Diferencia de Medias

December 5, 2022 | Author: Anonymous | Category: N/A
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4

PDJDPQ^D

Dstcaêstf` c Fibdrdi`fcl Qd`ielemêcs ad lc Fiberjc`fði

Dstcaêstf`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



;.;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`.

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