prob_set5 - Sureohp Vhw 8 DUH 594 Rfwrehu 4:/ 5334 Txhvwlrq...

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Unformatted text preview: Sureohp Vhw 8 DUH 594 Rfwrehu 4:/ 5334 Txhvwlrq 4 Khuh duh vrph phfkdqlfdo h{huflvhv xvlqj wkh olqhdu0txdgudwlf sureohp1 Iru wkh sureohp pd{ ] 5 4 + { w b { b { 5 , gw +4, vxemhfw wr { +4, @ 6 dqg { +5, @ 7 / zulwh grzq wkh Hxohu htxdwlrq dqg qg lwv vroxwlrq1 Zulwh wkh qhfhvvdu| frqglwlrqv xvlqj wkh Pd{lpxp Sulqflsoh ri wkh sure0 ohp pd{ ] 8 4 + x{ x 5 { 5 , gw +5, vxemhfw wr b { @ { x / { +4, @ 5 dqg { +8, @ { 8 1 %Jxhvv% wkdw wkh frvwdwh yduldeoh lv d olqhdu ixqfwlrq ri { / @ v + w , { 1 Zulwh grzq wkh RGH iru v + w , 1 Txhvwlrq 5 Wkh srlqw ri wklv h{huflvh lv wr ghyhors lqwxlwlrq iru vwhdg| vwdwh frpsdudwlyh vwdwlfv1 Li |rx qg lw hdvlhu wr zrun zlwk vshfl f ixqfwlrqv X + k , dqg f + { , / slfn d frxsoh ri frqyhqlhqw rqhv/ h1j1 frqvwdqw hodvwlflw|1 Wkhq wu| wr gr wkh sureohp xvlqj jhqhudo ixqfwlrqv dv zhoo1 Wkh vwrfn ri vk/ { + w , / jurzv dw d udwh b { + w , @ i + { , k / zkhuh k lv wkh kduyhvw dqg i + { , lv wkh orjlvwlf jurzwk fxuyh= i + { , @ { + { , 1 Wkh xwlolw| ri frqvxpswlrq lv X + k , / zkhuh X 3 + k , @ s + k , / wkh pdunhw sulfh1 Wkh h{wudfwlrq frvwv duh f + { , k / zlwk f 3 + { , 3 1 Wkh qhw xwlolw| ri kduyhvw lv X + k , f + { , k 1 Ilqg wkh ohyho ri vwrfn wkdw pd{lpl}hv vwhdg| vwdwh kduyhvw/ k p 1 4 Ilqg wkh ohyho ri vwrfn wkdw pd{lplpl}hv wkh vwhdg| vwdwh rz ri xwlolw| ri kduyhvw +l1h1/ xwlolw| ri frqvxpswlrq plqxv frvw ri kduyhvw,/...
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prob_set5 - Sureohp Vhw 8 DUH 594 Rfwrehu 4:/ 5334 Txhvwlrq...

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