Mathc initiation/a386

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00a.c

/* ---------------------------------- */
/* save as c00a.c                     */
/* ---------------------------------- */
#include "x_afile.h"
#include      "fa.h"
/* ---------------------------------- */
int main(void)
{
double i;

 clrscrn();
 printf(" Limit comparison test.                               \n\n\n");
 printf(" Let S.a_n and S.b_n be positive-term series.           \n\n");
 printf(" If there is a positive real number c such that       \n\n\n");
 printf("         lim n->oo (a_n/b_n) = c >0                   \n\n\n");
 printf(" The either both series converge or both series diverge.\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"
        "  %s,\\\n"
        "  %s\n\n"
        "  reset\n\n",a_xeq, b_xeq);   
 stop();

 clrscrn();
 printf(" a_n : n-> %s\n\n", a_neq);
 printf(" b_n : n-> %s\n\n", b_neq);
 printf(" c_n : n-> a_n/b_n\n\n");

 for(i=1; i<10; i++)
     printf(" c_%.0f = %5.3f || c_%.0f = %5.6f || c_%.0f = %5.8f\n",
     i,        a_n(i)/b_n(i),
     i*10,  a_n(i*10)/b_n(i*10),
     i*1000,a_n(i*1000)/b_n(i*1000) );
     
 printf("\n\n");
 stop();

 clrscrn();
 printf(" a_n : n-> %s  \n\n", a_neq);
 printf(" b_n : n-> %s\n\n\n", b_neq);
 printf(" Since S.b_n converge p-series with p = 5/2 >1.\n\n");
 printf(" It follows from the theorem that S.a_n is     \n\n");
 printf(" also converge.                              \n\n\n");

 stop();

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

Exemple de sortie écran :

 Limit comparison test.                               


 Let S.a_n and S.b_n be positive-term series.           

 If there is a positive real number c such that       


         lim n->oo (a_n/b_n) = c >0                   


 The either both series converge or both series diverge.

 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]\
  (8.*x + sqrt(x)) / (5 + x**2 + x**(7./2.)),\
  1/x**(5./2.)

  reset 
  Press return to continue.

Exemple de sortie écran :

 a_n : n-> (8.*n + sqrt(n)) / (5 + n**2 + n**(7./2.))

 b_n : n-> 1/n**(5./2.)

 c_n : n-> a_n/b_n

 c_1 = 1.286 || c_10 = 8.048970 || c_1000 = 8.03136880
 c_2 = 4.849 || c_20 = 8.131557 || c_2000 = 8.02227099
 c_3 = 6.601 || c_30 = 8.132805 || c_3000 = 8.01820862
 c_4 = 7.302 || c_40 = 8.125893 || c_4000 = 8.01577970
 c_5 = 7.628 || c_50 = 8.118413 || c_5000 = 8.01411947
 c_6 = 7.804 || c_60 = 8.111622 || c_6000 = 8.01289270
 c_7 = 7.907 || c_70 = 8.105669 || c_7000 = 8.01193861
 c_8 = 7.974 || c_80 = 8.100474 || c_8000 = 8.01116914
 c_9 = 8.018 || c_90 = 8.095921 || c_9000 = 8.01053154


 Press return to continue.

Exemple de sortie écran :

 a_n : n-> (8.*n + sqrt(n)) / (5 + n**2 + n**(7./2.))  

 b_n : n-> 1/n**(5./2.)


 Since S.b_n converge p-series with p = 5/2 >1.

 It follows from the theorem that S.a_n is     

 also converge.                              

 Press return to continue.