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\"+23/-^FC$\"+S?3.EFCF)7%$\"+sS?5bFC$\"+#*[BOIFCF)7%$\"+PtO=fFC$\"+%>2
F]$FCF)7%$\"+-1`EjFC$\"+Y*)\\-SFCF)7%$\"+nQpMnFC$\"+[,hNXFCF)7%$\"+Kr&
G9(FC$\"+,3/-^FCF)7%$\"+(R?5b(FC$\"+/4z,dFCF)7%$\"+iO=fzFC$\"+d/'[L'FC
F)7%$\"+FpMn$)FC$\"+g%\\7+(FCF)7%$\"+#>5bx)FC$\"+8z&4q(FCF)7%$\"+dMn$=
*FC$\"+;e)RV)FCF)7%$\"+An$=f*FC$\"+qJL+#*FCF)7%$\"+()********FC$\"+u**
******FCF)-%'COLOURG6&F7F8F)F)-%*THICKNESSG6#\"\"$-%+AXESLABELSG6%%\"x
G%\"yG%!G" 1 2 0 1 10 0 2 1 1 2 2 1.000000 56.000000 68.000000 0 0 "Cu
rve 1" "Curve 2" "Curve 3" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 6 "Fuente" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 257 12 "Ejemplo 1:\n\n" }
{TEXT -1 2 "  " }{XPPEDIT 18 0 "f := proc (x, y) options operator, arr
ow; x+y+3 end;" "6#>%\"fGf*6$%\"xG%\"yG7\"6$%)operatorG%&arrowG6\",(F'
\"\"\"F(F/\"\"$F/F-F-F-" }{TEXT -1 49 "   restringida al c\355rculo de
 radio 1 y centro 0.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "r
estart;\nwith(plots):\nwith(plottools):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "f:=(x,y)->x+y+3;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 969 "graf1:=plot3d(f(x,y),x=-1.
2..1.2,y=-1.2..1.2):\n\n\ngraf2:=plot3d(f(x,y),x=-1..1,y=-sqrt(1-x^2).
.sqrt(1-x^2)):\n\nfborde:=spacecurve([cos(t),sin(t),f(cos(t),sin(t))],
t=0..2*Pi,color=red,thickness=3):\n\nborde:=spacecurve([cos(t),sin(t),
0],t=0..2*Pi,color=red,thickness=3):\n\ninterior:=plot3d(0,x=-1..1,y=-
sqrt(1-x^2)..sqrt(1-x^2),color=pink):\n\ncirculo:=display3d(interior,b
orde):\n\ncilindro:=implicitplot3d(x^2+y^2=1,x=-1..1,y=-1..1,z=0..5,co
lor=yellow,\nstyle=wireframe):\n\nextremos:=display([point([-sqrt(2)/2
,-sqrt(2)/2,f(-sqrt(2)/2,-sqrt(2)/2)],color=blue,symbol=circle),\npoin
t([-sqrt(2)/2,-sqrt(2)/2,0],color=blue,symbol=circle),\n\npoint([sqrt(
2)/2,sqrt(2)/2,0],color=blue,symbol=circle),\npoint([sqrt(2)/2,sqrt(2)
/2,f(sqrt(2)/2,sqrt(2)/2)],color=blue,symbol=circle),\n\nline([-sqrt(2
)/2,-sqrt(2)/2,0],[-sqrt(2)/2,-sqrt(2)/2,f(-sqrt(2)/2,-sqrt(2)/2)],lin
estyle=3,color=black),\nline([sqrt(2)/2,sqrt(2)/2,0],[sqrt(2)/2,sqrt(2
)/2,f(sqrt(2)/2,sqrt(2)/2)],linestyle=3,color=black)]):\n" }{TEXT -1 
0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 44 "graf1,graf2,circulo,cili
ndro,fborde,extremos" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "dis
play3d([graf2,circulo,fborde,extremos],axes=normal,orientation=[-41,70
],style=patchnogrid);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }{TEXT 258 0 "" }{TEXT 259 10 "Ejemplo 2:" }}{PARA 0 "" 0 "" 
{TEXT -1 1 "\n" }{XPPEDIT 18 0 "f := proc (x, y) options operator, arr
ow; 2*x^2+y^2+1 end;" "6#>%\"fGf*6$%\"xG%\"yG7\"6$%)operatorG%&arrowG6
\",(*&\"\"#\"\"\"*$F'F0F1F1*$F(F0F1F1F1F-F-F-" }{TEXT -1 47 "  restrin
gida al c\355rculo de radio 1 y centro 0." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "restart;\nwith(plots):\nwith
(plottools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=(x,y)->2
*x^2+y^2+1;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 1103 "graf1:=plot3d(f(x,y),x=-1.2..1.2,y=-1.2..1.2):
\n\n\ngraf2:=plot3d(f(x,y),x=-1..1,y=-sqrt(1-x^2)..sqrt(1-x^2)):\n\nfb
orde:=spacecurve([cos(t),sin(t),f(cos(t),sin(t))],t=0..2*Pi,color=red,
thickness=3):\n\nborde:=spacecurve([cos(t),sin(t),0],t=0..2*Pi,color=r
ed,thickness=3):\n\ninterior:=plot3d(0,x=-1..1,y=-sqrt(1-x^2)..sqrt(1-
x^2),color=pink):\n\ncirculo:=display3d(interior,borde):\n\ncilindro:=
implicitplot3d(x^2+y^2=1,x=-1..1,y=-1..1,z=0..3,color=yellow,style=wir
eframe):\n\nextremos:=display([point([-1,0,f(-1,0)],color=blue,symbol=
circle),\npoint([-1,0,0],color=blue,symbol=circle),\n\npoint([1,0,f(1,
0)],color=blue,symbol=circle),\npoint([1,0,0],color=blue,symbol=circle
),\n\npoint([0,1,f(0,1)],color=blue,symbol=circle),\npoint([0,1,0],col
or=blue,symbol=circle),\n\npoint([0,-1,f(0,-1)],color=blue,symbol=circ
le),\npoint([0,-1,0],color=blue,symbol=circle),\n\nline([-1,0,f(-1,0)]
,[-1,0,0],linestyle=3,color=black),\nline([1,0,f(1,0)],[1,0,0],linesty
le=3,color=black),\n\nline([0,1,f(0,1)],[0,1,0],linestyle=3,color=blac
k),\nline([0,-1,f(0,-1)],[0,-1,0],linestyle=3,color=black)\n\n#,point(
[0,0,1],color=blue,symbol=circle)\n\n]):\n\n" }{TEXT -1 5 "\n\n\n\n\n
" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 44 "graf1,graf2,circulo,cilindr
o,fborde,extremos" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "displa
y3d([graf1],axes=normal,orientation=[-41,70],style=patchnogrid);" }}
{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }{TEXT 260 0 "" }{TEXT 261 10 "Ejemplo 3:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{XPPEDIT 18 0 "f := proc (x, y) options operator, arrow; x+y^2 end;" "
6#>%\"fGf*6$%\"xG%\"yG7\"6$%)operatorG%&arrowG6\",&F'\"\"\"*$F(\"\"#F/
F-F-F-" }{TEXT -1 32 "  restringida a [-1,1] x [-2,2]." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restar
t;\nwith(plots):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=(x
,y)->x+y^2;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 347 "g:=plot3d(f(x,y),x=-1..1,y=-2..2):\n\nc1:=space
curve([1,t,f(1,t)],t=-2..2,color=blue,thickness=3):\n\nc2:=spacecurve(
[-1,t,f(-1,t)],t=-2..2,color=blue,thickness=3):\n\nc3:=spacecurve([t,-
2,f(t,-2)],t=-1..1,color=red,thickness=3):\n\nc4:=spacecurve([t,2,f(t,
2)],t=-1..1,color=red,thickness=3):\n\nc:=spacecurve([t,0,f(t,0)],t=-1
..1,color=yellow,thickness=3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "display3d([g,c1,c2,c3,c4
,c],axes=boxed,orientation=[-106,70],style=patchnogrid);" }}{PARA 13 "
" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 262 0 "" }{TEXT 263 12 "Ej
emplo 4:\n\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{XPPEDIT 18 0 "f := pro
c (x, y) options operator, arrow; x*y*(x^2-y)^2 end;" "6#>%\"fGf*6$%\"
xG%\"yG7\"6$%)operatorG%&arrowG6\"*(F'\"\"\"F(F/,&*$F'\"\"#F/F(!\"\"F2
F-F-F-" }{TEXT -1 42 "  restringida a \{x>=0\} y a \{x>=0,  y>=0\}.\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart;\nwith(plots):
\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:=(x,y)->x*y*(x^2-y)
^2;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 151 "h:=plot3d(f(x,y),x=-1..1,y=0..1,numpoints=1000):\np:
=plot3d(0,x=-1..1,y=0..1,color=blue):\nc:=spacecurve([t,t^2,f(t,t^2)],
t=-1..1,color=red,thickness=3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "display(h,p,c);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 275 "g:=plot3d(f(x,y),x=0..1,y=0..1,num
points=1000):\n\np:=plot3d(0,x=0..1,y=0..1,color=blue):\n\nc1:=spacecu
rve([0,t,f(0,t)],t=0..1,color=blue,thickness=3):\n\n\n\nc2:=spacecurve
([t,0,f(t,0)],t=0..1,color=blue,thickness=3):\n\n\nc:=spacecurve([t,t^
2,f(t,t^2)],t=0..1,color=red,thickness=3):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display3d(p,g
,c1,c2,c);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
264 0 "" }{TEXT 265 11 "Ejemplo 5:\n" }}{PARA 0 "" 0 "" {TEXT -1 55 "H
allar la distancia del punto [1,1,1] al plano x+y+z=0." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "restart;\nwith(plottools):\nwith(pl
ots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "plano:=plot3d(-x-
y,x=-1..1,y=-1..1,color=pink):\n\npunto:=display(point([1,1,1],color=r
ed,symbol=circle)):\n\nlinea:=line([0,0,0],[1,1,1], color=blue, linest
yle=1):\n\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "display3d(
[plano,punto,linea],style=patchnogrid,scaling=constrained,\norientatio
n=[-37,68]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}
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