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calculo avanzado dos, Ejercicios de Cálculo

ejercicios de calculo avanzado dos

Tipo: Ejercicios

2021/2022

Subido el 26/09/2022

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@@lfudtllfudtle e eh eh IabhaiIabhaihrhrµµļl, ļl, EishEish˔˔am h Iaamvlfiµam h Iaamvlfiµmama
Hsfuhdl eh Fihafils KµHsfuhdl eh Fihafils Kµlsiflslsifls
Urlklgm fmdlkmrltivm - FµUrlklgm fmdlkmrltivm - Fµldfudm IIldfudm II
FlFljkjkim im fdfdijijµµltltiifmfm
Hd fljkim fdijµHd fljkim fdijµltifm hs ltifm hs ual rhldiele ual rhldiele lejitiel y lejitiel y prhmfuplath plrl prhmfuplath plrl dl fmjuaiele dl fmjuaiele fihatfihatµµļ﬌fl juaeild, ļ﬌fl juaeild, ehkiemehkiem
l quh hd fldhatljihatm bdmkld sh cl lfhdhrlem pmr dl prmeuffiµl quh hd fldhatljihatm bdmkld sh cl lfhdhrlem pmr dl prmeuffiµma iaeustrild eh blshs eh h`hftm iavhralehrm, dlma iaeustrild eh blshs eh h`hftm iavhralehrm, dl
ehstruffiµehstruffiµma eh dl flpl mzmam y dls dduvils µma eh dl flpl mzmam y dls dduvils µlfiels. Fmjm rh`hrhafil quh juhstrl dm brlvh eh hstl prmkdhjµlfiels. Fmjm rh`hrhafil quh juhstrl dm brlvh eh hstl prmkdhjµltifl, dlltifl, dl
MrblaizlfiµMrblaizlfiµma Jhthmrmdµma Jhthmrmdµmbifl Juaeild (MJJ) l﬌rjµmbifl Juaeild (MJJ) l﬌rjµm quh hd ;?<9 `uh hd shbuaem l˔m quh hd ;?<9 `uh hd shbuaem am am ls fµls fµldiem, smdm suphrlemldiem, smdm suphrlem
pmr ;?<0^pmr ;?<0^;
;Z.Z.
Hd fdijl, shbµHd fdijl, shbµua MJJ, ua MJJ, sh eh﬌ah fmjm sh eh﬌ah fmjm hd fmaguatm eh hd fmaguatm eh fmaeifimahs ltjms`µfmaeifimahs ltjms`µhrifls prmpils hrifls prmpils eh ua deh ua dublr ha fihrtmublr ha fihrtm
phrimem eh tihjpm. Ldbuals eh dls vlrilkdhs ehd fdijl sma7 cujhele, visikidiele, rleilfiµphrimem eh tihjpm. Ldbuals eh dls vlrilkdhs ehd fdijl sma7 cujhele, visikidiele, rleilfiµma smdlr, thjphrlturl,ma smdlr, thjphrlturl,
prhfipitlfiµprhfipitlfiµma, vihatm y mtrms. Fma hd prmpµma, vihatm y mtrms. Fma hd prmpµmsitm eh flrlfthrizlr y hstueilr hd fdijl dmfld ehd fljpus priafipld, hdmsitm eh flrlfthrizlr y hstueilr hd fdijl dmfld ehd fljpus priafipld, hd
_mditµ_mditµhfaifm hfaifm BrlafmBrlafmdmjkilam dmjkilam eish˔eish˔m, fmastruyµm, fmastruyµm y pusm ha jlrfcl dl Hstlfiµm y pusm ha jlrfcl dl Hstlfma eh Jmaitmrhm Ljkihatld HJLma eh Jmaitmrhm Ljkihatld HJL^^<
<ZZ
quh jieh ha tihjpm rhld7 thjphrlturl, cujhele rhdltivl, rleilfiµquh jieh ha tihjpm rhld7 thjphrlturl, cujhele rhdltivl, rleilfiµma smdlr bdmkld, aivhd eh dduvil, prhsiµma smdlr bdmkld, aivhd eh dduvil, prhsma lt-ma lt-
jms`µjms`µhrifl y hrifl y vhdmfiele ehd vhdmfiele ehd vihatm. _lrl hd vihatm. _lrl hd ehslrrmddm eh ehslrrmddm eh hsth trlklhsth trlklgm, ehsehgm, ehseh cttp7//hjl.pmdibrla.heu.fm/
cttp7//hjl.pmdibrla.heu.fm/,, shsh
mktuvm dl ia`mrjlfiµmktuvm dl ia`mrjlfiµma quh shrµma quh shrµl iasujm ha ua hghrfifim eh hstl lftiviele.l iasujm ha ua hghrfifim eh hstl lftiviele.
Mkghtivms eh lprhaeizlghMkghtivms eh lprhaeizlgh
<. <. Iathrprhtlr laldµIathrprhtlr laldµļtifl ļtifl y y bhmjµbhmjµhtrifljhath hd htrifljhath hd fmafhptm fmafhptm eh eh iathbrld iathbrld eh﬌aiel.eh﬌aiel.
;. ;. Lpdiflr Lpdiflr hd hd fmafhptfmafhptm eh m eh htmehtmems aujµms aujµhrifms hrifms eh ieh iathbrlfiathbrlfiµµma (rhbdls eh Vijpsma y trlphfims) plrl lprmxijlrma (rhbdls eh Vijpsma y trlphfims) plrl lprmxijlr
hd hd µµlrhl eh ual rhbiµlrhl eh ual rhbiµma pdlal ha dl smdufiµma pdlal ha dl smdufiµma eh situlfimahs prmkdhjl.ma eh situlfimahs prmkdhjl.
Iaeiflfimahs bhahrldhsIaeiflfimahs bhahrldhs
Laths eh iaifilr hd ehslrrmddm ehd trlklgm, hs ijpmrtlath thahr ha fuhatl dls sibuihaths iaeiflfimahs7Laths eh iaifilr hd ehslrrmddm ehd trlklgm, hs ijpmrtlath thahr ha fuhatl dls sibuihaths iaeiflfimahs7
Dhl lDhl lthatljhath thatljhath flel flel hauafilem hauafilem h iehh iehati﬌quµati﬌quµh fuµh fuµld hs dl iastruffiµld hs dl iastruffiµma y su prmpµma y su prmpµmsitm.msitm.
Ld rhbistrlr sus lpmrths am mdvieh hsfrikir ehtlddleljhath tmels dls hxpdiflfimahs y prmfhsms rhldizlemsLd rhbistrlr sus lpmrths am mdvieh hsfrikir ehtlddleljhath tmels dls hxpdiflfimahs y prmfhsms rhldizlems
plrl elr rhspuhstl l flel uam eh dms puatms> rhfuhreh quh sus lpmrths shrµplrl elr rhspuhstl l flel uam eh dms puatms> rhfuhreh quh sus lpmrths shrµla la dhdhµµļems ļems pmr pmr sus sus fmjplfmjpl˔˔ahrms ehahrms eh
trlklgm y shrµtrlklgm y shrµla ua iasujm plrl hd ehslrrmddm ehd trlklgm brupld.la ua iasujm plrl hd ehslrrmddm ehd trlklgm brupld.
Uhabl ha fuhatl dls plutls bhahrldhs eh plrtifiplfUhabl ha fuhatl dls plutls bhahrldhs eh plrtifiplfma y hatrhbl ha hd `mrm.ma y hatrhbl ha hd `mrm.
Vhjlal 6Vhjlal 6
Ha dl rhvisiµHa dl rhvisiµma y fmjhatlrims l dls plrtifiplfimahs eh dms fmjpl˔ma y fmjhatlrims l dls plrtifiplfimahs eh dms fmjpl˔ahrms, iehati﬌quh ahrms, iehati﬌quh lsphlsphftms ftms sijidlrhs, ei`hrhathssijidlrhs, ei`hrhaths
m quh fmjpdhjhatha su lpmrth ld `mrm.m quh fmjpdhjhatha su lpmrth ld `mrm.
Ha hstl htlpl ehd trlklgm fmdlkmrltivm, sh quihrh quh hxpdmrh dl alturldhzl eh dls chrrljihatls ehd laµHa hstl htlpl ehd trlklgm fmdlkmrltivm, sh quihrh quh hxpdmrh dl alturldhzl eh dls chrrljihatls ehd laµldisisldisis
aujµaujµhrifm hrifm ha ha hd hd fmathxtm fmathxtm ehd ehd ldfudm iathbrld fma prmkdhjls lpdiflems, plrl dms fuldhs am sh fmamfh ual smdufiµldfudm iathbrld fma prmkdhjls lpdiflems, plrl dms fuldhs am sh fmamfh ual smdufiµmama
laldµlalļtifl ļtifl m m am am hs hs lfid eh mkthahr7lfid eh mkthahr7
[hsuhdvl[hsuhdvluamuameh dms hghrfifims quh sh hxpmaha l fmatiaulfeh dms hghrfifims quh sh hxpmaha l fmatiaulfma ma hjpdhlem hd hjpdhlem hd htmem htmem quh sh quh sh subihrh, pukdiquh subihrh, pukdiquh susu
smdufiµsmdufiµma ha hd `mrm, rhvish hd lpmrth eh uam eh sus fmjpl˔ma ha hd `mrm, rhvish hd lpmrth eh uam eh sus fmjpl˔ahrms y rhbistrh si hs fmrrhftm m am hd prmfhsm gusti﬌flaemahrms y rhbistrh si hs fmrrhftm m am hd prmfhsm gusti﬌flaem
su rhspuhstl7su rhspuhstl7^^6
6,,55ZZ
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Hsfuhdl eh Fihafils KμHsfuhdl eh Fihafils Kμlsiflslsifls Urlklgm fmdlkmrltivm - FμUrlklgm fmdlkmrltivm - Fμldfudm IIldfudm II

FlFljkjkimim fdfdijijμμltltiifmfm

Hd fljkim fdijμHd fljkim fdijμltifm hsltifm hs ual rhldieleual rhldiele lejitiel ylejitiel y prhmfuplath plrlprhmfuplath plrl dl fmjuaieledl fmjuaiele fihatfihatμμļ﬌fl juaeild,ļ﬌fl juaeild, ehkiemehkiem l quh hd fldhatljihatm bdmkld sh cl lfhdhrlem pmr dl prmeuffiμl quh hd fldhatljihatm bdmkld sh cl lfhdhrlem pmr dl prmeuffiμma iaeustrild eh blshs eh hhftm iavhralehrm, dlma iaeustrild eh blshs eh hhftm iavhralehrm, dl ehstruffiμehstruffiμma eh dl flpl mzmam y dls dduvils μma eh dl flpl mzmam y dls dduvils μlfiels. Fmjm rhhrhafil quh juhstrl dm brlvh eh hstl prmkdhjμlfiels. Fmjm rhhrhafil quh juhstrl dm brlvh eh hstl prmkdhjμltifl, dlltifl, dl

MrblaizlfiμMrblaizlfiμma Jhthmrmdμma Jhthmrmdμmbifl Juaeild (MJJ) l﬌rjμmbifl Juaeild (MJJ) l﬌rjμm quh hd ;?<9 uh hd shbuaem l˔m quh hd ;?<9uh hd shbuaem l˔am jμam jμls fμls fμldiem, smdm suphrlemldiem, smdm suphrlem pmr ;?<0^pmr ;?<0^;;Z.Z. Hd fdijl, shbμHd fdijl, shbμua MJJ,ua MJJ, sh eh﬌ah fmjmsh eh﬌ah fmjm hd fmaguatm ehhd fmaguatm eh fmaeifimahs ltjmsμfmaeifimahs ltjmsμhrifls prmpilshrifls prmpils eh ua deh ua dublr ha fihrtmublr ha fihrtm phrimem eh tihjpm. Ldbuals eh dls vlrilkdhs ehd fdijl sma7 cujhele, visikidiele, rleilfiμphrimem eh tihjpm. Ldbuals eh dls vlrilkdhs ehd fdijl sma7 cujhele, visikidiele, rleilfiμma smdlr, thjphrlturl,ma smdlr, thjphrlturl, prhfipitlfiμprhfipitlfiμma, vihatm y mtrms. Fma hd prmpμma, vihatm y mtrms. Fma hd prmpμmsitm eh flrlfthrizlr y hstueilr hd fdijl dmfld ehd fljpus priafipld, hdmsitm eh flrlfthrizlr y hstueilr hd fdijl dmfld ehd fljpus priafipld, hd _mditμ_mditμhfaifmhfaifm BrlafmBrlafmdmjkilamdmjkilam eish˔eish˔aμaμm, fmastruyμm, fmastruyμm y pusm ha jlrfcl dl Hstlfiμm y pusm ha jlrfcl dl Hstlfiμma eh Jmaitmrhm Ljkihatld HJLma eh Jmaitmrhm Ljkihatld HJL^^<<ZZ quh jieh ha tihjpm rhld7 thjphrlturl, cujhele rhdltivl, rleilfiμquh jieh ha tihjpm rhld7 thjphrlturl, cujhele rhdltivl, rleilfiμma smdlr bdmkld, aivhd eh dduvil, prhsiμma smdlr bdmkld, aivhd eh dduvil, prhsiμma lt-ma lt- jmsμjmsμhrifl yhrifl y vhdmfiele ehdvhdmfiele ehd vihatm. _lrl hdvihatm. _lrl hd ehslrrmddm ehehslrrmddm eh hsth trlklhsth trlkl gm, ehsehgm, ehseh cttp7//hjl.pmdibrla.heu.fm/cttp7//hjl.pmdibrla.heu.fm/,, shsh mktuvm dl iamrjlfiμmktuvm dl iamrjlfiμma quh shrμma quh shrμl iasujm ha ua hghrfifim eh hstl lftiviele.l iasujm ha ua hghrfifim eh hstl lftiviele.

Mkghtivms eh lprhaeizlghMkghtivms eh lprhaeizlgh

<.<. Iathrprhtlr laldμIathrprhtlr laldμļtiflļtifl yy bhmjμbhmjμhtrifljhath hdhtrifljhath hd fmafhptmfmafhptm eheh iathbrldiathbrld eh﬌aiel.eh﬌aiel. ;.;. LpdiflrLpdiflr hdhd fmafhptfmafhptm ehm eh jμjμhtmehtmems aujμms aujμhrifmshrifms eh ieh iathbrlfiathbrlfiμμma (rhbdls eh Vijpsma y trlphfims) plrl lprmxijlrma (rhbdls eh Vijpsma y trlphfims) plrl lprmxijlr hdhd μμlrhl eh ual rhbiμlrhl eh ual rhbiμma pdlal ha dl smdufiμma pdlal ha dl smdufiμma eh situlfimahs prmkdhjl.ma eh situlfimahs prmkdhjl.

Iaeiflfimahs bhahrldhsIaeiflfimahs bhahrldhs

Laths eh iaifilr hd ehslrrmddm ehd trlklgm, hs ijpmrtlath thahr ha fuhatl dls sibuihaths iaeiflfimahs7Laths eh iaifilr hd ehslrrmddm ehd trlklgm, hs ijpmrtlath thahr ha fuhatl dls sibuihaths iaeiflfimahs

Dhl lDhl lthatljhaththatljhath flelflel hauafilemhauafilem h iehh iehati﬌quμati﬌quμh fuμh fuμld hs dl iastruffiμld hs dl iastruffiμma y su prmpμma y su prmpμmsitm.msitm.

Ld rhbistrlr sus lpmrths am mdvieh hsfrikir ehtlddleljhath tmels dls hxpdiflfimahs y prmfhsms rhldizlemsLd rhbistrlr sus lpmrths am mdvieh hsfrikir ehtlddleljhath tmels dls hxpdiflfimahs y prmfhsms rhldizlems plrl elr rhspuhstl l flel uam eh dms puatms> rhfuhreh quh sus lpmrths shrμplrl elr rhspuhstl l flel uam eh dms puatms> rhfuhreh quh sus lpmrths shrμlala dhdhμμļemsļems pmrpmr sussus fmjplfmjpl˔˔ahrms ehahrms eh trlklgm y shrμtrlklgm y shrμla ua iasujm plrl hd ehslrrmddm ehd trlklgm brupld.la ua iasujm plrl hd ehslrrmddm ehd trlklgm brupld.

Uhabl ha fuhatl dls plutls bhahrldhs eh plrtifiplfiμUhabl ha fuhatl dls plutls bhahrldhs eh plrtifiplfiμma y hatrhbl ha hd mrm.ma y hatrhbl ha hdmrm.

Vhjlal 6Vhjlal 6

Ha dl rhvisiμHa dl rhvisiμma y fmjhatlrims l dls plrtifiplfimahs eh dms fmjpl˔ma y fmjhatlrims l dls plrtifiplfimahs eh dms fmjpl˔ahrms, iehati﬌quhahrms, iehati﬌quh lsphlsphftmsftms sijidlrhs, eihrhathssijidlrhs, eihrhaths m quh fmjpdhjhatha su lpmrth ld mrm.m quh fmjpdhjhatha su lpmrth ldmrm. Ha hstl htlpl ehd trlklgm fmdlkmrltivm, sh quihrh quh hxpdmrh dl alturldhzl eh dls chrrljihatls ehd laμHa hstl htlpl ehd trlklgm fmdlkmrltivm, sh quihrh quh hxpdmrh dl alturldhzl eh dls chrrljihatls ehd laμldisisldisis aujμaujμhrifmhrifm haha hdhd fmathxtmfmathxtm ehdehd fμfμldfudm iathbrld fma prmkdhjls lpdiflems, plrl dms fuldhs am sh fmamfh ual smdufiμldfudm iathbrld fma prmkdhjls lpdiflems, plrl dms fuldhs am sh fmamfh ual smdufiμmama laldμlaldμļtiflļtifl mm amam hshs μμlfid eh mkthahr7lfid eh mkthahr [hsuhdvl[hsuhdvl uamuam eh dms hghrfifims quh sh hxpmaha l fmatiaulfiμeh dms hghrfifims quh sh hxpmaha l fmatiaulfiμmama hjpdhlem hdhjpdhlem hd jμjμhtmemhtmem quh shquh sh subihrh, pukdiquhsubihrh, pukdiquh susu smdufiμsmdufiμma ha hd mrm, rhvish hd lpmrth eh uam eh sus fmjpl˔ma ha hdmrm, rhvish hd lpmrth eh uam eh sus fmjpl˔ahrms y rhbistrh si hs fmrrhftm m am hd prmfhsm gusti﬌flaemahrms y rhbistrh si hs fmrrhftm m am hd prmfhsm gusti﬌flaem su rhspuhstl7su rhspuhstl7^^6 6 ,, 5 5 ZZ

Hsfuhdl eh Fihafils KμHsfuhdl eh Fihafils Kμlsiflslsifls Urlklgm fmdlkmrltivm - FμUrlklgm fmdlkmrltivm - Fμldfudm IIldfudm II

HstHstueiueilalath <.th <. [hb[hbdldl ehd Urehd Urlphfilphfimm yy eheh VijVijpsmpsmaa Xtidifh dl rhbdl ehd trlphfim y dl [hbdl eh Vijpsma <Xtidifh dl rhbdl ehd trlphfim y dl [hbdl eh Vijpsma <// 66 plrl mkthahr ua vldmr lprmxijlem eh dl iathbrld7plrl mkthahr ua vldmr lprmxijlem eh dl iathbrld

Ϗ/Ϗ/;;

siasia xx xx

etet aa :: 0 0

Fmjplrh dms rhsudtlems mkthaiems fma dls ems rhbdls y hsfrikl ual fmafdusiμFmjplrh dms rhsudtlems mkthaiems fma dls ems rhbdls y hsfrikl ual fmafdusiμma.ma.

HstueilHstueilath ;ath ;.. IathbrlIathbrldhsdhs hdhdμμļptiflļptiflss. Dl sibuihath iathbrld prmpmrfimal dl firfuahrhafil eh ual hdipsh7. Dl sibuihath iathbrld prmpmrfimal dl firfuahrhafil eh ual hdipsh

∗∗ 66

??

<< ∛∛ ;; 66 siasia;;^ γγ eγeγ

Hjpdhh dl rhbdl eh Vijpsma <Hjpdhh dl rhbdl eh Vijpsma <//6 fma6 fma aa : 3 plrl lprmxijlr dl firfuahrhafil.: 3 plrl lprmxijlr dl firfuahrhafil.

Hstueilath 6.Hstueilath 6. DlDl sibuihath iathbrld rhprhshatl dlsibuihath iathbrld rhprhshatl dl hahrbhahrbμμļl blalelļl blalel pmrpmr hd ehsdizljihatm ehhd ehsdizljihatm eh ual pltiahtlual pltiahtl clfilclfil lklgm smkrh ual fmdial sia riffiμlklgm smkrh ual fmdial siariffiμmama ll xx jhtrms ljhtrms l plrtir ehplrtir eh dl fijldl fijl eh dleh dl fmdial, ehspuμfmdial, ehspuμhs ehhs eh tt shbuaems7shbuaems

HH ((xx)) ::

bJbJ ∗∗ ;;ϏϏ

 xx

??

hh∛∛tt

;; (^) //;; etet

emaehemaeh bb :: 9 9 ,, 3 3 yy JJ : 0?. Vi dl vhdmfiele ehd pltialemr l dms: 0?. Vi dl vhdmfiele ehd pltialemr l dms tt shbuaems hsshbuaems hs

vv ::

;;HH ((xx)) JJ Xsh dl rhbdl eh Vijpsma <Xsh dl rhbdl eh Vijpsma <//6 fma6 fma aa : <? plrl lprmxijlr dl vhdmfiele ehd pltialemr l ;: <? plrl lprmxijlr dl vhdmfiele ehd pltialemr l ;jj l plrtir eh dll plrtir eh dl fijl eh dl fmdial.fijl eh dl fmdial.

HstueiHstueilath 5.lath 5. _rmkdhj_rmkdhjll eh fmstmeh fmstm Vh rhquihrh fmastruir ua tμVh rhquihrh fmastruir ua tμuahd fma dl mrjl quh sh juhstrl ha dl ﬌burluahd fma dlmrjl quh sh juhstrl ha dl ﬌burl <.<.

@iburl <7 Uμ@iburl <7 Uμuahduahd

Hsth ehkh thahr ual dmabitue eh 6?? pihs eh dlrbm y 8? pihs eh lafcm ha dl klsh. Dls shffimahs trlasvhrsldhsHsth ehkh thahr ual dmabitue eh 6?? pihs eh dlrbm y 8? pihs eh lafcm ha dl klsh. Dls shffimahs trlasvhrsldhsμμ tihaha dl mrjl eh ua lrfm eh dl furvltihaha dlmrjl eh ua lrfm eh dl furvl yy : ;8fms: ;8fms

ϏϏxx 8?8? Clstl su thrjialfiμClstl su thrjialfiμma, dl suphr﬌fih iathral ehd tμma, dl suphr﬌fih iathral ehd tμuahd (hxfduyhaem hd fljiam) shrl trltlel fma ua shddlemruahd (hxfduyhaem hd fljiam) shrl trltlel fma ua shddlemr rhsisthath ld lbul quh tihah ua fmstm ehrhsisthath ld lbul quh tihah ua fmstm eh $$<.28 pmr pih fulerlem.<.28 pmr pih fulerlem. L½FuμL½Fuμˀˀ ld shrμld shrμl hd fmstm eh lpdiflr hd shddlemr=.l hd fmstm eh lpdiflr hd shddlemr=. Xditifh dl rhbdl ehd trlphfim yXditifh dl rhbdl ehd trlphfim y aa : <? plrl ehthrjialr dl dmabitue eh dl furvl ehd tμ: <? plrl ehthrjialr dl dmabitue eh dl furvl ehd tμuahd.uahd.

Hsfuhdl eh Fihafils KμHsfuhdl eh Fihafils Kμlsiflslsifls Urlklgm fmdlkmrltivm - FμUrlklgm fmdlkmrltivm - Fμldfudm IIldfudm II

rleilfiμrleilfiμma hstuvm hxpuhstl dl suphr﬌fih eh ua sisthjl ha fihrtm iathrvldm eh tihjpm y sh fldfudl fma7ma hstuvm hxpuhstl dl suphr﬌fih eh ua sisthjl ha fihrtm iathrvldm eh tihjpm y sh fldfudl fma

CChh ::

 tt``

ttii

HHhh((υυ ))eυ.eυ.

EmaehEmaeh ttii hs ua tihjpm iaifild yhs ua tihjpm iaifild y tt`` hs ua tihjpm ﬌ald.hs ua tihjpm ﬌ald. Hd prmpμHd prmpμmsitm ha hstl htlpl hs jheirmsitm ha hstl htlpl hs jheir CC (^) hh plrlplrl ua eμua eμļl uslaemļl uslaem dms eltmsdms eltms sujiaistrlems pmrsujiaistrlems pmr HJL yHJL y rhfurrihaemrhfurrihaem ldld jμjμhtmemhtmem eh teh trlphfims.rlphfims. _lrl hstm_lrl hstm sh ehksh ehkh7h

l.l. EhsfEhsflrblr ha hd sibuihath dianlrblr ha hd sibuihath dian cttps7//kit.dy/6aAljRDcttps7//kit.dy/6aAljRD dmsdms eltms lrrmglems peltms lrrmglems pmrmr HJL hdHJL hd eeμμļlļl 55 eheh lkrid ehlkrid eh ;?;<. Hsth lrfcivm hs hd iasujm hshafild eh hstl lftiviele.;?;<. Hsth lrfcivm hs hd iasujm hshafild eh hstl lftiviele.

Ha hd lrfcivm Hxfhd (Ha hd lrfcivm Hxfhd (cttps7//kit.dy/6aAljRDcttps7//kit.dy/6aAljRD), cly eihz cmgls eh fμ), cly eihz cmgls eh fμldfudmldfudm aujhrleaujhrlelsls fmafma dmsdms eeμμļbi-ļbi- tms ehd fhrm (??) ld auhvh (?9). L su brupm dh fmrrhspmaeha dl cmgl fma dms eltms quh fmiafieltms ehd fhrm (??) ld auhvh (?9). L su brupm dh fmrrhspmaeha dl cmgl fma dms eltms quh fmiafiel fma hd μfma hd μudtijmudtijm eeμμļbitmļbitm ehdehd aμaμujhrm eh su suk-brupm.ujhrm eh su suk-brupm.

Xa hghjpdm eh dl lsibalfiμXa hghjpdm eh dl lsibalfiμma hs7 Vi hd aμma hs7 Vi hd aμujhrm eh su brupm hs ;6, hd μujhrm eh su brupm hs ;6, hd μudtijmudtijm eeμμļbitmļbitm hs 6hs 6 pmr tlapmr tlatmtm dh fmrrhspmaehdh fmrrhspmaeh dl cmgl eh fμdl cmgl eh fμldfudm ?6. Mtrm hghjpdm, si su brupm hs ;?, hd μldfudm ?6. Mtrm hghjpdm, si su brupm hs ;?, hd μudtijudtijmm eeμμļbitm hsļbitm hs ?,?, dhdh fmfmrrrrhsphspmaehmaeh dldl dldl cmglcmgl eheh fμfμldfudm ??. Vi su brupm ehslrrmddl hd trlklgm fma ual cmgl eistiatl l dl quh dh fmrrhspmaeh eh lfuhrem fma dlldfudm ??. Vi su brupm ehslrrmddl hd trlklgm fma ual cmgl eistiatl l dl quh dh fmrrhspmaeh eh lfuhrem fma dl rhbdl lathrimr, dl amtl hs fhrm fmjl fhrm (?,?) puatms.rhbdl lathrimr, dl amtl hs fhrm fmjl fhrm (?,?) puatms.

k.k. IehaIehati﬌flr dms eltms dl fmdujati﬌flr dms eltms dl fmdujal eh dll eh dl rleilfrleilfiμiμma ^[LEIZ.ma ^[LEIZ.

f.f. [hfm[hfmastruastruir brμir brμl﬌fljhath dl uafiμl﬌fljhath dluafiμma ha hd iathrvldm elem. Amtl7 Ha dl hdlkmrlfiμma ha hd iathrvldm elem. Amtl7 Ha dl hdlkmrlfiμma eh dl brμma eh dl brμl﬌fl sh ehkh thahrl﬌fl sh ehkh thahr fuielfuielem ehem eh jlahgjlahglr dllr dl hsfldl eh tldhsfldl eh tld mrjl quh hstl sh vhl fmjpdhtl ymrjl quh hstl sh vhl fmjpdhtl y eh tljl˔eh tljl˔am lehfulem. Am mdvieha rmtudlram lehfulem. Am mdvieha rmtudlr hghs, fma sus fmrrhspmaeihaths uaielehs eh jheiel y titudlr dl brμhghs, fma sus fmrrhspmaeihaths uaielehs eh jheiel y titudlr dl brμl﬌fl.l﬌fl.

e. Fldfudlr hd μe. Fldfudlr hd μlrhllrhl klgmklgm dldl furvfurvll uslaem hduslaem hd jμjμhtmemhtmem eheh trlphfims.trlphfims.

h.h. XslaXslaemem iathiathbrlfiμbrlfiμmama aujμaujμhrihriflfl^^6 6 ,, 55 Z y hd thmrhjl ehd vldmr jheim plrl iathbrldhs, fldfudh ha hd iathvldm ehZ y hd thmrhjl ehd vldmr jheim plrl iathbrldhs, fldfudh ha hd iathvldm eh tihjpm eh dl tlkdl hd vldmr eh dl rleilfiμtihjpm eh dl tlkdl hd vldmr eh dl rleilfiμma jheil.ma jheil.

.. HsfrHsfrikir ual fmafduikir ual fmafdusiμsiμma ehd hghrfifim.ma ehd hghrfifim.

[hhrhafils[hhrhafils

^<Z Hstlfiμ^<Z Hstlfiμma eh Jmaitmrhm Ljkihatld HJL7ma eh Jmaitmrhm Ljkihatld HJL7 cttp7//hjl.pmdibrla.heu.fm/cttp7//hjl.pmdibrla.heu.fm/..

^;Z^;Z MrblaMrblaizlfiμizlfiμmama JhthmrJhthmrmdμmdμmbiflmbifl JuaeiJuaeild7ld7 cttps7//pukdif.wjm.iat/hscttps7//pukdif.wjm.iat/hs..

^6Z^6Z VthwVthwlrt, G. (;?lrt, G. (;??3). Fμ?3). Fμldfudm eh ual Plrilkdh, trlasfhaehaths thjprlals. Iathraltimald Ucmjpsma Heitmrhs.ldfudm eh ual Plrilkdh, trlasfhaehaths thjprlals. Iathraltimald Ucmjpsma Heitmrhs.

^^5Z5Z UUccmmjjllss,, BB.. KK..,, && RRhhiirr,, JJ.. EE.. ((;?;???00).). FFμμldfldfududm7m7 uauall vvlrlrililkdkdh.h. __hlhlrsrsmama HeHeufuflflfiμiμma7ma7 cttps7//cttps7// www-hkmmns2-;5-fmj.dmbiakikdim.pmdibrla.heu.fm/=id:65;<www-hkmmns2-;5-fmj.dmbiakikdim.pmdibrla.heu.fm/=id:65;< ..