Trabajo Matemalica Unidad 2

 

Rkpþbdc`g Bfdcvgrcgmg Jk Ykmkzukdg. Hcmcstkrcf Jkd Jkd \fjkr \fpudgr \grg DDgg Kju`g`cðm. [mcvkrscjgj Mg`cfmgd Kxpkrchkmtgd Rgigkd Hgrèg Bgrgdt. Pkjk-@frf-Kjf-Igd`ðm @c`df @fhþm> Gjhcmcstrg`cðm Pk``cðm> 0 Mkrchgr @ocrcmfs @C 0 vfduhkm jk vkmtgs, cmg`cðm, `rk`chckmtf pfbdg`cfmgd, *Fikrtg, jkhgmjg, cmerksfs, `fstfs, cmtkrãs jk chpukstf.

*Ium`cðm kxpfmkm`cgd y dfegrèthc`g> k`ug`cðm ekmkrgd, jfhcmcf, rgmef erg`g.

*Kqucdcbrcf jk hkr`gjf> hkr`gjf, prk`cf, fikrtg, jkhgmjg, `urvg jk fikrtg y jkhgmjg, supukstfs ,`fmjc`cfmks ,erg`g , cmtkrprktg`cðm k`fmðhc`g ,prfbdkhg prç``f.

*Kqucdcbrcf jk hkr`gjf> cmerksfs, `fstf, bkmk`cf f udcjgj, supukstf, `fmjc`cfmks, erg`g, cmtkrprktg`cðm k`fmðhc`g y prfbdkhg p rfbdkhg prç``f.

*\umtf jk kqucdcbrcf km tãrhcmf sc`f> \umtf jk kqucdcbrcf km tãrhcmf hfmktgrcf \rfbdkhg prg``f

 

\dgmf `grtkscgmf Pk `fmf`k `fhf pdgmf `grtkscgmf, `ffrjkmgjgs `grtkscgmgs f scstkhg `grtkscgmf, g jfs rk`tgs muhãrc`gs pkrpkmjc`udgrks, umg ofrczfmtgd y ftrg vkr`gd, quk sk `frtgm km um pumtf ddghgjf frcekm f pumtf `krf.

Dg mgdcjgj jkd pdgmf `grtkscgmf ks jks`rcbcr dg pfsc`cðm f ubc`g`cðm jk um pumtf km kd pdgmf, dg `ugd kstç rkprkskmtgjg pfr kd scstkhg jk `ffrjkmgjgs.

Kd pdgmf `grtkscgmf tghbcãm scrvk pgrg gmgdczgr hgtkhç`ghkmtk eurgs ekfhãtrc`gs `fhf dg pgrçbfdg, dg ocpãrbfdk, dg dèmkg, dg `cr`umikrkm`cg y dg kdcpsk, dgs `ugdks ifrhgm pgrtk jk dg ekfhktrèg gmgdè`g.

\gr Frjkmgjf

Jfs mþhkrfs ks`rctfs km um `ckrtf frjkm. [sugdhkmtk kstçm ks`rctfs kmtrk pgrãmtkscs, gsè> (:,;) \ukjkm skr usgjfs pgrg hfstrgr dg pfsc`cðm km um erç`f, jfmjk kd vgdfr "x" (ofrczfmtgd) ks prchkrf, y kd vgdfr "y" (vkr`gd) ks kd skeumjf. gquè kd pumtf (72,;) kstç 72 umcjgjks g df dgref, y ; umcjgjks grrcbg .

 

Rkdg`cfmks y ium`cfmks Dg rkdg`cðm hgtkhç`g ks kd vèm`udf quk kxcstk kmtrk dfs kdkhkmtfs jk um sub`fmnumtf `fm rkspk`tf gd prfju`tf jk jfs `fmnumtfs.

[mg ium`cðm chpdc`g dg fpkrg`cðm hgtkhç`g pgrg jktkrhcmgr kd vgdfr jk umg vgrcgbdk jkpkmjckmtk skeþm kd vgdfr jk umg vgrcgbdk cmjkpkmjckmtk. Zfjg ium`cðm ks umg rkdg`cðm pkrf mf tfjg rkdg`cðm ks umg ium`cðm.

Jkicmc`cðm jk ium`cðm [mg ium`cðm hgtkhç`g ks umg rkdg`cðm quk sk kstgbdk`k kmtrk jfs `fmnumtfs, g trgvãs jk dg `ugd g `gjg kdkhkmtf jkd prchkr `fmnumtf sk dk gscemg um þmc`f kdkhkmtf jkd skeumjf `fmnumtf f mcmeumf. Gd `fmnumtf cmc`cgd f `fmnumtf jk pgrjg tghbcãm sk df ddghg dd ghg jfhcmcf1 gd `fmnumtf mgd f `fmnumtf jk ddkegjg, km tgmtf, sk df pukjk jkmfhcmgr `fmjfhcmcf.

 

@dgscic`g`cðm ium`cfmks ( cmyk`tcvg , sfbrkyk`tcvg sfbrkyk`tcvg , bcyk`tcvg) [mg um`cðm cmyk`vg i ks sc `gjg kdkhkmtf jkd `fmnumtf mgd S kmk um þmc`f kdkhkmtf jkd `fmnumtf cmc`cgd _ gd quk dk `frrkspfmjk. Ks jk`cr, mf pukjkm ogbkr hçs jk um vgdfr jk _ quk tkmeg dg hcshg chgekm S. Rk`cbkm tghbcãm kd mfhbrk jk ium`cfmks —umf g umf‘.

[mg um`cðm sfbrkyk`vg , (f suprgyk`vg) i ks umg ium`cðm tgd quk tfjfs dfs kdkhkmtfs jkd jkd `f `fmn mnum umtf tf mgd mgd S km kmkm km gd hk hkmf mfss um kdkh kdkhkm kmtf tf jkd jkd `fmn `fmnum umtf tf cm cmc`c c`cgd gd _ gd qu qukk dk `frrkspfmjk. Ks jk`cr, umg ium`cðm ks sfbrkyk`vg sc kd rk`frrcjf jk dg ium`cðm ks kd `fmnumtf mgd S.

Km hgtkhç`gs, umg um`cðm ks  bcyk`vg sc ks gd hcshf khpf cmyk`vg y sfbrkyk`vg1 ks jk`cr, sc tfjfs dfs kdkhkmtfs jkd `fmnumtf jk sgdcjg kmkm umg chgekm jcsmtg km kd `fmnumtf jk ddkegjg, y g `gjg kdkhkmtf jkd `fmnumtf jk ddkegjg dk `frrkspfmjk um kdkhkmtf jkd `fmnumtf jk sgdcjg.

Ium`cðm Rkgd Pk ddghg Ium`cðm RKGD, g tfjg ium`cðm ium`cðm jk vgrcgbdk rkgd (pkrtkmk`ckmtk g R, kd `fmnumt `fmnumtf f jk dfs mþhkrfs rkgdks), jkmcjg jk R km R, tgd quk gsf`cg mþhkrfs rkgdks `fm mþhkrfs rkgdks. Gd sk÷gdgr quk ks jk vgrcgbdk rkgd, sk pgrtk jk dg bgsk jk quk kd `fmnumtf jk pgrjg, ks R, vgdk jk`cr kd `fmnumtf jk Mþhkrfs RKGDKP.

 

Ygrcgbdk Kd tãr tãrhcm hcmf f vgr vgrcgb cgbdk dk puk pukjk jk rki rkikrc krcrsk rsk g umf jk dfs sceuck sceuckmtk mtks> s> Km Hg Hgtkh tkhç` ç`g, g, Dðe Dðec`g c`g,, Kstgjès`g y @ckm`cgs. Ygrcgbdk (hgtkhç`gs), ks um sèhbfdf quk pukjk skr rkkhpdgzgjf f quk tfhg um vgdfr muhãrc`f km umg k`ug`cðm f kxprkscðm, hgtkhç`g km ekmkrgd.

Jfhcmcf jk umg vgrcgbdk  i(x @fmnumtf bçsc`f jk mþhkrfs f `gmjgjks quk sk pukjkm cjkm`gr km um skeumjf `fmnumtf. Km çdekbrg kdkhkmtgd, kd jfhcmcf jk umg ium`cðm y 8 x.) ks kd `fmnumtf jk vgdfrks quk pukjk tfhgr dg vgrcgbdk cmjkpkmjckmtk jfhcmcf jk umg vgrcgbdk.

Rgmef jk umg vgrcgbdk Pk jkmk kd rgmef f rk`frrcjf jk umg vgrcgbdk kstgjès`g `fhf dg jcikrkm`cg kmtrk kd hgyfr y kd hkmfr vgdfr jk dg vgrcgbdk. Kd rgmef cmjc`g dg dfmectuj jkd cmtkrvgdf km kd quk sk ogddgm tfjfs dfs jgtfs jk dg jcstrcbu`cðm.

 

Dg `fhpfsc`cðm jk ium`cfmks Dg `fhpfsc`cðm jk ium`cfmks ks dg chgekm rksudtgjf jk dg gpdc`g`cðm su`kscvg jk jfs f hçs ium`cfmks sfbrk um hcshf kdkhkmtf x. Dg `fhpfsc`cðm jk ium`cfmks sk rkgdczg gpdc`gmjf jc`ogs ium`cfmks km frjkm jk jkrk`og g czquckrjg, jk hgmkrg quk km (e f i)(x) prchkrf g`tþg dg ium`cðm i y dukef dg e sfbrk i(x).

Ium`cðm cmvkrsg Pk ddghg ium`cðm cmvkrsg f rk`èprf`g jk umg ium`cðm i g umg mukvg ium`cðm `uyf jfhcmcf ks dg chgekm jk dg ium` ium`cðm cðm cm cmc`cgd, c`cgd, y su chgekm ks kd jfhcmcf jk dg ium`cðm cmc`cg cmc`cgd.d. Ks jk`cr, sc dg ium`cðm e ks dg ium`cðm cmvkrsg jk i, kmtfm`ks sk `uhpdk quk sc i (b) 8 g, kmtfm`ks e(g)8b.

Zcpfs jk Ium`cfmks Rkgdks jk umg sfdg Ygrcgbdk>

[m`cðm Cjkmjgj f Dcmkgd (jk prchkr ergjf) Ium`cðm @ugjrç`g (jk skeumjf ergjf) Ium`cðm @þbc`g (jk tkr`kr ergjf) Ium`cðm Rgèz (pukjk `fmtkmkr jk `ugdquckr èmjc`k) Ium`cfmks \fdcmfhcgdks \fdcmfhcgdks (ium`cfmks jk 0kr ergjf km gjkdgmtk)

 

Ium`cðm dcmkgd [mg ium`cðm dcmkgd ks gqukddg `uyg kxprkscðm ggdekbrgc`g dekbrgc`g ks j jkd kd pf y 8 hx , sckmjf h um mþhkrf mþhk rf `ugdqu `ugdquckrg ckrg jcsm jcsmtf tf jk  Ks kd `fmnumtf ifrhgjf pfr dgs chçekmks. Pfm dfs vgdfrks quk tfhg dg ium`cðm "S" (vgrcgbdk jkpkmjckmtk), pfr ksf sk jkmfhcmg —i(x)‘, su vgdfr jkpkmjk jkd vgdfr quk dk jkhfs g "_". Dg hgmkrg hçs kik`vg pgrg jktkrhcmgr kd Rgmef `fmscstk km erg`gr dg ium`cðm y vkr dfs vgdfrks quk tfhg —S‘ jk gbgnf og`cg grrcbg. F skg sfm dfs vgdfrks quk kmk dg vgrcgbdk —y‘ pgrg jktkrhcmgjfs vgdfrks jk x, km ksg ium`cðm (dfs vgdfrks quk rkgdhkmtk sgdkm). Gsè quk kd rgmef ks um sub`fmnumtf jkd `fmjfhcmcf.

ium`cðm cðm dcm dcmkgd kgd ks umg dèmk dèmkgg rk`tg km um scstkh scstkhgg jk `ff `ffrjk rjkmg mgjg jgss Dg ergi`g>  jk umg ium` `grtkscgmgs. Pfm sckhprk ium`cfmks jkd pf S8(pfdcmfhcf jk prchkr ergjf), ks jk`cr, y8gx+b F hçs usgjf> y8 hx + m Jfmjk h ks dg pkmjckmtk y m ks kd pumtf jk cmtkrsk``cðm km kd knk y.

 

Gpdc`g`cfmks k`fmðhc`gs Kmtrk dgs ium`cfmks quk sk udczgm km k`fmfhèg pgrg og`kr hfjkdfs jk sctug`cfmks jk hkr`gjf sk kstujcgm dgs ium`cfmks jk fikrtg, km dg `ugd umg khprksg quk igbrc`g y vkmjk um jktkrhcmgjf prfju`tf udczg kstg ium`cðm pgrg rkdg`cfmgr dg `gmjgj jk prfju`tfs quk kstç jcspukstg g firk`kr km kd hkr`gjf `fm kd prk`cf umctgrcf gd quk sk pukjk vkmjkr ksg `gmjgj. S dgs ium`cfmks jk jkhgmjg, km dg `ugd Dg khprksg udczg kstg ium`cðm pgrg rkdg`cfmgr dg `gmjgj jk prfju`tfs jkhgmjgjg pfr dfs `fmsuhcjfrks, `fm kd prk`cf umctgrcf gd quk sk pukjk vkmjkr ksg `gmjgj, jk g`ukrjf `fm dg jkhgmjg.

Hfjkdfs dcmkgdks jk cmerksf Ks df quk dg khprksg rk`cbk pfr dg g`vcjgj mgturgd quk rkgdczg, km ftrgs pgdgbrgs ks kd rksudt rks udtgj gjf f jk ogb ogbkr kr vkm vkmjcj jcjf f um prf prfju` ju`tf tf f prk prkstg stgrr um skr skrvc` vc`cf, cf, ju jurgm rgmtk tk um pkr pkrcfj cfjf f jktkrhcmgjf. Cmerksf 8 \rk`cf x `gmjgj Knkhpdfs> 7) [mg `gsg kjctfrcgd vkmjk dcbrfs g umg jktgddcstg km $9.;< pfr dcbrf. Kmtfm`ks, ¶@uçmtf ks kd cmerksf pfr 0< dcbrfs6 Pfdu`cðm> Cmerksf 8 \rk`cf x `gmjgj Cmerksf 8 9.;< x 0< Kd cmerksf pfr 0< dcbrfs ks 8 $73;

 

@fstf Kd `fm`kptf jk `fstfs tftgdks ks kd quk cm`duyk dg suhg jk tfjfs dfs `fstfs quk kstçm gsf`cgjfs gd prf`ksf jk prfju``cðm jk um bckm, f gd suhcmcstrf jk um skrvc`cf, pfr df tgmtf kmtrk hçs sk prfju`k, hgyfr skrç kd `fstf km kd quk sk cm`urrk. Dfs `fstfs tftgdks sk jcvcjkm km jfs `fhpfmkmtks> ` fhpfmkmtks> `fstfs nfs y `fstfs vgrcgbdks. [mg ium`cðm `fstf kspk`c`g kd `fstf @ `fhf umg ium`cðm jk dg `gmjgj jk gr`udfs x. Km `fmsk`ukm`cg, @(x) ks kd `fstf jk x gr`udfs, y kmk dg ifrhg> @fstf 8 @fstf vgrcgbdk + @fstf nf Km dg quk kd `fstf vgrcgbdk ks umg ium`cðm jk x y kd `fstf nf ks `fmstgmtk. [mg ium`cðm `fstf jk dg ifrhg> @(x) 8 hx + b

[tcdcjgj Dg udcjgj ks kd cmerksf mktf, f df quk qukjg jk dfs cmerksfs jkspuãs jk rkstgr dfs `fstfs. Pc dg udcjgj jkpkmjk dcmkgdhkmtk km kd mþhkrf jk gr`udfs, kmtfm`ks dg pkmjckmtk h sk ddghg dg udcjgj hgrecmgd. Dg udcjgj, kd cmerksf, y kd `fstf sfm rkdg`cfmgjfs pfr dg sceuckmtk iðrhudg> [dcjgj 8 Cmerksf − @fstf [8C−@ Pc dg udcjgj ks mkegvg, pfr knkhpdf −$;