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\},i->gradient(f)[i]=lambda*gradient(g)[i]),[1,2,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.makeequationsGf*6$%\"FG%\"GG6\"6$%)operatorG%&a rrowGF)-%$mapG6$-%%subsG6$<$/%\"gG9%/%\"fG9$f*6#%\"iGF)F*F)/&-%)gradie ntG6#F86#F9*&%'lambdaG\"\"\"&-F@6#F5FBFEF)F)F)7%FE\"\"#\"\"$F)F)F)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "makeequations(2*x+3*y-z,x^2 +y^2+z^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/\"\"#,$*&%'lambdaG\" \"\"%\"xGF)F%/\"\"$,$*&F(F)%\"yGF)F%/!\"\",$*&F(F)%\"zGF)F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solve(\{x^2+y^2+z^2=9,op(%) \});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<&/%'lambdaG,$-%'RootOfG6$,&! \"(\"\"\"*&\"\"#F,)%#_ZGF.F,F,/%&labelG%$_L4G#F,\"\"$/%\"zG,$F'#!\"$\" \"(/%\"yG,$F'#\"\"*F;/%\"xG,$F'#\"\"'F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "makeequations2:=(F,G)->map(subs(\{f=F,g=G\},i->gradie nt2(f)[i]=lambda*gradient2(g)[i]),[1,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/makeequations2Gf*6$%\"FG%\"GG6\"6$%)operatorG%&arrow GF)-%$mapG6$-%%subsG6$<$/%\"gG9%/%\"fG9$f*6#%\"iGF)F*F)/&-%*gradient2G 6#F86#F9*&%'lambdaG\"\"\"&-F@6#F5FBFEF)F)F)7$FE\"\"#F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "lagrangesolve2:=(F,G,c)->solve(\{G= c,op(makeequations2(F,G))\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/l agrangesolve2Gf*6%%\"FG%\"GG%\"cG6\"6$%)operatorG%&arrowGF*-%&solveG6# <$/9%9&-%#opG6#-%/makeequations2G6$9$F3F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "lagrangesolve2(x+2*y,x^2+y^2,4);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%/%'lambdaG,$-%'RootOfG6$,&*$)%#_ZG\"\"#\"\"\"\" \"&F/!\"\"/%&labelG%$_L2G#F0\"\"%/%\"yG,$F'F6/%\"xG,$F'F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"yG$\"+#Qa))y\"!\"*/%\"xG$\"+7>FW*)!#5/%'lambdaG$ \"+X*p,f&F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 115 "Your assignment: solve problems 4, 16, \+ 20 in section 14.8 using Maple. If you can produce relevant illustrat ions," }}{PARA 0 "" 0 "" {TEXT -1 113 "do so. For 4, you have all the tools to produce nice pictures. 16 is a two constraint problem, so y ou will have" }}{PARA 0 "" 0 "" {TEXT -1 110 "to set things up yoursel f (I haven't done this). If someone is good at programming, they migh t be able to get" }}{PARA 0 "" 0 "" {TEXT -1 108 "Maple to set up thei r equations for them... for 20, you have what you need. Be careful t hat you don't let " }}{PARA 0 "" 0 "" {TEXT -1 98 "Maple lose solution s for you in 20 (as you might in the previous example if you aren't ob servant)." }}}}{MARK "39 4 0" 98 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }