Mathc initiation/a379

Sommaire

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	c00a.c

/* ---------------------------------- */
/* save as c00a.c                     */
/* ---------------------------------- */
#include "x_afile.h"
#include      "fa.h"
/* ---------------------------------- */
int main(void)
{
int     n =  2*300;
double  a =  1.;
double oo =  1000.;

 clrscrn();
 printf(" If S.a_n is a serie, let f(x) = a_n \n");
 printf(" and let f be the function obtained \n");
 printf(" by replacing n with x.\n\n");
 printf(" Use the integral test to determine whether\n");
 printf(" the serie converge or diverge.\n\n");
 printf(" If f is a positive valued function. (verify)  \n");
 printf(" If f is continuous on [1,oo).       (verify)  \n");
 printf(" If f' is negative.                  (verify)\n\n");
 printf(" Then f is decreasing on [1,oo).             \n\n");

 printf(" The serie converge (diverge) if\n");
 printf("     / oo\n");
 printf("    |\n");
 printf("    |   f(x) dx = Converge (diverge)\n");
 printf("    |\n");
 printf("   /   1\n\n");
 stop();

 clrscrn();
 printf("# Copy and past this file into the screen of gnuplot\n\n"
        "  set zeroaxis lt 3 lw 1\n"
        "  set grid\n"
        "  plot [0.:20.] [-.01:0.1]\\\n"
        "       1/(3+2*x)**2\n\n\n\n\n\n\n\n\n\n"
        "  reset");
 stop();
 
 clrscrn();
 printf(" Compute the derivative of f when x = %0.3f\n\n", 2.); 
 printf("  with fx_x(%0.3f) = %0.8f\n\n\n",2., fx_x(f,2.,H));
 printf("     / oo\n");
 printf("    |\n");
 printf("    |   %s dx = %.12f\n", feq, simpson(f,a,oo,n));
 printf("    |\n");
 printf("   /   %+.2f\n\n\n\n", a);
 printf(" Converge then the serie S.a_n converge. \n\n");

 stop();

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

Exemple de sortie écran :

 If S.a_n is a serie, let f(x) = a_n 
 and let f be the function obtained 
 by replacing n with x.

 Use the integral test to determine whether
 the serie converge or diverge.

 If f is a positive valued function. (verify)  
 If f is continuous on [1,oo).       (verify)  
 If f' is negative.                  (verify)

 Then f is decreasing on [1,oo).             

 The serie converge (diverge) if
     / oo
    |
    |   f(x) dx = Converge (diverge)
    |
   /   1

 Press return to continue.

Exemple de sortie écran :

# Copy and past this file into the screen of gnuplot

  set zeroaxis lt 3 lw 1
  set grid
  plot [0.:20.] [-.01:0.1]\
       1/(3+2*x)**2


 Compute the derivative of f when x = 2.000

  with fx_x(2.000) = -0.03200000


     / oo
    |
    |   1/(3+2*x)^2 dx = 0.100938025253
    |
   /   +1.00



 Converge then the serie S.a_n converge. 

 Press return to continue.