Guà - A 3

 

Ualverslhfh _fatd Xd`æs. _ehe Gds Æakeges.

KUÀF HE ECE^OLOLD_ A³? Fslkafturf Ofrrerf

3 @ìtdhds Oufatltftlvds pfrf gf Kestlÿa. 3 Lakealeràf Od`erolfg.

XE@F XE @F33 ZF ZFGD GD^E ^E_ _ E] E]X^ X^E@ E@D_ D_ HE JU JUAO AOLD LDAE AE_ _ HE HD HD_ _ ZF ZF^L ^LFN FNGE GE_. _. DYXL@LSFOLßA AD ODAHLOLDAFHF. Yrdnge`f A³6.- Heter`lae gds extre`ds regftlvds he gfs slkuleates juaoldaes3 f) j(x,y)0 :x-8y-x>->y> ^. (?,-6) `fx. 8 > >  n) j(x,y)0 >x +y -x ->y ^. (-6/>,6)`àa,(9,6)ptd. he slggf,(6/>,6)`àa. > > o) k(x,y)0 y -x ^. (9,9)ptd. he slggf > > h) j(x,y)0 x +?y +8x-,?/>)`àa > > e) j(x,y)0 y-y -?x-:x   ^. (-6/8,6/>)`fx ? > j) j(x,y)0 x -?xy+y +y+5 ^. (6,6)`àa, (6/>,6/8pt. He slggf > > k) j(g,b)0 >gb-g +>:8b-69g->b  ^. (6>>,6>;)`æx ?

?

m) j(x,y)0 x +y -xy m) j(x,y)0>x>+y>->y+8x+6 l) j(x,y)0 x?+y?+?y>-?x-  c) j(x,y)0 x?+y>-:x>+y-6 b) j(x,y)0 8xy>->x>y-x g) j(x,y)0 y>-x>+>x-8y+? `) j(x,y)0 x>+y>-8x->y+;

^. (9,9)ptd. he slggf, (6/?,6/?)`àa ^. (-6,>)`àa

Yrdnge`f A³>.- _updakf que ea gf prdhuoolÿa he olertd frtàougd se requlerea ‗x‐ mdrfs`æqulaff e ‗y‐ mdrfs-trfn `æqula mdrfs-trfnfcfhdr fcfhdr,, y que he fouerhd fouerhd f ua estuhld estuhld he lakealeràf lakealeràf se heter`laÿ heter`laÿ que eg odstd he prdhuoolÿa estæ hfhd pdr O(x,y) ea hÿgfres, hdahe3 O(x,y)0 >x?-:xy+y>+599 Heter`lae eg aó`erd he mdrfs-`æqulaf y he mdrfs-trfnfcfhdr aeoesfrlds pfrf prdhuolr eg frtàougd fg odstd `àal`d.

^. (?,-?y>. ´O ´Ouæ uæat atfs fs ua ualh lhfh fhes es he of ofhf hf frtà frtàou ougd gd he hene nea a prdh prdhuo uolr lrse se hlfrlf`eate pfrf que eg jfnrlofate gdkre gf `æxl`f utlglhfh hlfrlf4. ^. >8u he F y 65u he N.

 

Yrdnge`f A³8.- _ef Y uaf juaolÿa he prdhuoolÿa hfhf pdr3 Y(g,b)0 9,58g>-9,9>g?+6,=-9,9 hÿgfres y ? hÿgfres pdr glnrf. Gfs ofatlhfhes VF  y VN (ea glnrfs) he F y N que puehea veaherse ofhf se`faf estæa hfhfs pdr gfs juaoldaes he he`fahf odacuatf3 VF0 899(YN-YF) y VN0 899(YN) hdahe YF y YN sda gds preolds he veatf (ea hÿgfres pdr glnrf) he F y N respeotlvf`eate. Heter`lafr gds preolds he veatf que `fxl`lzfa gfs utlglhfhes (U) he gf od`pföàf. ^. F05,59hdg/glnrf y N0:hÿg/glnrf Yrdnge`f A³:.- Ea uaf jænrlof, gds trfnfcfhdres se mfa ogfsljlofhd ea > `faerfs3 F y N. Gds trfnfcfhdres tlpd F kfafa $S pdr cdrafhf, `leatrfs que gds heg tlpd N kfafa $[. Yfrf fgofazfr olertf prdhuoolÿa ea uaf cdrafhf, se mf heter`lafhd fu`eatfr gds sfgfrlds he gds trfnfcfhdres, sà se e`pgefa ] trfnfcfhdres heg tlpd F e \ heg tlpd N, eatdaoes eg aó`erd he hÿgfres heg odstd he gf cdrafhf es3 y ?+x>-=xy+:99. ´Ouæatds trfnfcfhdres he ofhf tlpd henea e`pgefrse f jla he que eg odstd he gf cdrafhf sef `àal`d sà se requlerea pdr gd `eads ? trfnfcfhdres he ofhf tlpd pdr uaf cdrafhf4. ^. 88 trfn. tlpd F y 66 trfn. tlpd N Yrdnge`f A¹;.- Eg óalod fg`foìa he od`estlnges he uaf pequeöf od`ualhfh rurfg veahe hds `frofs he cukd he afrfacf megfhd3 uaf `frof gdofg, que dntleae f ua odstd he ?9 ualhfhes `daetfrlfs pdr gftf, y uaf `frof afoldafg, `uy odadolhf, que dntleae f ua odstd he 89 ualhfhes `daetfrlfs pdr gftf. Eg hueöd ofgougf que sl gf `frof gdofg se veahe f ‗x‐ ualhfhes `daetfrlfs pdr gftf y gf `frof afoldafg se veahe f ‗y‐ ualhfhes `daetfrlfs pdr  gftf, ofhf hàf veaheræ fprdxl`fhf`eate ;9-5x+8y gftfs he gf `frof gdofg y =9+:x-;y gftfs he gf `frof afoldafg. ´Vuì preold heneràf jlcfr eg hueöd f ofhf `frof pfrf `fxl`lzfr gfs utlglhfhes dntealhfs he veatf heg cukd4. Yrdnge`f A³=.jfnrlofate prdhuoe ofcfs reotfakugfres y gfs f uaf e`presf heter`lafhf pfrf Ua eg fg`foeaf`leatd he sus prdhuotds. Heter`lae gfsveahe hl`easldaes regftlvfs he uaf ofcf reotfakugfr sla tfpf, que tleae ua vdgu`ea espeoljlod, sl se hesef e`pgefr gf `àal`f ofatlhfh he `fterlfg (rehuoolÿa he odstds) ea su egfndrfolÿa. Yrdnge`f A³