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Mathc initiation/Fichiers c : c30cb

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Installer et compiler ces fichiers dans votre répertoire de travail.

c2b.c
/* --------------------------------- */
/* save as c2b.c                     */
/* --------------------------------- */
#include  "x_hfile.h"
#include       "fb.h"
/* --------------------------------- */
int main(void)
{
double i;

 clrscrn();
 printf(" Does lim x->0 %s exist ?\n\n", feq);
 printf(" Substituing 0 for x gives 0/0.\n");
 stop();


 clrscrn();
 printf(" f : x-> %s\n\n", feq);

 printf(" Approximate f(x) by the right,\n");
 printf(" for x near 0.\n\n");

 for(i=1; i>0.1; i+=-.1)
     printf(" f(%+.1f) = %8.3f || f(%+.2f) = %5.6f || f(%+.3f) = %5.8f\n",
     i,    f(i),
     i*.1, f(i*.1),
     i*.01,f(i*.01)
     );
 stop();


 clrscrn();
 printf(" f : x-> %s\n\n", feq);

 printf(" Approximate f(x) by the left,\n");
 printf(" for x near 0.\n\n");

 for(i=-1; i<-0.1; i+=.1)
     printf(" f(%+.1f) = %8.3f || f(%+.2f) = %5.6f || f(%+.3f) = %5.8f\n",
     i,    f(i),
     i*.1, f(i*.1),
     i*.01,f(i*.01)
     );
 stop();


 clrscrn();
 printf(" With the table we arrive at the following conjecture.\n\n");
 printf("     lim x->0 %s = -6\n\n", feq);

 stop();

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


On peut obtenir le même résultat en utilisant la Règle de L'Hôpital. [wikipedia].
  (sin(x)-7*x )'/(x*cos(x))' = (cos(x)-7)/(cos(x)-x*sin(x))  
  
  et lim x->0   (cos(x)-7)/(cos(x)-x*sin(x))  = (1 -7)/(1-1*0) = -6

Exemple de sortie écran :

 Does lim x->0 ( sin(x)-7*x ) / (x*cos(x) ) exist ?

 Substituing 0 for x gives 0/0.
 Press return to continue.

Exemple de sortie écran :

 f : x-> ( sin(x)-7*x ) / (x*cos(x) )

 Approximate f(x) by the right,
 for x near 0.

 f(+1.0) =  -11.398 || f(+0.10) = -6.031800 || f(+0.010) = -6.00031668
 f(+0.9) =   -9.861 || f(+0.09) = -6.025737 || f(+0.009) = -6.00025651
 f(+0.8) =   -8.760 || f(+0.08) = -6.020321 || f(+0.008) = -6.00020267
 f(+0.7) =   -7.949 || f(+0.07) = -6.015549 || f(+0.007) = -6.00015517
 f(+0.6) =   -7.341 || f(+0.06) = -6.011417 || f(+0.006) = -6.00011400
 f(+0.5) =   -6.884 || f(+0.05) = -6.007925 || f(+0.005) = -6.00007917
 f(+0.4) =   -6.543 || f(+0.04) = -6.005070 || f(+0.004) = -6.00005067
 f(+0.3) =   -6.296 || f(+0.03) = -6.002851 || f(+0.003) = -6.00002850
 f(+0.2) =   -6.129 || f(+0.02) = -6.001267 || f(+0.002) = -6.00001267
 f(+0.1) =   -6.032 || f(+0.01) = -6.000317 || f(+0.001) = -6.00000317
 Press return to continue.


Exemple de sortie écran :

 f : x-> ( sin(x)-7*x ) / (x*cos(x) )

 Approximate f(x) by the left,
 for x near 0.

 f(-1.0) =  -11.398 || f(-0.10) = -6.031800 || f(-0.010) = -6.00031668
 f(-0.9) =   -9.861 || f(-0.09) = -6.025737 || f(-0.009) = -6.00025651
 f(-0.8) =   -8.760 || f(-0.08) = -6.020321 || f(-0.008) = -6.00020267
 f(-0.7) =   -7.949 || f(-0.07) = -6.015549 || f(-0.007) = -6.00015517
 f(-0.6) =   -7.341 || f(-0.06) = -6.011417 || f(-0.006) = -6.00011400
 f(-0.5) =   -6.884 || f(-0.05) = -6.007925 || f(-0.005) = -6.00007917
 f(-0.4) =   -6.543 || f(-0.04) = -6.005070 || f(-0.004) = -6.00005067
 f(-0.3) =   -6.296 || f(-0.03) = -6.002851 || f(-0.003) = -6.00002850
 f(-0.2) =   -6.129 || f(-0.02) = -6.001267 || f(-0.002) = -6.00001267
 f(-0.1) =   -6.032 || f(-0.01) = -6.000317 || f(-0.001) = -6.00000317
 Press return to continue.


Exemple de sortie écran :

 With the table we arrive at the following conjecture.

     lim x->0 ( sin(x)-7*x ) / (x*cos(x) ) = -6

 Press return to continue.