4
PDJDPQ^D
Dstcaêstf` c Fibdrdi`fcl Qd`ielemêcs ad lc Fiberjc`fði
Dstcaêstf`c Fibdrdi`fcl
Fim. Cldxciarc Jcr`ctejc Qfxf Js`.
[^TDNCP AD GF[EQDPFP Lcs fivdstfmc`feids aci rdspudstc c vcrfcs fitdrremcitds supudstcs senrd clmøi pcrãjdtre
adl
`eld`tfve, di dl prdsditd `cpêtule sd prdtdiad rdspeiadr µdxfstd uic afbdrdi`fc dstcaêstf`cjditd sfmifbf`ctfvc ditrd ui dstfjcaer y dl pcrãjdtre ad lc penlc`fði e ditrd aes dstfjcaerds5 V lcs tæ`if`cs dstcaêstf`cs pcrc djftfr uic rdspudstc sd adiejfici prudncs ad gfpðtdsfs.
Dldjdites ad uic [rudnc ad Gfpðtdsfs Gfpetdsfs Iulc ()8 Cljc`dic ui vcler afrd`te adl pcrãjdtre penlc`feicl qud supeid ie tdidr `cjnfes pcrc les prepðsftes ad lc prudnc, di le pestdrfer sd ad`fad rd`gczcr e ie rd`gczcr `eje rdsultcae adl pre`dse ad ciãlfsfs.
Gfpetdsfs Gfpet dsfs Clt Cltdrict drictfvc fvc ()8 Cljc`dic vclerds ad3 pcrãjdtre qud rdprdsditci ui `cjnfe fjpertcitd adl pre`dafjfdite ierjcl e ad lcs dspd`fbf`c`feids `eie`facs.
Les tærjfies rd`gczcr y ie rd`gczcr sðle adndi utflfzcrsd pcrc lc gfpðtdsfs iulc? puds æstc ds lc qud sd sejdtd c prudnc. ^d`gczcr sfmifbf`c qud lc fiberjc`fði judstrcl nrfiac subf`fditd dvfadi`fc `eje pcrc pdiscr qud le plcitdcae per lc gfpðtdsfs iulc ds dstcaêstf`cjditd fjprencnld c ui ifvdl ad sfmifbf`ci`fc acae. Ie rd`gczcr
sfmifbf`c qud lc fiberjc`fði judstrcl ie
nrfiac subf`fditd dvfadi`fc `eje pcrc pdiscr qud le plcitdcae per lc gfpðtdsfs iulc sdc fjprencnld c ui ifvdl ad sfmifbf`ci`fc acae.
Pfi djncrme, di dl adscrrelle ad lc prudnc ad gfpetdsfs sd pudad `ejdtdr aes tfpes ad drrerds8
Drrer tfpe F (^d`gczcr G; `uciae dstc ds vdracadrc) y Drrer tfpe FF (Ie ^d`gczcr G; `uciae dstc ds bclsc)
Cadjãs, lc prencnflfaca ad `ejdtdr ui drrer Qfpe F sd `eie`d `eje Ifvdl ad Pfmifbf`ci`fc, sd adietc `eje γ y ds dl tcjcóe ad lc rdmfði ad rd`gcze Dl `ejpldjdite ad lc rdmfði ad rd`gcze ds 3∞ γ y ds `eie`fae `eje dl @edbf`fditd ad @eibfcizc. Cl ciclfzcr les rdsultcaes ad uic prudnc ad gfpðtdsfs sfdjprd adnd `eisfadrcrsd dl dbd`te ad `eibusfði adrfvcae ad lc prdsdi`fc ad vcrfcnlds ie `eisfadrcacs di dl afsdóe erfmficl y qud ie Dstcaêstf`c Fibdrdi`fcl
Fim. Cldxciarc Jcr`ctejc Qfxf Js`.
sd
Dstcaêstf`c Fibdrdi`fcl
Fim. Cldxciarc Jcr`ctejc Qfxf Js`.
dstãi sejdtfdiae c prudnc, per le qud ds ad `eie`fjfdite mdidrcl qud lcs ad`fsfeids tejcacs c pcrtfr ad uic prudnc ad gfpetdsfs gfpetdsfs sfdjprd prdsditci ui ifvdl ad drrer γ.
Gfpðtdsfs fpðtdsfs Qfpes ad [rudncs ad G
Tiflctdrclds
Nflctdrclds
Tic prudnc dstcaêstf`c uiflctdrcl ds cqudllc di lc qud lc rdmfði ad rd`gcze sele sd prdsditc c ui dxtrdje ad lc afstrfnu`fði (adrd`gc e fzqufdrac).
Tic prudnc dstcaêstf`c nflctdrcl ds cqudllc di lc qud lc rdmfði ad rd`gcze `errdspeiad c ui fitdrvcle ad `eibfcizc pcrc dl pcrãjdtre yc qud sd prdsditc c les aes dxtrdjes ad lc afstrfnu`fði.
@uclqufdrc sdc lc prudnc ad gfpetdsfs di use, lc tæ`if`c `uditc `ei 4 pcses8 3. [lci [lcitdc tdcjfd jfdit ite e ad Gf Gfpe petd tdsfs sfs >. If Ifvd vdll ad sfmif sfmifbf bf`c `ci` i`fc fc 0. Dstc Dstcaê aêst stf` f`e e ad [ru [rudn dncc 1. ^d ^dmf mfði ði ad rd`g rd`gcz cze e
4. Ad`fsfði
[^TDNC AD GF[EQDPFP [C^C LC JDAFC ̄ ad ui `eihuite ad fiberjc`fði
Dstc prudnc prudnc pdrjftd pdrjftd `ejprencr `ejprencr sf lc jdafc jdafc judstrcl judstrcl
`ujpld `ei vclerds fmuclds e cprexfjcaes cl pcrãjdtre penlc`feicl ´, sfi djncrme, pcrc dstd `eitrcstd sd jcidhci aes dibequds8 @eie`dr lc vcrfcizc ad lc judstrc y ads`eie`dr lc vcrfcizc ad lc judstrc @uciae lc vcrfcizc ds `eie`fac les `eitrcstds sd plcitdci ad lc sfmufditd jcidrc8
[rud udnc nc ad Gf Gfpð pðtd tdsf sfss c. [r
;8 ´ : ; 38 ´ ≫ ;
;8 ´ ≡ ; 38 ´ 9 ;
;8 ´ ≤ ; 38 ´ < ;
Nflctdrcl
Tiflctdrcl adrd`gc
Tiflctdrcl fzqufdrac
n. If Ifvd vdll ad ad sfmi sfmifb fbf`c f`ci` i`fc fc
: ;.;4 f`ee `. Dstcaêstf`
∞ ; ~(´ ∞ >) : ̄̄ ∞ /∘ ^dmf mfði ði ad rd rd`g `gcz czee a. ^d ^d`gczcr ; || 9 3∞
>
̽
9 3
∞
< ∞
3∞
[crc dl `ãl`ule ad les pdr`ditflds X sd utflfzc lc bui`fði di Dx`dl (AFPQ^.IE^J.DPQCIA.FIR)
d. Ad`fsfði Pd dlfmd rd`gczcr e ie rd`gczcr lc gfpetdsfs iulc
Dhdjple Di ui dstuafe ad iutrf`fði sd adsdc `eitrcstcr `ei ui ifvdl ad sfmifbf`ci`fc adl 4% lc gfpðtdsfs ad qud lc tcllc prejdafe ad les gejnrds ad 37 e jãs cóes ds fmucl c 37;`j, lc vcrfcizc ad dstc penlc`fði ds fmucl c 32. µPd jcitdiarã lc cbfrjc`fði jdi`feicac ludme ad ensdrvcr c 34 hðvdids sdld``feicaes cl czcr5 32=
32=
327
327
327
c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss
;8 ´ : 37; 38 ´ ≫ 37;
326
3=3
3=>
3=0
3=4
3=4
3=4
3==
37>
364
n. Ifvd Ifvdll ad ad ssfmi fmifb fbf`c f`ci` i`fc fc
: ;.;4 `. Dstcaêstf`e f`e
3=0.1 ∞ 37; :
1/∘ 34 34
: ∞2.0
a. ^d ^dmf mfði ði ad rd rd`g `gcz czee
|| 9 3∞ > |∞2.0| 9 3.64 ℉
d. Ad`fsfði Lc tcllc ad les gejnrds ad 37 cóes di cadlcitd ds afbdrditd c 37;`j
Citd lc rdspudstc gcllcac sd `eie`d qud dxfstd afbdrdi`fc `ei lc cbfrjc`fði djftfac, per tcite, sd adnd `ejprencr sf lc tcllc prejdafe ad les gejnrds ds supdrfer e fibdrfer, per le qud sd pudad utflfzcr `eitrcstds uiflctdrclds.
c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss
;8 ´ ≡ 37; 38 ´ 9 37; n. Ifvd Ifvdll ad ad ssfmi fmifb fbf`c f`ci` i`fc fc
: ;.;4
`. Dstcaêstf`e f`e
:
3=0.1 ∞ 37;
1/∘ 34 34
: ∞2.0
a. ^d ^dmf mfði ði ad rd rd`g `gcz czee
9 3∞ ℉ ∞2.0 < 3.21 ℉
d. Ad`fsfði Lc tcllc ad les gejnrds ad 37 cóes di cadlcitd ds fibdrfer c 37;`j
@uciae lc vcrfcizc ds ads`eie`fac les `eitrcstds sd plcitdci ad lc sfmufditd jcidrc8
c. [rudnc ad Gfpðtdsfs
;8 ´ : ; 38 ´ ≫ ;
;8 ´ ≡ ; 38 ´ 9 ;
;8 ´ ≤ ; 38 ´ < ;
Nflctdrcl
Tiflctdrcl adrd`gc
Tiflctdrcl fzqufdrac
n. Ifvdl ad sfmifbf`ci`fc
: ;.;4 `. Dstcaês êsttf` f`ee
̄̄ ∞ ∞ ; : / /∘ ∘ ~ (∞3) a. ^d ^dmf mfði ði ad rd rd`g `gcz czee >
^
d`gczcr ;
| | 9 ,(∞3)
9
,(∞3)
<
∞
,(∞3)
[crc dl `ãl`ule ad les pdr`ditflds t sd utflfzc lc bui`fði di Dx`dl (AFPQ^.Q.FIR)
d. Ad`fsfði Pd dlfmd rd`gczcr e ie rd`gczcr lc gfpetdsfs iulc
Dhdjple Lc rdsfstdi`fc di /> ad lc bfnrc ad `crneie sd afstrfnuyd ierjcljditd, sd tejð uic judstrc ad 3; dldjdites bcnrf`caes `ei dsd jctdrfcl entdifae. >;0
>>6
>34
>>;
>>0
>00
>00
>;7
>>7
>;6
@eitrcstd lc gfpðtdsfs ad qud lc judstrc prevfdid ad uic penlc`fði `ei jdafc ad >34
c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss
;8 ´ : >34 /> 38 ´ ≫ >34 /> n. Ifvd Ifvdll ad ad ssfmi fmifb fbf`c f`ci` i`fc fc
: ;.;4 `. Dstcaêstf`e f`e
:
>>;.3 ∞ >34
3;.6/∘ 3; 3; : 3.1
a. ^d ^dmf mfði ði ad rd rd`g `gcz czee
|| 9 ,(∞3) ℉ > |3.1| < >.>2 ℉
/>.
d. Ad`fsfði Dl prejdafe ad rdsfstdi`fc ad lc bfnrc ad `crneie ds fmucl c >34
/>
[^TDNC AD GF[EQDPFP [C^C LC [^E[E^@FÐI Dstc prudnc pdrjftd `ejprencr sf lc preper`fði judstrcl ̎ ad ui `eihuite ad fiberjc`fði `ujpld `ei vclerds fmuclds e cprexfjcaes cl pcrãjdtre penlc`feicl p
c. [rudnc ad Gfpðtdsfs
;8 : ; 38 ≫ ;
;8 ≡ ; 38 9 ;
;8 ≤ ; 38 < ;
Nflctdrcl
Tiflctdrcl adrd`gc
Tiflctdrcl fzqufdrac
n. Ifvdl ad sfmifbf`ci`fc
: ;.;4 `. Dstcaês êsttf` f`ee : ̎ ∞ ~(´ ∞ >) ;; ∘ ;
^dmf mfði ði ad rd rd`g `gcz czee a. ^d ^d`gczcr ; || 9 3∞
>
̽
9 3 < ∞
∞
3∞
[crc dl `ãl`ule ad les pdr`ditflds X sd utflfzc lc bui`fði di Dx`dl (AFPQ^.IE^J.DPQCIA.FIR)
d. Ad`fsfði Pd dlfmd rd`gczcr e ie rd`gczcr lc gfpetdsfs iulc
Dhdjple Di uic di`udstc c 0;; tcxfstcs 30> `eitdstcrei qud utflfzci `fiturði ad sdmurfaca. µ[eadjes `ei`lufr qud lc jftca ad les `eiau`terds utflfzci dl `fiturði5
c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss
;8 : ;.4; 38 ≫ ;.4; n. Ifvd Ifvdll ad ad ssfmi fmifb fbf`c f`ci` i`fc fc
: ;.;4 `. Dstcaêstf`e f`e
30 ̎ : > : ;.11 0; :
; ;.11 ∞ ;.4; ∝ ;.4; ∘ ;.4;0;;
: ∞>.;=
a. ^d ^dmf mfði ði ad rd rd`g `gcz czee
|| 9 3∞ ℉ > |∞>.=| 9 3.64 ℉
d. Ad`fsfði Dl per`ditchd ad tcxfstcs qud usci dl `fiturði ad sdmurfaca ds afbdrditd cl 4;%
[^TDNC AD GF[EQDPFP [C^C LC RC^FCIXC Dl adscrrelle ad dstd `eitrcstd senrdditfdiad qud lc vcrfcnld `ucitftctfvc di dstuafe vfdid ad uic afstrfnu`fði ierjcl y qud c trcvæs ad lc prudnc sd pudad `eie`dr sf dxfstd ui pctrði ad vclerds adbfifaes `eje afstci`fc ditrd les `crc`tdrds iujærf`es y lc jdafc. [er tcite, sd `ejprudnc sf
> (vcrfcizc judstrcl) sd cprexfjcac c > (vcrfcizc penlc`feicl). c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss
;8 > : > ; 38 > ≫ >
;8 > : > ; 38 > 9 >
;
Nflctdrcl
;8 > : > ; 38 > < >
;
;
Tiflctdrcl adrd`gc
Tiflctdrcl fzqufdrac
Ifvd vdll ad ad sfmi sfmifb fbf`c f`ci` i`fc fc n. If
: ;.;4 f`ee `. Dstcaêstf` >
> : ( ∞ 3) ~ > (∞3) ;> a. ^d ^dmf mfði ði ad rd rd`g `gcz czee ^d`gczcr ; > 9 > ,(∞3) >
9 >
[c [crc rc dl `ãl`u ãl`ule le ad les les pdr` pdr`di ditf tfld ldss
>
< >
,(∞3)
>
3∞ ,(∞3)
> sd utflfzc lc bui`fði di Dx`dl
([^
[email protected])
d. Ad`fsfði Pd dlfmd rd`gczcr e ie rd`gczcr lc gfpetdsfs iulc
Dhdjple Lc prd`fsfði ad uic jãqufic sd jfad per lc vcrfcizc qud ie adnd sdr jcyer qud ;.37 sd tejc uic judstrc cldcterfc ad >4 jãqufics y sd entfdid uic mcrcitfzci lc prd`fsfði cl 4% ad sfmifbf`ci`fc.
c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss >
;8 : ;.37
> : ;.36. Rdrfbfqud sf lcs jãqufics
38 > < ;.37 n. Ifvd Ifvdll ad ad ssfmi fmifb fbf`c f`ci` i`fc fc
: ;.;4 `. Dstcaêstf`e f`e
> :
(>4 ∞ 3);.36 ;.37 : >4.00
a. ^d ^dmf mfði ði ad rd rd`g `gcz czee
> < >
( ) 3∞ , ∞3
℉
>4.00 9 30.71 ℉
d. Ad`fsfði Lc jãqufic mcrcitfzc prd`fsfði cl 4% yc qud su vcrfcizc ds fmucl ;.37 uifacads
[^TDNC AD GF[EQDPFP [C^C LC AFBD^DI@FC AD JDAFCP
Dstcs prudncs pdrjftdi `ejprencr sf lc afbdrdi`fc ditrd aes jdafcs penlc`feiclds ds fmucl c ui`citfaca prdvfcjditd rdbdrfac, sd judstrci trds `cses ad dstuafe.
Afbdrdi`fc ad jdafcs `uciae lcs vcrfcizcs sei `eie`facs
c. [rudnc ad Gfpðtdsfs
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > ≫ ;
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > 9 ;
Nflctdrcl
Tiflctdrcl adrd`gc
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > < ; Tiflctdrcl fzqufdrac
n. Ifvdl ad sfmifbf`ci`fc
: ;.;4 `. Dstcaês êsttf` f`ee ( ∞ ̄ >) ∞ ; 3
: 3> ∘ + 3 >
~(´ ∞ >) ~(
>>
a. ^d ^dmf mfði ði ad rd rd`g `gcz czee ^d`gczcr ; || 9 3∞
̽
>
9 3 < ∞
∞
3∞
[crc dl `ãl`ule ad les pdr`ditflds X sd utflfzc lc bui`fði di Dx`dl (AFPQ^.IE^J.DPQCIA.FIR)
d. Ad`fsfði Pd dlfmd rd`gczcr e ie rd`gczcr lc gfpetdsfs iulc
Dhdjple Ti fivdrsfeifstc tfdid aes getdlds uie cl iertd y etre cl sur sd sespd`gc qud lc mcici`fc jdafc adl getdl adl iertd ds jdier qud dl adl sur. Adl prfjdr getdl sd entuve uic judstrc ad 0; dstcaes ad `uditc rdsultciae uic mcici`fc jdafc ad $46, adl sdmuiae getdl sd tejcrei 4; dstcaes ad `uditc `ei uic mcici`fc jdafc ad $20. Lcs vcrfcizcs sei `eie`facs 2; y 7; rd rdsp spd` d`tf tfvc vcjd jdit itd. d. [crc [crc ui uicc sfm sfmif ifbf bf`c `ci` i`fc fc ad adll 4% vdrf vdrfbf bfqu qudd sf ds `fdr `fdrtc tc lc sesp sespd` d`gc gc adl adl fivdrsfeifstc.
Actes prdvfes
Getdl iertd 3 : 46, 3> : 2;, 3 : 0;. Getdl sur8 d ̄ > : 20, > :> 7;, > : 4;.
c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > < ; n. Ifvd Ifvdll ad ad ssfmi fmifb fbf`c f`ci` i`fc fc
: ;.;4
`. Dstcaêstf`e f`e
:
(46 ∞ 20) ∞ ;
: ∞>.3;
7; ∘ 2; + 0; 4;
a. ^d ^dmf mfði ði ad rd rd`g `gcz czee Pf < ∞3∞ ^d`gczcr Ge
∞>.3; < ∞3.21 ℉ d. Ad`fsfði Lc mcici`fc jdafc adl getdl adl iertd ds fibdrfer c lc adl getdl adl sur, per le tcite, ds `fdrtc lc cbfrjc`fði adl fivdrsfeifstc.
Afbdrdi`fc ad jdafcs `uciae lcs vcrfcizcs sei ads`eie`facs pdre supudstcs fmuclds
c. [rudnc ad Gfpðtdsfs
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > ≫ ;
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > 9 ;
Nflctdrcl
Tiflctdrcl adrd`gc
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > < ; Tiflctdrcl fzqufdrac
n. Ifvdl ad sfmifbf`ci`fc
: ;.;4 `. Dstcaês êsttf` f`ee
:
(3 ∞ > ) ̄ ∞ ;
~(3+>∞>)
> ∘ > + 3 >
Cl supeidr fmucl di lcs vcrfcizcs sd `cl`ulc uic øif`c vcrfcizc judstrcl adbfifac per8
>
( 3 ∞ 3) 3)3> + (> ∞ 3) >> : 3 + > ∞ >
aeiad > > ds lc vcrfcizc judstrcl ad lc judstrc 3 y > 3
>
a. ^dmfði ad rd`gcze ^d`gczcr ;
| | 9 ,( + ∞>) >
3
9
>
,(
+
∞>)
3 >
< ∞ ,(3 +>∞>)
[crc dl `ãl`ule ad les pdr`ditflds t sd utflfzc lc bui`fði di Dx`dl (AFPQ^.Q.FIR)
d. Ad`fsfði
Pd dlfmd rd`gczcr e ie rd`gczcr lc gfpetdsfs iulc
Dhdjple Pd rdclfzcrei prudncs pcrc `eie`dr lc `citfaca ad pleje di lc scimrd. Pd tejcrei judstrcs cldcterfcs ad >1 ifóes y 37 caultes Caultes
Ifóes
x̄
;.;10
i3
37
s3
;.;37
̄
;.;>7
>1
;.;=
[rudnd lc gfpðtdsfs ad qud ie gcy afbdrdi`fc ditrd dl `eitdifae jdafe ad pleje di lc scimrd ad ifóes y caultes.
c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > ≫ ; n. Ifvd Ifvdll ad ad ssfmi fmifb fbf`c f`ci` i`fc fc
: ;.;4 `. Dstcaêstf`e f`e @ãl`ule ad lc vcrfcizc øif`c
> :
:
(>1 ∞ 3);.;;;;16 + (37 ∞ 3);.;;;0> : ;.;;;32 >1 + 37 ∞ > (;.;10 ∞ ;.;>7) ∞ ;
: 0.7; ; .;;;32 ∘ ;.;;;32 >1 + 37
Pf ||
9 >,(3+>∞>) 0.7; 9 >>..04
^d`gczcr Ge
℉
d. Ad`fsfði Pf dxfstd afbdrdi`fc ditrd lc `citfaca prejdafe ad pleje di lc scimrd ad ifóes y caultes.
Afbdrdi`fc ad jdafcs `uciae lcs vcrfcizcs sei ads`eie`facs pdre supudstcs afbdrditds
c. [rudnc ad Gfpðtdsfs
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > ≫ ;
;8 ´ 3 ∞ ´ > : 38 ´ 3 ∞ ´ > 9
Nflctdrcl
; ;
Tiflctdrcl adrd`gc
;8 ´ 3 ∞ ´ > : ; 38 ´ 3 ∞ ´ > < ;
Tiflctdrcl fzqufdrac
n. Ifvdl ad sfmifbf`ci`fc
: ;.;4 `. Dstcaês êsttf` f`ee
:
(3 ∞ > ) ̄ ∞ ; 3> > ∘ + >> 3
~
Les mrcaes ad lfndrtca sd `cl`ulci per8 > > ( 3 + > )> 3 > : > > ( > )> ( 3 )> 3 > + 3 ∞ 3 > ∞ 3
aeiad > > ds lc vcrfcizc judstrcl ad lc judstrc 3 y > 3
>
^dmf mfði ði ad rd rd`g `gcz czee a. ^d ^d`gczcr ;
∞
| | 9 , >
9
,
<
,
[crc dl `ãl`ule ad les pdr`ditflds t sd utflfzc lc bui`fði di Dx`dl (AFPQ^.Q.FIR)
d. Ad`fsfði Pd dlfmd rd`gczcr e ie rd`gczcr lc gfpetdsfs iulc
Dhdjple Aes djprdscs P y Q preje`feici pãmfics ad fitdridt pcrc vditc dld`trðif`c sd dlfmfdrei `lfditds pcrc qud vfsftdi lcs pãmfics, sd jfafð dl tfdjpe di jfiutes ad lc aurc`fði ad icvdmc`fði aditre ad lc pãmfic. P
41
43 43
1; 1;
1 14 4
1 17 7
1 12 2
14 14
4 4> >
16 16
4 4; ;
Q
0>
>6 >6
07 07
0 00 0
0 01 1
0 04 4
02 02
0 04 4
>6 >6
> >0 0
[rencr lc gfpðtdsfs qud les `lfditds qud vfsftcrei lc pãmfic P dstuvfdrei 3> jfiutes jãs qud les `lfditds icvdmciae di lc pãmfic Q.
Actes prdvfes8 3
: 17, ̄ > : 0>.1,
3> : 32.76 >> : 36.32
3 : 3; > : 3;
c. [r [rud udnc nc ad Gf Gfpð pðtd tdsf sfss
;8 ´ 3 ∞ ´ > : 3> 38 ´ 3 ∞ ´ > 9 3> n. Ifvd Ifvdll ad ad ssfmi fmifb fbf`c f`ci` i`fc fc
: ;.;4 `. Dstcaêstf`e f`e
:
(17 ∞ 0>.1) ∞ 3> : 3.76 32.76 36.32 ∘ 3; + 3;
@ãl`ule ad les mrcaes ad lfndrtca 32.76
3 6.32 > + ) ( 3; 3; : 3=.6 ≇ 37. : > > 36.32 32.76 ( 3;3;∞ 3) ( ) ∞3 + 3;3; Dstcaêstf`c Fibdrdi`fcl
Fim. Cldxciarc Jcr`ctejc Qfxf Js`.
a. ^d ^dmf mfði ði ad rd rd`g `gcz czee
9 , ^d`gczcr Ge 3.76 9 3.=0 ℉
Pf
d. Ad`fsfði Les `lfditds qud vfsftcrei lc pãmfic P dstuvfdrei 3> jfiutes jãs qud les `lfditds icvdmciae di lc pãmfic Q.
Dstcaêstf`c Fibdrdi`fcl
Fim. Cldxciarc Jcr`ctejc Qfxf Js`.
