Mathc initiation/a24

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c002.c

/* --------------------------------- */
/* save as c002.c                    */
/* --------------------------------- */
#include  "x_hfile.h"
#include       "fa.h"
/* --------------------------------- */
int main(void)
{
double h = .001; 
pt2d   Q = i_pt2d(-.5,-.5);

 clrscrn();

 printf(" Find the equation of the tangent\n\n");
 printf(" at the point P(%.2f,%.2f),\n\n",Q.x,Q.y);
 printf(" on the plan x = %.2f for f(x,y).\n\n\n",Q.x);
 printf(" f : (x,y)-> %s\n\n\n", feq);

 printf(" Cartesian form :\n\n"); 
 printf(" z = %f y %+f\n\n",
        fxy_y(f,h,Q),
        f(Q.x,Q.y)-fxy_y(f,h,Q)*Q.y);       

 printf(" Parametric form :\n\n"); 
 printf(" x = %f\n",Q.x);
 printf(" y = t\n");
 printf(" z = %f t %+f\n\n",
          fxy_y(f,h,Q),
          f(Q.x,Q.y)-fxy_y(f,h,Q)*Q.y);

 stop();

 return 0;
}
/* --------------------------------- */
/* --------------------------------- */

Exemple de sortie écran :

Find the equation of the tangent

 at the point P(-0.50,-0.50),

 on the plan x = -0.50 for f(x,y).


 f : (x,y)-> (x*y**2)/(x**2+y**4)


 Cartesian form :

 z = 0.959996 y +0.079998

 Parametric form :

 x = -0.500000
 y = t
 z = 0.959996 t +0.079998

 Press return to continue.

Equation d'une tangente :

                          x constant

   y = f(x)               z = f(x,y)


   y = ax + b             z = ay + b        
                              
   
   a = f'(x)              a = f_y(x,y) 
   
   b = y - ax             b = z - ay 
   b = y - f'(x)x         b = z - f_y(x,y)y
   b = f(x) - f'(x)x      b = f(x,y) - f_y(x,y)y