Matematicas (7-1 - 7-3) Guia Nro 3

 

MIQXMXRAMÑI MIQXMXRA MÑI BHRADXMUD ODH^B NB^ID^HD Ä^BD HB ODXBOÄXMADQ HLABIXB GRDI GLQÍ HR^DIJL CÑVBW DÔL >6>6

JRÏD # 1 ‑ J^RVLQ7 :-4, :-1 ‑ EBAKD7 OD]L >2 ‑ GRIML ; Cbb hbtdccdhdobitb bstb odtbrmdc y hbsdrrlccd cd datmvmhdh qub sb s b biaubitrd dc emidc. Hbnbs H bnbs alisbrvdr bstd juïd y bitrbjdr slcl bc hbsdrrlccl hb cd datmvmhdh, cd audc pubhb sbr bivmdhd dc alrrbl l dc wkdtsdpp hbc hlabitb (qub sb biaubitrdi dc pmb hb bstd p äjmid) l bitrbjdhd bi eïsmal bi cd Mistmtuamñi sbj÷i cds ebakds bstmpucdhds.

^BV^BQBIXDAMÑI HBAMODC HB RI I×OB^L ^DAMLIDC Xlhl i÷obrl rdamlidc pubhb bxprbsdrsb bi elrod hbamodc, pdrd cl audc sb hmvmhb bc iuobrdhlr bitrb bc hbilomidhlr. Vlr bgbopcl7

28282828 28…… ? ∞>,28 ∞>,̂28 6,11111 11111 … ? 6,1 6,̂1 ∞>,282828

 y   sb ccdodi Cds bxprbsmlibs hbamodcbs hbamodcbs pbrmñhmals, plrqub kdy uid amerd l ui nclqub hb amerds qub sb rbpmtbi mihbemimhdobitb. Bc rbstl sb ccdodi hbamodcbs bxdatls l emimtls, yd qub pubhbs alitdr tlhds sus amerds.

LVB^DAMLIBQ ALI I×OB^LQ ^DAMLIDCBQ ^balrhbols qubsmjil. ui i÷obrl rdamlidc bs ibjdtmvl sm bc iuobrdhlr y bc hbilomidhlr tmbibi hmebrbitb

;  ? ∞;  ? ∞ ;  ∞1 1 1 Audihl sb rbsubcvbi lpbrdamlibs ali rdamlidcbs ibjdtmvls, alivbiamlidcobitb sb tlod bc smjil ibjdtmvl bi bc iuobrdhlr. Kdy qub tbibr bi aubitd qub pdrd lpbrdr hls i÷obrls rdamlidcbs, sb hbnb bopcbdr cd omsod rbprbsbitdamñi pdrd donls, yd sbd alol erdaamlidrml l alol hbamodc.

Vdrd rbslcvbr huhds b miqumbtuhbs, alouimadrsb ali bc hlabitb dc tbcíelil 166 :25 =>81 l dc alrrbl bcbatrñimal gudighurdijlFjodmc.alo  gudighurdijlFjodmc.alo 

 

MIQXMXRAMÑI MIQXMXRA MÑI BHRADXMUD ODH^B NB^ID^HD Ä^BD HB ODXBOÄXMADQ HLABIXB GRDI GLQÍ HR^DIJL CÑVBW DÔL >6>6

 Dhmamñi y sustrdaamñi hb i÷obrls rdamlidcbs ^balrhbols qub pdrd dhmamlidr l sustrdbr erdaamlibs ali mjudc hbilomidhlr, hbgdols bc omsol hbilomidhlr y sb suodi l sb rbstdi cls iuobrdhlrbs. Cubjl sb smopcmemad bc rbsuctdhl sm bs plsmncb.

Vdrd dhmamlidr l sustrdbr i÷obrls rdamlidcbs ali hmebrbitb hbilomidhlr , sb hbnbi alivbrtmr bi rdamlidcbs hb mjudc hbilomidhlr plr obhml hb cd dopcmemadamñi do pcmemadamñi l cd smopcmemadamñi. Cubjl, sb suodi l sb rbstdi y, sm bs plsmncb, sb smopcmemad bc rbsuctdhl.

qub  alismstb bi Vdrd edamcmtdr bc prlabhmombitl sb pubhb usdr cd –rbjcd hb cd adrmtd‟, qub  ouctmpcmadr bi aruz y bsarmnmr cls rbsuctdhls drrmnd, y cubjl ouctmpcmadr cls hbilomidhlrbs y bsarmnmr bc rbsuctdhl dndgl. Qb rbsubcvb cd lpbrdamñi lp brdamñi hbc iuobrdhlr y sb smopcmemad sm bs plsmncb.

+ ∞= ∞=  ? 48: ? 8=  (41= ) + (∞ 44>) ? 42546; 46; 15  ∞>2  ? ∞2  + ∞; ∞;6 (∞ 146) + (∞ ;42) ? ∞82426   ?  6 ? ∞4>2 426 16 5 Ouctmpcmadamñi hb i÷obrls rdamlidcbs Vdrd ouctmpcmadr i÷obrls rdamlidcbs , sb ouctmpcmadi cls iuobrdhlrbs bitrb sï y cls hbilomidhlrbs bitrb sï. Cubjl, sb smopcmemad bc rbsuctdhl, sm bs plsmncb. Lnsbrvd cls bgbopcls hlihb sb ouctmpcmad –bi cïibd‟.

Vdrd rbslcvbr huhds b miqumbtuhbs, alouimadrsb ali bc hlabitb dc tbcíelil 166 :25 =>81 l dc alrrbl bcbatrñimal gudighurdijlFjodmc.alo  gudighurdijlFjodmc.alo 

 

MIQXMXRAMÑI MIQXMXRA MÑI BHRADXMUD ODH^B NB^ID^HD Ä^BD HB ODXBOÄXMADQ HLABIXB GRDI GLQÍ HR^DIJL CÑVBW DÔL >6>6

Lnsbrvd ui bgbopcl hbc usl hb bstd lpbrdamñi bi cd rbslcuamñi hb prlncbods7 Bi ui jrupl hb >8 bstuhmditbs, sb sdnb qub

  (hls tbramls) sli ougbrbs. ¼Auäitls 

bstuhmditbs sli ougbrbs y auäitls sli klonrbs<

Vdrd rbslcvbr bstb prlncbod, ndstd ali ouctmpcmadr >8 plr cd erdaamñi qub alrrbsplihb d cds ougbrbs. Alol >8 bs ui bitbrl, plhbols pl hbols alivbrtmrcl bi erdaamñi plimíihlcb ui 4 alol hbilomidhlr.

 >8 Ú >  ? 8;  ? 45  (>8 ) Ú (>) ? >8 4 1 y ali4 Úuid1 smopcb 1 rbstd bialitrdols qub kdy ; Dsï qub bi bc jrupl kdy 45 ougbrbs, klonrbs (>8 >8∞∞ 45 45 ? ;). Hmvmsmñi hb i÷obrls rdamlidcbs Vdrd hmvmhmr i÷obrls rdamlidcbs, sb ouctmpcmad cd prmobrd erdaamñi ( hmvmhbihl) plr cd erdaamñi mivbrtmhd hb cd sbjuihd erdaamñi (hmvmslr). Cubjl, sb smopcmemad bc rbsuctdhl sm bs plsmncb. Lnsbrvd cls bgbopcls bi hlihb cd sbjuihd erdaamñi sb bsarmnb mivbrtmhd pdrd alivbrtmr cd lpbrdamñi bi uid ouctmpcmadamñi.

Lnsbrvd ui bgbopcl hbc usl hb bstd lpbrdamñi bi cd rbslcuamñi hb prlncbods7 Ri trlial hb pdrtb<

  obtrls hb clijmtuh sb hmvmhb bi 2 pdrtbs mjudcbs. ¼Auäitl omhb adhd 

Bi bstb adsl, sb hmvmhb cd erdaamñi alrrbsplihmbitb d cd obhmhd hbc trlial bitrb 2. Alol 2 bs ui bitbrl, plhbols alivbrtmrcl bi erdaamñi plimíihlcb ui 4 alol hbilomidhlr.

( 44) 441 ) ú (24) ? ( 44 44) 1 ) Ú (42) ?  414ÚÚ42 ?  221   Vdrd rbslcvbr huhds b miqumbtuhbs, alouimadrsb ali bc hlabitb dc tbcíelil 166 :25 =>81 l dc alrrbl bcbatrñimal gudighurdijlFjodmc.alo  gudighurdijlFjodmc.alo 

 

MIQXMXRAMÑI MIQXMXRA MÑI BHRADXMUD ODH^B NB^ID^HD Ä^BD HB ODXBOÄXMADQ HLABIXB GRDI GLQÍ HR^DIJL CÑVBW DÔL >6>6 Dsï qub adhd pdrtb alrtdhd hbc trlial prmiampdc omhb

  obtrls. 

 Datmvmhdhbs  Datmvmhdh bs hb dprbihmzdgb dprbihmzdgb 4.  Bxprbsd cls smjumbitbs i÷obrls rdamlidcbs bi elrod hbamodc. Qm bs ibabsdrml, utmcmzd uid adcaucdhlrd.

>.  ^bsubcvb cds smjumbitbs lpbrdamlibs.

(:=) + (∞ 842)  (∞ 42; ) + (∞ 44 4>)  4: ∞ 2   >8pdrd4> 1.  Glsí tmbib hls rbampmbitbs hb dabmtb djrbjdrcb dc oltlr hb su vbkïaucl, bc audc  tmbib uid adpdamhdh hb  hb jdcñi.  d)  ¼Auäitl dabmtb hb oltlr djrbjñ Glsí d su dutloñvmc, sm vdamñ alopcbtdobitb cls bivdsbs< n)  ¼Auäitl cb edctñ pdrd ccbidr plr alopcbtl bc oltlr hbc vbkïaucl<

 

 

 

 

8.  Gucmdid vd dc supbrobradhl y aloprd  `j hb adrib,  `j hb drrlz,  `j hb erutd y   `j hb pdpd. ¼Auäitls `mcljrdols hb obradhl aloprñ Gucmdid< Vdrd rbslcvbr huhds b miqumbtuhbs, alouimadrsb ali bc hlabitb dc tbcíelil 166 :25 =>81 l dc alrrbl bcbatrñimal gudighurdijlFjodmc.alo  gudighurdijlFjodmc.alo 

 

MIQXMXRAMÑI MIQXMXRA MÑI BHRADXMUD ODH^B NB^ID^HD Ä^BD HB ODXBOÄXMADQ HLABIXB GRDI GLQÍ HR^DIJL CÑVBW DÔL >6>6 2.  Cmhd tmbib hls kmgls. Qu kmgl odylr tmbib

 dôls y su kmgl obilr tmbib  dôls. ¼Auäc  

bs cd hmebrbiamd hb bhdh bitrb b itrb bc kmgl odylr y bc obilr< 5.  ^bsubcvb cds smjumbitbs lpbrdamlibs.

(4>2 ) Ú (:1)  (4>2 ) Ú (:1)  (4>2 ) Ú (:1)  (4>2 ) Ú (:1) 

(4>2 ) Ú (:1) 

:. 

Hbtbromid auäitls bstuhmditbs gubjdi adhd uil hb cls hbplrtbs y auäc bs bc hbplrtb oäs plpucdr.

 o hb cdrjl<     =.  Qm sb tmbib ui adncb hb   obtrls pdrd hmvmhmrcl bi 8 pdrtbs mjudcbs, ¼auäc sbrä cd ;.  ¼Auäitds pmbzds hb  o hb clijmtuh sb lntmbibi hb uid tdncd hb

clijmtuh hb adhd pdrtb<

Vdrd rbslcvbr huhds b miqumbtuhbs, alouimadrsb ali bc hlabitb dc tbcíelil 166 :25 =>81 l dc alrrbl bcbatrñimal gudighurdijlFjodmc.alo  gudighurdijlFjodmc.alo