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{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 14 "Plano tangente" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(plots):\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
49 "Ingresamos una funci\363n diferenciable en un punto " }{XPPEDIT 
18 0 "P = (a, b);" "6#/%\"PG6$%\"aG%\"bG" }{TEXT -1 5 " con " }{TEXT 
257 7 "-2<a <2" }{TEXT -1 4 "  y " }{TEXT 258 1 " " }{TEXT 256 8 "-2<b
<2. " }{TEXT -1 65 "Elegimos, a partir del gr\341fico, un rango adecua
do para el eje z. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "f:=(x
,y)->sin(x*y);\na:=1.2;\nb:=.8;\n" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "graf:=plot3d(f(x,y),x=-2..2,y=-2..2,style=patchnogrid
):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "p:=pointplot3d([a,b,f(a,b)],s
ymbol=circle,color=red,thickness=3):\n\nminz:=-1:\nmaxz:=2:\n\n" }
{TEXT -1 26 "Recta paralela al eje  x.\n" }{MPLTEXT 1 0 64 "rx:=spacec
urve([a+x,b,0],x=-a-2..2-a,color=black,thickness=2):\n\n" }{TEXT -1 
21 "Plano vertical por rx" }{MPLTEXT 1 0 84 "px:=implicitplot3d(y=b,x=
-2..2,y=-2..2,z=minz..maxz,color=grey,style=patchnogrid):\n\n" }{TEXT 
-1 14 "Curva sobre rx" }{MPLTEXT 1 0 1 "\n" }{TEXT -1 0 "" }{MPLTEXT 
1 0 70 "gx:=spacecurve([a+x,b,f(a+x,b)],x=-a-2..2-a,color=blue,thickne
ss=3):\n\n" }{TEXT -1 19 "Recta tangente a gx" }{MPLTEXT 1 0 21 "\n\nf
x:=diff(f(x,y),x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "mx:=eval(fx,
\{x=a,y=b\});" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "lx:
=spacecurve([x,b,mx*(x-a)+f(a,b)],x=-2..2,color=black,thickness=3):\n
\n\n" }{TEXT -1 23 "Curva paralela al eje y" }{MPLTEXT 1 0 73 "\ngy:=s
pacecurve([a,b+y,f(a,b+y)],y=-b-2..2-b,color=green,thickness=3):\n\n\n
" }{TEXT -1 14 "Tangente a gy\n" }{MPLTEXT 1 0 20 "\nfy:=diff(f(x,y),y
);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "my:=eval(fy,\{x=a,y=b\});" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "\n\nly:=spacecurve([a,y,my*(y-b)+f(
a,b)],y=-2..2,color=black,thickness=3):\n\n" }{TEXT -1 27 "En la direc
ci\363n del vector " }{XPPEDIT 18 0 "v = (sqrt(2)/2, sqrt(2)/2);" "6#/
%\"vG6$*&-%%sqrtG6#\"\"#\"\"\"F*!\"\"*&-F(6#F*F+F*F," }{TEXT -1 1 "\n
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "mv:=evalf(mx*sqrt(2)/2+my*sqrt(
2)/2):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "gv:=spacecurve([a+t*sq
rt(2)/2,b+t*sqrt(2)/2,f(a+t*sqrt(2)/2,b+t*sqrt(2)/2)],t=-2-a*sqrt(2)/2
..2-b*sqrt(2)/2,color=yellow,thickness=3):\n" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 300 "lv:=spacecurve([a+t*sqrt(2)/2,b+t*sqrt(2)/2,mv*t+f(a
,b)],t=-2..2,\ncolor=black,thickness=3):\n\nrv:=spacecurve([a+t*sqrt(2
)/2,b+t*sqrt(2)/2,0],t=-3..1.5,\ncolor=blue,thickness=2):\n\npv:=impli
citplot3d(-sqrt(2)/2*(x-a)+sqrt(2)/2*(y-b)=0,\nx=-2.5..2.5,y=-2.5..2.5
,z=minz..maxz,color=grey,style=patchnogrid):\n" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 1 "\n" }{TEXT -1 29 "En la direcci\363n del gradiente" }
{MPLTEXT 1 0 2 "\n\n" }{TEXT -1 0 "" }{MPLTEXT 1 0 21 "mg:=sqrt(mx^2+m
y^2):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "gg:=spacecurve([a+t*mx,b
+t*my,f(a+t*mx,b+t*my)],t=-2-a*mx..2-b*my,color=cyan,thickness=3):\n" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 282 "lg:=spacecurve([a+t*mx/mg,b+t*my
/mg,f(a,b)+mg*t],t=-2-a*mg/mx..2-b*mg/my,\ncolor=coral,thickness=3):\n
\nrg:=spacecurve([a+t*mx,b+t*my,0],t=-3..1.5,\ncolor=blue,thickness=3)
:\n\npg:=implicitplot3d(-my*(x-a)+mx*(y-b)=0,\nx=-2.5..2.5,y=-2.5..2.5
,z=minz..maxz,color=grey,style=patchnogrid):\n\n\n" }{TEXT -1 18 "El p
lano tangente\n" }{MPLTEXT 1 0 105 "\nplanotangente:=plot3d(f(a,b)+mx*
(x-a)+my*(y-b),x=-3+a..3+a,y=-3+b..3+b,\ncolor=pink,style=patchnogrid)
:\n\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 40 "rx,px,gx,lx,  gy,ly,  r
v,pv,lv,gv  gg,lg" }{TEXT -1 2 ":\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 69 "display3d([p,graf],orientation=[157,63],view=minz..ma
xz,axes=framed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "mx;my;mv;mg;\n" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 111 "\ndisplay3d([p,graf,lv,ly,lx,lg,gx,gy,gv,g
g,planotangente],\norientation=[170,82],view=[-2..2,-2..2,minz..maxz])
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "0 0 0" 
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