sec 13.1 curvas en el espacio

> with(plots);
[ animate , animate3d , animatecurve , arrow, changecoords , complexplot , complexplot3d ,
conformal , conformal3d , contourplot , contourplot3d , coordplot , coordplot3d ,
densityplot , display , fieldplot , fieldplot3d , gradplot , gradplot3d , graphplot3d ,
implicitplot , implicitplot3d , inequal , interactive , interactiveparams , intersectplot ,
listcontplot , listcontplot3d , listdensityplot , listplot , listplot3d , loglogplot , logplot ,
matrixplot , multiple , odeplot , pareto , plotcompare , pointplot , pointplot3d , polarplot ,
polygonplot , polygonplot3d , polyhedra_supported , polyhedraplot , rootlocus ,
semilogplot , setcolors , setoptions , setoptions3d , spacecurve , sparsematrixplot ,
surfdata , textplot , textplot3d , tubeplot ]
> spacecurve([cos(t),sin(t),t],t=0..4*Pi,axes=normal);
> spacecurve([cos(t),sin(t),t],t=0..4*Pi,axes=FRAME);
Ejercicio 5
> limit(exp(3*t),t=0);limit(t^2/(sin(t))^2,t=0);limit(cos(2*t),t=0);
>
1
1
1
Ejercicio 29
> spacecurve([t,t*sin(t),t*cos(t)],t=15..15,axes=normal,numpoints=100);
Ejercicio 33
>
x:=(1+cos(16*t))*cos(t);y:=(1+cos(16*t))*sin(t);z:=1+cos(16*t
);spacecurve([x,y,z],t=0..5,axes=normal,numpoints=100);
x := ( 1 + cos( 16 t ) ) cos( t )
y := ( 1 + cos( 16 t ) ) sin( t )
z := 1 + cos( 16 t )
> x^2+y^2-z^2;L:=combine(x^2+y^2-z^2);
( 1 + cos( 16 t ) ) 2 cos( t ) 2 + ( 1 + cos( 16 t ) ) 2 sin( t ) 2 − ( 1 + cos( 16 t ) ) 2
L := 0
Ejercicio 26 pagina 823
> restart;xt:=sin(t);yt:=cos(t);zt:=(sin(t))^2;
xt := sin( t )
yt := cos( t )
zt := sin( t ) 2
> combine(z-x^2);combine(x^2+y^2);
z − x2
x2 + y2
> with(plots):implicitplot3d({x^2+y^2=1,z=x^2},x=-3..3,y=3..3,z=0..5,scaling=constrained,axes=boxed);
> spacecurve([xt,yt,zt],t=-Pi..Pi,axes=normal,numpoints=100);
> G:=implicitplot3d([x^2+y^2=1,z=x^2],x=-2..2,y=2..2,z=0..2,color=[yellow,green],scaling=constrained,axes=box
ed):H:=spacecurve([xt,yt,zt],t=Pi..Pi,axes=normal,numpoints=100):
display(H,G);
> spacecurve([xt,yt,zt],t=Pi..Pi,color=black,axes=normal,thickness=4,numpoints=100);
> H:=spacecurve([xt,yt,zt],t=Pi..Pi,color=black,axes=normal,thickness=4,numpoints=100):dis
play(H,G);