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{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Consideremos un punto en la superficie de nivel.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "p:=(1/2,1/2,1/2);" }}{PARA 0 "" 0 "" {TEXT -1 59 "Hal lemos y grafiquemos el vector gradiente trasladado a P.\n" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 62 "g:=(u,v,w)->eval(evalm(grad(f(x,y,z),[x,y,z] )),\{x=u,y=v,z=w\}):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "v:=plottool s[arrow]([p],evalm(g(p)),.06,.2,.1,color=red):" }}}{PARA 13 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "display3d(\{ v,F\},scaling=constrained,orientation=[108,87]);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Ahora dibujaremos el plano tangente a la superficie en el punto P.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "h:=dotprod(g (p),[x,y,z]-vector([p]),'orthogonal')=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "plano:=implicitplot3d(h,x=-2..2,y=-2..2,z=-2..2):\n" }}}{EXCHG {PARA 0 "> " 0 "" 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