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一條令許多人昏倒的題目 Lagrange Multiplier
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??l???S????赹???}? Lagrange Multiplier 94,02,10,20,18 ??????}?????????e????????????? ??????????x?????????e?????A?? ????????L????????????????????????? ?W????????????s???f????????f??s ?p??????????????ò??h???S???f???? ?????????W????????W????? http://freeman2.com/tutc0001.htm 94,02,10,20,21 94,02,16,07,26 ???????????С?С?W?W???????W?????x?? 94,02,16,07,27 93,12,13,21,19? 93,12,13,17:29:19 ?????????????? http://mathforum.org/library/drmath/view/52071.html Date: 11/24/98 at 16:29:56 From: Sam Subject: LaGrange Multiplier ?????????????????? ???? ??????????ε???}???????P??????S?? ??LaGrange Multiplier?????}????????? ???}????ΛQ???@?????????У?????????? ??l?????????????}??????_????????? ??????_??????????????@?N?}??????? ??????}???E?????????????@????}???? ???????}??????Y???_???????l???????? ?磬?@?Y????l???I?}?? ???? ???l????????l??????????c??????????? ????????????c???????c??????x??? ??????????S???????}?? y = 2x - 3 y = x^2 ???? ?F???????}????@??????????????????? ??????l????? ????????????м????M???x?x??Sam ???? ??????W·???????????}???@????????S?? ????赹???}??????????????????????? ?????????????????????????OС???????? ?????????x?????d??????????? ?^???????]????????????? 93,12,13,21,52? 94,01,22,10,54? ????s11/24/98 at 17:07:04 ?l??s??D??? Doctor Santu ????s??????????S???? ?????á? ???????H???????????????????@??? ??? y = 2x - 3 y = x^2 ????????????????????}???????F?????? ????????????????????????????? ?S?????????????????f??????x?_???x?? ?@????}?????OС????????????????? ??????c??g????x?? (x[1],y[1]) ?? (x[2],y[2]) ???c?? ?@????????????c?M??????????????x?? ?????c???????????}????????c????? ????l???????????c????????l??????? ??????????????c??g????x???O??? ?????????]?s????????????OС?????? ???????? sqrt[(x[1]-x[2])^2 + (y[1]-y[2])^2], ??r???????l?? y[1] = 2x[1] - 3, ?? y[2] = x[2]^2. ???c???λ???????????? ??????????????????}????н?????????? ????????_?????sqrt???P?S???? ??????c??g???x???????С????c ??????c??g???x????????С???????? ?????_??????????S????? ?????????????????? y ?? x ????N?????? ????????????????????????}????????? ?????????S???????^???????????S?????? ???@?????_?О顣 ????D????????W??? http://mathforum.org/dr.math/ 94,01,22,11,27? 94,01,22,11,45? ???????P??????S??????}?????W?????D ???????????????g???????????з??g ????????????????? ????????????D??}?D??  ??????????????? y = 2x - 3 y = x^2 ?????????????c?S???????S?????A???? ?????????????????^????????? ??????????????D??}?????????}?? ?????????????}???????e?????]?н??}?? G(x,y) = (x-1)*(x-1) + (y-2)*(y-2) R(x,y) = x + y - 3 = 0 G(x,y) ?????????? (Goal) R(x,y) ????????l?? (Restriction) ??????????O?????????????? ??????????OС??????С??????? ?O?????????????????? ?OС????????????????O???OС????? ??????????S??????O??n???y???OС???? ?}???K??Q??????????????????????? ?????????????????á???????????? ???????????????????????????????? ??????????~?? ?}????? ?OС???????? G(x,y) = (x-1)*(x-1) + (y-2)*(y-2) ???????l?? R(x,y) = x + y - 3 = 0 ??????O??n???У?????????l????y??? ????l????????????? ????N????l??????{???顸??????? ??? ??鲻?????????????????????????? ??????????? x+y=5 ?c x+y-5=0 ???? ??? ???OС???????? G(x,y) ??c????????l?? R(x,y) ????????}??? ???????? L(x,y)=G(x,y)+lambda*R(x,y) ???? lambda???????S????????? ???????????????????????S????????l?? ???????????????????c?????????e?? ??????l?? R(x,y) ?a??????????????? ????????????????????? ???????l??????{???????????N?? ????????????c????????????? 94,02,02,19,06????? ???? ????l??????{???顸??????????????? ?l???? ???????l???e?`??? x+y=5 ??μ{???????????? ?????????????????S????(x+y)?????e???? ??????? ????????????????????S??????Y?? ?????????????x+y=0???e?`??????? ????????壬????x+y=5???????????? ???????l????????{???顸????? ??????Y?????????????????l????? ??????????S???????}?r????????? ?????????????????S?????????? ??Ψ??????l??????{???顸????? ??????????????????????N???? ??????????S??????{?????????? ????????????^???У?????l???@? ????????????????????????? ????l???? ???????l????????????S???????}?r??? ??F??????S?????_?}???????c?? 94,02,02,19,39????? ????????l?? R(x,y) ?a????? ???? = 0??????????? ?}??????飨????? = 0???? ?OС?? G(x,y) = (x-1)*(x-1) + (y-2)*(y-2) ????? R(x,y) = x + y - 3 ????N??? G(x,y) ?? R(x,y) ?? ???? G(x,y) ?????? R(x,y) ????? ??????s????????????????? ???}???E??????x???????????? L(x,y)=G(x,y)+lambda*R(x,y) ???^????????????ú??????????????? L(x,y)=(x-1)*(x-1) + (y-2)*(y-2)+lambda*(x + y - 3) ???^???s????????? G(x,y) ?? R(x,y) ?? ??e?????????l????? ??????????????? = 0??????? G, R?? G(x,y) = (x-1)*(x-1) + (y-2)*(y-2) R(x,y) = x + y - 3 ????????? ?? ?OС?? G(x,y) = (x-1)*(x-1) + (y-2)*(y-2) ????? R(x,y) = x + y - 3 ?? ?? ?OС?? R(x,y) = x + y - 3 ????? G(x,y) = (x-1)*(x-1) + (y-2)*(y-2) ?? ???J?? G(x,y) ?????????????? G(x,y)???S?????????????? C(x,y) = x + y - 3 D(x,y) = (x-1)*(x-1) + (y-2)*(y-2) ?????N????l???l???? ???????????????????á???????????e ?OС??????? G(x,y) ?????????????i???? ?????????? R(x,y) ?ǹ????????????? ??????????????????c?????? ?OС??????? G(x,y) ?????????????i???? ??顸?OС????????????ж????x?? ?????? G(x,y) ??????? ?????? G(x,y) ???????????? G(x,y) = (x-1)*(x-1) + (y-2)*(y-2) ???????? ????i?????????????ИOС?????? ??????棬 ?????????? R(x,y) ?ǹ????????????? ??? R(x,y) = x + y - 3 ??????????@?? ????????l????? R(x,y) = x + y - 3 = 0 ?i?? x, y ?P?S R(x,y) = x + y - 3 = ??????? x, y ?o?P ?F??????????}??????????? y = 2x - 3 y = x^2 ?????????? y - 2x + 3 = 0 y - x^2 = 0 ??????????????????????????????? ??????????????????????????}?? ????????^????D????г?????c???x??? sqrt[(x[1]-x[2])^2 + (y[1]-y[2])^2] ?]?С?????????????????????????? ????OС??????O????? ?m????x???????????????????^ ???x?????????????????????????????? ??????????????????鳣?????ɡ?? ???????????f?????? ???????????????????????????? 94,01,22,12,48? ..... ???????????????????}???????????S???? ??????L????????????????????W?????? http://freeman2.com/tutc0001.htm ..... 94,01,28,11,19? ?????????????????????????D?????? ?????????g?????x???}????????c??? ???S???????P????R?? ???????????S?????????????}?? ????????????????l???? y = 2x - 3????????????? y = x^2????????????????? ??D???????????c?ǘOС?????x?????s sqrt[(x[1]-x[2])^2 + (y[1]-y[2])^2] ??D???????V?x??????_????????? ??? sqrt[] ??????????????????x??? (x[1]-x[2])^2 + (y[1]-y[2])^2??????????? ?? G() ???????????? ?? R1()????????????? ?? R2()?????????????? ?????????????????????????  ????????}????W????? ????????}????D?Ρ?  ?????S?????????????????????????? ?????S???????????????S?????c?????? ????????????????????D????????s  ???x??? G() ????????????????????s ?????????????????????? ???????? L() ????????????s ???????????????????????????????? ???? ????????????????????????????c?? ?????????????????????????????c?? ???????????????R1()??????????? G()?? ???????????????????S???? ????????????????R2()??????????? G()?? ????????????????????S???? ??K????M??Q?????????? L() ?? 94,01,28,12,07? 94,01,28,14,18? ???????????????{??????l??????? ???????????????????????l???????? ????????????????o????l???????? ????????????????????????????????? ????]??????l????????????????????? ??????????????? ????????????????????????????????????? ???????????S???????????? 94,01,28,14,28? 94,02,01,08,56? ???O????????????????????????D???}?? ???O????l?????????????????D???}?? ?t ?????????????????????????? ????????????????????? ????l???p?????????????? ????????o??????????????????? ??? ????????????????????? ??????????l????s???? ????????o??????????????????? ?む?????????????????c???? ?@?????W????????}??? ????????O????}???? ?@?Y????f?????????????????}??? ???????r????????{?????? 94,02,01,09,09? 94,01,28,15,40? ???????????????????????????????? ??????????????????x?????????????? ???????????????????????????? ??????? ?? ???????   ?????????????????????r??????????? ??????c???????????????????????????f ?????????o??c?? ???????N??r?????a???o??c?s ???????????????????С??c?? ??????????????????????c?? ??????????????????D???c?? ?@???N??r?????a?????????????????? ???????????????????????????????? ????o??c?????????????Д??@???????? ????С??c?????????c?????D???c?? ????????????????????????????? ???????l???????????????????????p??? ?????}???????????????????????????? ????????????????????????????????? ???????????????p???????????Ψ? ??? ?????????????????????ε??????x?? ??P????? ?????? ???????????????? ???????????????? ???????????????? ???????????????? ??????????????? ??????????????? ???????D???t?????????x??  94,01,28,16,16? ?????????????W? http://freeman2.com/tutc0001.htm ???????????????? http://freeman2.com/freeman1.htm ????????????????? http://freeman2.net/listfnet.htm ?????????????W??? http://freeman2.us/indexdlj.htm 94,02,09,15,47? ???W????? ?κνy??a?D?Ρ? ?κνy??a????? ??W??M?? ???M??X????????a?? ?y??a??Mλ??a?????? ????????g????d?? http://freeman2.com/htm_char.zip ??????????g????d?? http://freeman2.com/rootc.zip 94,02,09,15,55? ?????????????????????????g????d  [sound]http://freeman2.net/dlj_0111.wma[/sound] ????????? 1,187,131 http://freeman2.us/dlju0001.zip ???????Ц 1,116,088 http://freeman2.us/dlju0002.zip Everynight 2,560,279 http://freeman2.us/dlju0003.zip ????f?Z 3,579,334 http://freeman2.us/dlju0004.zip ??????B 4,142,667 http://freeman2.us/dlju0005.zip С?ǹ??? 4,230,799 http://freeman2.us/dlju0006.zip ??????g???f?? 4,218,628 http://freeman2.us/dlju0007.zip ???????x?_????????? 4,879,395 http://freeman2.us/dlju0008.zip ÷????С?y??? 5,105,916 http://freeman2.us/dlju0009.zip ?????? 5,856,853 http://freeman2.us/dlju0010.zip ???? 6,283,159 http://freeman2.us/dlju0011.zip ???P 7,569,815 http://freeman2.us/dlju0012.zip ??????????? 9,065,337 http://freeman2.us/dlju0013.zip ?x?x??????? 17,479,084 http://freeman2.us/dljv0001.zip ?????????? 17,840,635 http://freeman2.us/dljv0009.zip ????????· 22,460,839 http://freeman2.us/dljv0021.zip ÷???????y??? 17,955,337 http://freeman2.us/dljv0044.zip ?????? 15,188,962 http://freeman2.us/dljv0051.zip ·??????????? 14,263,325 http://freeman2.us/dljv0056.zip ???A???? 15,602,195 http://freeman2.us/dljv0060.zip |
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