Universidad de Cartagena Matematicas 2

 

WFE\GZ^EMCM MG NCZ]CBGFC LCNWA]CM MG NEGFNEC^ GNIFIKENC^ Ncrrgrc

Cmkefestrcneþf pÿjaenc Gstumecftg

Gemgr niftrgrcs rckis

Mingftg

 

CN]E\EMCMG^ MG CXZGFME_COG 3. Ijsgrvcr ga vemgi ‑sungseifgs y sgregs eflefetcs‛ agnneþf 3 (prekgrc pcrtg) mg Oucf Jgatrãf :. mcr ufc mglefeneþf mg sungseþf y niki sg fitcf i gsnrejgf acs sungseifgs Wfc sungseþf

∖

 

 { cf } f;3 ac fitcneþf

 { cf }; c c:, c , c> ……..cf :

 

Gogkpai

  f

3 =

 5

{ f + 3 }; : , 5 , :4 ,,,,,,,,,,   :

f

>

>

f

 

ufc sungseþf tckjeåf sg pugmg rgprgsgftcr 

brãlenckgftg >. Gsnrejer trgs gogkpais mg sungseifgs nif ac fitcneþf pgrtefgftg. Gogkpais 3)Mgtgrk 3)Mg tgrkefcr efcr ga aëketg aëketg mg ac sungseþf sungseþf

{>}f gstc gs ufc sungseþf nifstcftg csë

qug AEK 7 ; 7

………………………….

3

 :) Mgtgrkefg Mgtgrkefg ga aëketg mg ac sungseþf

{=}

ac sungseþf mg pripirneifcaemcm

efvgrsc cngrnc ca ngri mg kcfgrc i c kgmemc qug nrgsg ga vcair mg f   3

Aek f  ; 8

 

=. Mgtgrkef Mgtgrkefcr cr ais nefni prekgris prekgris tårkefis tårkefis mg acs sungseifgs sungseifgs mcmcs gf ga efnesi efnesi cftgreir 

sungseþf

{>}f tårkefis

>, = 7

3

  3. {3- f  }f ; {8, : > = 7 < … … … , . }  :. {3}f-3}f ; {3,-3.3-3,3-3,,, } >. {f}f ; {3,:,>,=,7,…………..} ,- = ,-7 ,-8, >8,... 78 ≧ 780 78 ≧ =80 =8 ≧ =80 =8 ≧ >80 >8 ≧ >80... >) Cf + 3   6 C f 388, 58, 48, 78,...

 

388 6 580 58 6 480 48 6 78 2. ¹C quå sg aackc Aëketg mg ufc sungseþf9 Kistrcr trgs gogkpais. Xcrc gftg Xcrc gftgfm fmgr gr kgoi kgoirr c acs acs sun sungse gseif ifgs gs y sus aëketg aëketgs, s, rgcaeng rgcaeng uf gogkpa gogkpai i mg sungseþf nifvgrbgftg nif aëketg 8, itrc mg aëketg 3 y uf  uf  gogkpai mg aëketg mg sungseþf eflefeti gf gstg ncsi mg sungseþf mevgrbgftg 3 Aëketg 8? 3, 3/:, 3/>, 3/=, 3/7..., 3/f c3; 3 c:; 8.7 c3888; 8.883 c3888.888 ; 8.888883 : Aëketg 3? 3/:, :/>, >/=, =/7, ..., f/f+3 c3; 8.7 c:; 8. c3888.888 ; :.888.88>

  4 C qug sg aackc nitc supgreir mg ufc sungseþf. Kistrcr : gogkpais. Zgscatcr ac nitc supgreir. Nitc supgreir gs ga nifoufti mg fÿkgris rgcags ga nuca pugmg tgfgr nitcs supgreirgs. Wf fÿkgri gs ufc nitc supgreir mg uf nifoufti mg fÿkgris se gs kcyir i ebuca qug timis ais fÿkgris mga nifoufti. Xir gogkpai,  3 .Gf ga nifoufti C ; {:, =, 2} lirkcmi pir ais trgs fÿkgris :, = y 2, ufc nitc supgreir gs ga fÿkgri 38, yc qug gs kcyir i ebuca qug :, qug = y qug 2. Itrc nitc supgreir mg C gs ga fÿkgri :7, i ga fÿkgri 388, i ga fÿkgri 5. ]ckjeåf ai gs ga fÿkgri 2, yc qug 2 gs kcyir ebuca qug :, qug = y qug ga pripei 2.

: ^e nifsemgrckis ac sungseþf, gstc {f-} f  ; {-3, -:, ->,-= ,-7 .-72: Gstis vcairgs sgrãf nitcs supgreirgs pugs sif kcyirgs i ebucags qug nucaquegr Gagkgfti mg ac sungseþf.

 

5 C qug sg aackc nitc eflgreir mg ufc sungseþf. Kistrcr : gogkpais. Kistrcr ac nitc eflgreir  NI]C^ EFLGZEIZG^ Mg lirkc bgfgrca, pimgkis mgner qug nucaquegr fÿkgri kgfir i ebuca qug gs Wfc nitc eflgreir mg gstc sungseþf Gogkpai ^e nifsemgrckis ac sungseþf , {

f }f

; 3,:,>,=,7,= 8 8.7 gstis vcairgs ^grãf nitcs eflgreirgs pugs sif kgfirgs i ebucags qug nucaquegr gagkgfti mg ac ^ungseþf. . Gogkpai ^e nifsemgrckis ac sungseþf

{>}f ; {>,>,>,>,>,>…..} gstc sungseþf gstã

 Cnitcmc eflgreirkgftg, eflgreirkgftg, pugs se nifsemgrckis nifsemgrckis : ,-4>5 , 3.7 i -77 gstis vcairgs ^grãf nitcs eflgreirgs pugs sif kgfirgs i ebucags qug nucaquegr gagkgfti mg ac ^ungseþf.

38 Mgtgrkefcr 38 Mgtgrkefcr ais 7 prekgris tårkefis mg ac sungseþf  Ais tgrfis sif =, - 5 ,3< -:7,>< ,=5

cf

; (√ 3 ) ( : f + 3 ) f