|\^/|     Maple V Release 3 (SUNY at Albany)
._|\|   |/|_. Copyright (c) 1981-1994 by Waterloo Maple Software and the
 \  MAPLE  /  University of Waterloo. All rights reserved. Maple and Maple V
 <____ ____>  are registered trademarks of Waterloo Maple Software.
      |       Type ? for help.
Warning: new definition for   norm
Warning: new definition for   trace


> `Computation of the tangent plane to the ellipsoid (x/2)^2+(y/3)^2+(z/5)^2=2 at the point (0,3,5)`; 

> f := solve((x/2)^2+(y/3)^2+(z/5)^2=2,z);

                       2      2      1/2              2      2      1/2
        f := 5/6 (- 9 x  - 4 y  + 72)   , - 5/6 (- 9 x  - 4 y  + 72)

> f := f[1];
                                       2      2      1/2
                        f := 5/6 (- 9 x  - 4 y  + 72)

> fx03 := simplify( subs(x=0,y=3, diff(f,x)) );

                                   fx03 := 0

> fy03 := simplify( subs(x=0,y=3, diff(f,y)) );

                                  fy03 := -5/3

> `The picture of the tangent plane is given by`;


> z := simplify( fx03*(x-0)+fy03*(y-3) + 5 );

                               z := - 5/3 y + 10

> tangent := plot3d(z, x=-1..1,y=2..4, grid=[5,5]):
> ellip := plot3d({f,-f}, x=-2.8..2.8, y=-4..4):
> with(plots): display3d({tangent,ellip});


                                                                              
                                                                              
                                                                              
                                                                              
                               ---------------                                
                       --------------------------------                       
                   ----------------------------------------                   
                ----------------------------------------------                
               ------------------------------------ ------------              
              /-------------------------------------- ----------\             
              /-------------------------------- -----------------             
              ////------------------ ------------ ------- -----\\             
              -\-----//---- ----------- -- --------\------\-\\\\-             
               -----//-/-----/ /------/----\---\\---\\\---------              
                 -------------/---\/--/----\--\/--\\/--------//               
                    -\--------------------------------------                  
                        -------------------------//-----                      
                                 ---------------                              
                                                                              
                                                                              
                                                                              
                                                                              
                                                                              
> #let's now write a procedure for computing the tangent plane to a surface at a point.;
#let's now write a procedure for computing the tangent plane to a surface at
> #let's now write a procedure for compu\                                      

> ting the tangent plane to a surface at a point.;
> > 


> 
> TPlane := proc(f,pt)
TPlane := proc(f,pt)
> local fx,fy,v;
local fx,fy,v;
> fx := simplify( subs(x=op(2,pt)[1], y=op(2,pt)[2], diff(f,x)) ):
fx := simplify( subs(x=op(2,pt)[1], y=op(2,pt)[2], diff(f,x)) ):
> fy := simplify( subs(x=op(2,pt)[1], y=op(2,pt)[2], diff(f,y)) ):
fy := simplify( subs(x=op(2,pt)[1], y=op(2,pt)[2], diff(f,y)) ):
> simplify( fx*(x-x0) + fy*(y-y0) + z0 );
simplify( fx*(x-x0) + fy*(y-y0) + z0 );
> end;
end;

TPlane := proc(f,pt)
          local fx,fy,v;
              fx := simplify(subs(x = op(2,pt)[1],y = op(2,pt)[2],diff(f,x)));
              fy := simplify(subs(x = op(2,pt)[1],y = op(2,pt)[2],diff(f,y)));
              simplify(fx*(x-x0)+fy*(y-y0)+z0)
          end

> TPlane(x^2+y^2,[1,1]);
TPlane(x^2+y^2,[1,1]);

                2 1[1] x - 2 1[1] x0 + 2 1[2] y - 2 1[2] y0 + z0

> u := [a,b];
u := [a,b];

                                  u := [a, b]

> op(2,u);
op(2,u);

                                       b

> op(u);
op(u);

                                      a, b

> u[2];
u[2];

                                       b

> op(2,u);
op(2,u);

                                       b

> op(2,u)[1];
op(2,u)[1];

                                      b[1]

> v := (a,b);
v := (a,b);

                                   v := a, b

> op(2,v);
op(2,v);
Error, wrong number (or type) of parameters in function op
> v := [(a,b)];
v := [(a,b)];

                                  v := [a, b]

> op(2,v)[2];
op(2,v)[2];

                                      b[2]

> v;
v;

                                     [a, b]

> v := [[a,b]];
v := [[a,b]];

                                 v := [[a, b]]

> op(2,v);
op(2,v);
Error, improper op or subscript selector
>