkom`b pfrf 3> 32 prjabsf (FU^)

3

5

2



32

32

662

52

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62>

62>

^j`átcf eb pbeoejs Uobapj eb bkrblf 4 < 6>> 6>> > > ?2 652 62> 62> 62> 62>

62>

62> ukoefebs 6 sbafkf

8 66> > 32

>

 

62.66 - @f dolurf 62.36 aubstrf uk rblostrj eb` A^S pfrcof`abktb ``bkj, cjrrbspjkeobktb f væ`vu`fs eb cjktrj` kbuaætocj eb = pu`lfefs. Supjklf qub rbcomb `js pbeoejs eb væ`vu`fs qub fpfrbcbk bk `f soluobktb tfm`f (prbsbktfejs pjr jrebk eb ``blfef). F abeoef qub ``blf cfef pbeoej, ustbe ebmb ebcoeor so `j fcbptf j `j rbchfzf. ºVuï pbeoejs fcbptfráf pfrf bamfrqub:

Sb usfk `fs soluobktbs dórau`fs9 Okvbktfroj prjybctfej 1 Okvbktfroj sbafkf` fktbrojr + A^S - ]bqubroaobktj aæxoaj FU^ 1 Cfktoefe eospjkom`b bk `f sbafkf fktbrojr + A^S - ^beoejs rblostrfejs hfstf b` soluobktb A^S.

Bs oapjrtfktb sböf`fr qub so `f cfktoefe bk afkj bs sudocobktb pfrf cumror b` proabr j `js soluobktbs pbrojejs, kj kbcbsotfajs fsolkfr ukoefebs bk `f do`f eb cfktoefe eb A^S.

8

 

B`babkj Cjiokbtbs eb mj`fs Cfk bk a fkj 6> 6 ^rjkóstcj 5> Jrebkbs eb c`obkb 4> Okvbkfroj prjy. bk afkj =2 C fktefe A^S

5>

3>

52

3>

32

6>

2

2

>

22

62

2>

=>

42

62

5>

y b` FU^ pfrf `f sbafkf 5 sb rbeucoræ f 2 ukoefebs. Sb fcbptf b` pbeoej.



^frf b` pbeoej eb ukoefebs. Sb fcbptf b` pbeoej. Sb fcbptfk `js pbeoejs =, 3 y 5.

?

 

62.6= - @js rbqubroaobktjs prjkjstocfejs pfr f`fs sbos sbafkfs soluobktbs, bk b` cfsj eb uk tf`ferj b`ïctrocj eb afkj, sjk9 62, 5>, 6>, =>, 2> y 3> ukoefebs. B` ebpfrtfabktj eb afrgbtokl hf rblostrfej pbeoejs qub tjtf`ozfk =>, =2, 6> y => ukoefebs, `js cuf`bs ebmbræk bktrblfrsb eurfktb `f proabrf sbafkf (`f fctuf`) , y `f sblukef, tbrcbrf y cufrtf sbafkfs. Fctuf`abktb, `f baprbsf tobkb bk okvbktfroj 3> tf`ferjs eb afkj. @f pj`átocf eb pbeoejs cjksostb bk jrebkfr pjr `jtbs eb 4> ukoefebs. B` tobapj eb bspbrf bs eb ukf sbafkf. f) Ebsfrrj``b b` rblostrj eb` A^S cjrrbspjkeobktb f `js tf`ferjs eb afkj.

Sb usfk `fs soluobktbs dórau`fs9 Okvbktfroj prjybctfej 1 Okvbktfroj sbafkf` fktbrojr + A^S - ]bqubroaobktj aæxoaj FU^ 1 Cfktoefe eospjkom`b bk `f sbafkf fktbrojr + A^S - ^beoejs rblostrfejs hfstf b` soluobktb A^S.

Bs oapjrtfktb sböf`fr qub so `f cfktoefe bk afkj bs sudocobktb pfrf cumror b` proabr j `js soluobktbs pbrojejs, kj kbcbsotfajs fsolkfr ukoefebs bk `f do`f eb cfktoefe eb A^S.

B`babkj Cfk bk afkj 3> ^rjkóstcj Jrebkbs eb c`obkb Okvbkfroj prjy. bk afkj Cfktefe A^S Okocoj A^S Okvbkfroj eospjkom`b pfrf prjabsf (FU^)

F

^j`átcf eb pbeoejs Uobapj eb bkrblf 5 2

4> ukoefebs 6 sbafkf

6

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3

62

5>

6>

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2>

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2

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B` okocoj eb` A^S sb sb ``bvfræ f cfmj ukf sbafkf fktbs eb` rbqubroaobktj rbqubroaobktj eb cfktoefe eb A^S. Bstj sb vb rbd`bifej bk `f tfm`f. m) Rk eostromuoejr eb `js tf`ferjs eb afkj prbsbktf uk pbeoej pjr 62 ukoefebs. ºCuæ` sbráf `f dbchf eb bamfrqub fprjpofef bkvofr pfrf tjej b` pbeoej:

@f dbchf eb bamfrqub fprjpofef sbráf bk `f sbafkf =, ebmoej f qub sb tobkbk 62 ukoefebs eospjkom`bs bk FU^ (6> eb `f sbafkf 6 y 2 eb `f sbafkf =) y b` eostromuoejr só`j kbcbsotf 62.

6>

 

62.63 - Sb hf fprjmfej uk prjkóstocj prjkóstocj eb =5> ukoefebs bk bkbrj, 3=> ukoefebs bk dbmrbrj y =5> ukoefebs bk afrzj, pfrf ukf dfao`of eb prjeuctjs ebtbctjrbs eb sosajs, qub Afry`fke Futjaft Fut jaftbe, be, Okc. Dfmroc Dfmrocf f bk sus okstf`fc okstf`fcojk ojkbs bs eb ]jcgpj ]jcgpjrt. rt. Urbs prjeuct prjeuctjs, js, F, M y C, cjkstotuybk bstf dfao`of. Bk `js ejs ù`toajs föjs, `fs prjpjrcojkbs eb `f abzc`f eb `js prjeuctjs F, M y C hfk soej eb 32, 5> y =2% , rbspbctovfabktb. @f lbrbkcof cjksoebrf qub `js rbqubroaobktjs rbqubroaobktjs eb` prjkóstocj prjkóstocj abksuf` bstæk ukodjrababkt ukodjrababktbb eostromuoe eostromuoejs js f `j `frlj eb `fs cuftrj sbafkfs eb cfef abs. Fctuf`abktb hfy 6> ukoefebs eospjkom`bs eb` prjeuctj C. @f cjapföáf dfmrocf b` prjeuctj C bk `jtbs eb 5>, y b` tobapj eb bspbrf bs eb = sbafkfs. Sb hf prjlrfa prjlrfafej fej b` frromj frromj eb ukf cfktoefe cfktoefe eb prjeucc prjeuccoók oók eb 5> ukoefe ukoefebs bs eb` pbrojej pbrojej fktbrojr, pfrf `f sbafkf 6. @f cjapföáf hf fcbptfej pbeoejs eb =2, 6=, 8, 6>, = y 3 ukoefebs eb prjeuctj C bk `fs sbafkfs 6 f 4, rbspbctovfabktb. ^rbpfrb uk prjmfm`b A^S pfrf b` prjeuctj C y cf`cu`b `fs cfktoefebs eb okvbktfroj eospjkom`b pfrf prjabsf.

66

 

C B`babkj B`babkj Cfk bk afkj 6> 6> ^rjkóstcj Jrebkbs eb c`obkb Okvbkfroj prjy. bk afkj Cfktefe A^S Okocoj A^S Okvbkfroj eospjkom`b pfrf prjabsf (FU^)

Bkbrj (=5> ukoefebs) Rkoefebs eb b`ba C 1 (.=2 * =5>) / 5 6 = 3 5

Dbmrbrj (3=> ukoefebs) Rkoefebs eb b`ba C 1 (.=2 * 3=>) / 5 6 = 3 5

5> ukoefebs ^j`átcf eb pbeoejs = sbafkfs Uobapj eb bkrblf Afrzj (=5> ukoefebs) Rkoefebs eb b`ba C 1 (.=2 * =5>) / 5 6 = 3 5

62

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