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=sin(u)*cos(v)-cos(v)*cos(u);Z:=-sin(v)+cos(v)*sin(u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG,&*&-%$cosG6#%\"uG\"\"\"-F(6#%\"vGF+F+*&\"\" #F+-%$sinGF-F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG,&*&-%$sinG6 #%\"uG\"\"\"-%$cosG6#%\"vGF+F+*&-F-F)F+F,F+!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG,&-%$sinG6#%\"vG!\"\"*&-F'6#%\"uG\"\"\"-%$cosGF(F /F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "A:=[diff(X,u),diff(Y ,u),diff(Z,u)];B:=[diff(X,v),diff(Y,v),diff(Z,v)];" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"AG7%,$*&-%$sinG6#%\"uG\"\"\"-%$cosG6#%\"vGF,!\"\" ,&*&-F.F*F,F-F,F,F'F,F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG7%,&* &-%$cosG6#%\"uG\"\"\"-%$sinG6#%\"vGF,!\"\"*&\"\"#F,-F)F/F,F,,&*&-F.F*F ,F-F,F1F'F,,&F4F1F6F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "C: =[A[2]*B[3]-A[3]*B[2],A[3]*B[1]-A[1]*B[3],A[1]*B[2]-A[2]*B[1]]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "U:=expand(combine(C[2]));sol ve(U,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG,(*&-%$sinG6#%\"vG\" \"\"-%$cosGF)F+!\"\"*(\"\"#F+-F-6#%\"uGF+)F,F0F+F+*&-F(F2F+F4F+F." }} {PARA 11 "" 1 "" {XPPMATH 20 "6$,$*&\"\"#!\"\"%#PiG\"\"\"F(-%'arctanG6 #,&*&F%F(-%$cosG6#%\"uGF(F(-%$sinGF0F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "U:=expa nd(combine(C[1]));solve(U,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"U G,(*&-%$cosG6#%\"uG\"\"\")-F(6#%\"vG\"\"#F+!\"\"*&-%$sinGF)F+F,F+F1*&- F4F.F+F-F+F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*&\"\"#!\"\"%#PiG\" \"\"F(,$-%'arctanG6#,&-%$cosG6#%\"uGF(-%$sinGF0F(F&" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " U:=expand(combine(C[3]));solve(U,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"UG,(*&-%$sinG6#%\"vG\"\"\"-%$cosGF)F+F+*(\"\"#F+-F-6#%\"uGF+)F,F /F+!\"\"*(F/F+-F(F1F+F3F+F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*&\" \"#!\"\"%#PiG\"\"\"F(-%'arctanG6#,&*&F%F(-%$cosG6#%\"uGF(F(*&F%F(-%$si nGF0F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "plot3d([X,Y,Z] 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distance \340 O de la projection sur xOy du point courant\",\n #maximize(r*sin(theta),theta=0..Pi/2),maximize(maximize(r*sin(theta),p hi=0..Pi/2),theta=0..Pi/2))#;\n#========================== " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r edefined\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*dM_dthetaG7%,&*0\"\"% \"\"\"%\"aGF)-%$sinG6#,$*&\"\"#F)%&thetaGF)F)F))-F,6#,$*&F0F)%$phiGF)F )F0F)-%$cosGF-F)-F,6#F1F)-F96#F7F)F)*(,&F)F)*(F*F))F+F0F)F2F)F)F)-F9F; F)F " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# *&,&\"\"\"F%*&)-%$sinG6#,$*&\"\"#F%%&thetaGF%F%F-F%)-F)6#$\"+Fjzq:!\"* F-F%F%F%-F)6#F.F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "fsolv e(subs(a=.1,phi=evalf(Pi)/4.,diff(r*sin(theta),theta)),theta=0..Pi/2); \nevalf(subs(theta=%,a=1,phi=evalf(Pi)/4.,r*sin(theta)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Fjzq:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+++++5!\"*" 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