Excedentes Del Productor y Consumidor Con Integrales Word

 

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GRHGLG@\G LGI VTELWH\ET _ HE@XWAOLET HE@ O@\GKTJIGX

Ae`ekrjcáj prgsg`tjlj pjrj huapior he` ies rgquosotes lg ij gvjiujhoø` lgi hurse lg Ajtgaêtohj OO. Krupe= 64 Xudkrupe= 7  

O`tgkrj`tgs=

Hbj`hjcg O`hoe, Muioj`j lgi Voijr  Lojz Vghbg, Lj`otzj Hjreio`j Tgjtgkuo \errgs, Vjuij Roeajrj Xjijs Soiijr, Jroj`j Aoig`j \ja Soihj, Iozajyio` Iebj`j

Xj` Muj` lg Iurokj`hbe, G`gre lgi 464:

 

4

J

`ugstres

pjlrgs

per 

ku kuoj ojr` r`es es g` gi hjao hjao`e `e herr herrgh ghte te he` he` su jpeye jpe ye o`h o`he`l e`loho ohoe`j e`jii y j `ugst `ugstre re qugrol qugrolee  precgser per tg`gr`es tg`gr`es lgajsojl lgajsojljj pjhog`hoj.

 

8

Á`lohg

Tgsuag`............................................... Tgsuag`......................... ............................................ ............................................ ....................................................... ................................. søie lgspuïs, y trjs `e pehes o`tg`tes cjiioles, sg prelume ij cerajiozjhoø` rokuresj lg ij loshopio`j. Ies predigajs tápohes qug logre` erokg` ji hêihuie o`co`otgsoaji heag`zjre` j pij`tgjrsg g` ij ïpehj hiêsohj lg ij j`tokuj Krgh Kr ghoj oj (sokie OOO j. H.), pgre `e sg g`he`trjre` aïteles sostgaêtohes lg rgseiuhoø` bjstj bjs tj log logho` ho`ugv ugvgg sokies sokies lgs lgspuï puïss (g` gi sokie RSOO per edrj lg Osjjh @gwte` y Kettcrogl Igod`oz). G` ie qug jtjúg j ijs lgrovjljs gxostg` les he`hgptes lg tope

kgeaïtrohe qug ig logre` erokg`= 

Gi predigaj lg ij tj`kg`tg j u`j hurvj (Jpeie`oe lg Vgrkg)



Gi \gergaj lg ies gxtrgaes= aêxoaes y aá`oaes (Vogrrg lg Cgrajt)

G` su he`mu`te logre` erokg` j ie qug jhtujiag`tg sg he`ehg heae hêihuie locgrg`hoji. G` gi Xokie RSOO ies ajtgaêtohes pgrlogre` gi aogle qug ies krogkes igs bjdáj` tg`ole j ies o`co`otgsoajigs= Mebj``gs Ngpigr y De`jvg`turj Hjvjiogro cugre` ies proagres g` usjries, gapgzjre` j j`ljr u` hjao`e qug iigvjráj g` agloe sokie ji lgshudroaog`te lgi hêihuie o`co`otgsoaji. J aglojles lgi sokie RSOO ijs hj`toljlgs o`co`otgsoajigs cugre` hj hjlj lj vgz vgz aê aêss us usjl jljs js pj pjrj rj rg rgse seiv ivgr gr pr pred edig igaj ajss lg hêih hêihui uies es lg tj tj`k `kg` g`tg tgs, s, êrgj êrgjs, s, veiýag`gs> ies proagres ljráj` erokg` ji hêihuie locgrg`hoji, ies etres j ij o`tgkrji.

 

2 J co`jigs lgi sokie RSOO sg so`tgtozjre` g` les he`hgptes ies jikerotaes usjles per sus  prglghgsergs,  prglghgserg s, g` ie qug bey iijajaes «lgrovjlj¾ g «o`tgkrji¾. Ij bosteroj lg ij ajtgaêtohj rghe`ehg qug Osjjh @gwte` y Kettcrogl Igod`oz se` ies hrgjlergs lgi hêihuie locgrg`hoji g o`tgkrji. Giies lgsjrreiijre` rgkijs pjrj aj`opuijr ijs lgrovjljs (rgkijs lg lgrovjhoø`) g Osjjh Djrrew lgaestrø qug ij lgrovjhoø` y ij o`tgkrjhoø` se` epgrjhoe`gs o`vgrsjs.  @gwte` lgsjrreiiø g` Hjadrolkg su prepoe aïtele pjrj gi hêihuie lg tj`kg`tgs. G` :337 g`he`trø u` jikerotae pjrj lgrovjr cu`hoe`gs jikgdrjohjs qug heo`holáj he` gi lgshudogrte per Cgrajt. J co`jigs lg :337 sg lglohø j rggstruhturjr ijs djsgs lg su hêihuie, o`tg`tj`le lgsiokjrsg lg ies o`co`otgsoajigs, g o`trelume gi he`hgpte lg ciuxoø`, qug pjrj ïi grj ij vgieholjl he` ij qug u`j vjrojdig «ciuyg¾ (vjráj) he` gi togape. Kettcrogl Igod`oz, per su pjrtg, cerauiø y lgsjrreiiø gi hêihuie locgrg`hoji g` :3;7. Cug gi proagre g` pudiohjr ies aosaes rgsuitjles qug Osjjh @gwte` lgshudrogrj :6 júes j`tgs, lg aj`grj o`lgpg`log`tg. G` su o`vgstokjhoø` he`sgrvø u` hjrêhtgr kgeaïtrohe y trjtø j ij lgrovjlj heae u` hehog`tg o`hrgag`tji y `e heae u`j vgieholjl, vog`le gi sg`tole lg su herrgspe`lg`hoj he` ij pg`log`tg lg ij rghtj tj`kg`tg j ij hurvj g` lohbe  pu`te. Igod`oz gs gi o`vg`ter lg lovgrses sáadeies ajtgaêtohes. J ïi sg lgdg` ies `eadrgs lg= hêihuie locgrg`hoji y hêihuie o`tgkrji, jsá heae ies sáadeies lg lgrovjlj y', c'(x) y ly/lx y gi sáadeie lg ij o`tgkrji ∮. Vjrghg, per giie, gao`g`tgag`tg rjze`jdig g`hujlrjr gi gstuloe lg sus he`hgptes y tïh`ohjs g` u` ajrhe o`ohoji lg hjrêhtgr prêhtohe, g` gi qug gi j`êiosos lg predigajs jlao`o jla o`ostr strjto jtove vess táp tápohe ohess iigvg iigvg lg ael aelee `j `jtur turji ji j ij `ghgso `ghgsolj ljll lg ’lgsh ’lgshudr udror‑ or‑ ies he`hgptes dêsohes lg gstjs rjajs lg ij ajtgaêtohj. Gi gxhglg`tg lgi he`suaoler sg lgco`g heae ij locgrg`hoj g`trg ies he`suaolergs lospugstes j pjkjr per u` jrtáhuie (gs

 

? lghor, su vjierjhoø`, e gi aêxoae qug gstê` lospugstes j pjkjr) y gi prghoe rgji qug  pjkj`, aog`trjs qug gi gxhglg`tg lgi preluhter sg lgco`g heae ij locgrg`hoj g`trg  preluhtergs lospesohoø` vg`lgr (gs lghor, su heste ajrko`ji, e gi aá`oae qug sg vg`lgráj u` jrtáhuie pjrj) y gi prghoe rgji qug rghodg`. Lgpg`log`le lgi he`tgxte, gi gxhglg`tg lgi he`suaoler y gi gxhglg`tg lgi preluhter sg puglg` hjihuijr pjrj u` o`lovolue he`suaoler, preluhter, e u`oljl lg preluhhoø` / he`suae, e puglg hjihuijrsg  pjrj teles ies he`suaolergs e preluhtergs lg u` u` agrhjle.

Hjpátuie OO= \geráj lg ies Gxhglg`tgs lgi He`suaoler y Vreluhte. 4.:. Gxhglg`tgs lgi He`suaoler= 

Ies he`suaolergs heaprj` u`j hj`toljl y*ji prghoe p*. Vgre bjy ` he`suaolergs qug gstjráj` lospugstes j pjkjr u` prghoe aês jite. Gi gxhglg`tg lgi he`suaoler sg lgco`g heae ij locgrg`hoj g`trg ies qug gstjráj` lospugstes j pjkjr ies he`suaolergs per u`j lgtgrao`jlj hj`toljl lg preluhte y ie qug gcghtovjag`tg pjkj`.

4.4. Gxhglg`tgs lgi Vreluhter=

 

:6 Huj`le sg gstjdighg u` prghoe lgi agrhjle, teles ies preluhtergs ecrghg` gsg preluhte ji prghoe lgi agrhjle> pgre bjy ` preluhtergs qug gstjráj` lospugstes j ecrghgr gi  preluhte j u` prghoe prghoe ag`er. Gi gxhglg`tg lgi preluhter gs ij locgrg`hoj g`trg gi prghoe qug pgrhodg gi preluhter y gi  prghoe qug gstjráj` gstjráj` lospugstes j ecrghgr hjlj uu`j `j lg ijs u`oljlgs u`oljlgs lgi prelu preluhte. hte.

Hjpátuie OOO= J`jiosos Ajtgajtohes 

Gi gxhglg`tg lgi he`suaoler sgrê cerajle per gi êrgj lgi troê`kuie cerajle per  ies pu`tes ’j‑, ’e‑, y ’Vg‑lg ij cokurj. Ij ghujhoø` qug rgprgsg`tj lohbj êrgj gs ij sokuog`tg=

 

:: :

 Gxhglg`tg∔ he`suaoler 1

4

∛ j∔ h l+ d

 ^

j∔

 Q

l∛j + d∛h l +d

le`lg gi proagr qugdrjle iotgrji gs ij hj`toljl lg gquoiodroe qug sgráj ij djsg lgi troê`kuie, y gi tïrao`e g`trg herhbgtgs gs ij jiturj lgi aosae.



Gxhglg`tgss lgi he`suaoler= Gxhglg`tg

(  )

d j∔ h 4 l +d 

Gxhglg`tg lgi preluhter=

( )

l j ∔h 4 l +d 

4

4

Gxhglg`tg \etji= : 4

4

∛(j ∔h ) d+ l



Gxhglg`tg Tgijtove= d 4

l

1

d l

4

Hjpotuie OS= Jpiohjhoø` j ij Jlao`ostrjhoø` y Ghe`eaáj