Mathc initiation/Fichiers c : c78eh2
Installer et compiler ces fichiers dans votre répertoire de travail.
c01h.c |
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/* --------------------------------- */
/* save as c1h.c */
/* --------------------------------- */
#include "x_hfile.h"
#include "fh.h"
/* --------------------------------- */
int main(void)
{
double x = 1.8;
clrscrn();
printf(" x = %0.1f \n\n\n",x);
printf(" %s \t\t\t\t\t= %0.8f \n", f1eq, f1(x));
printf(" %s \t= %0.8f \n\n\n", f2eq, f2(x));
stop();
return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */
Vérifions par le calcul :
x = 1.8
tanh(3x) = 0.99995920
(3*tanh(x)+tanh(x)**3)/(1+3tanh(x)**2) = 0.99995920
Press return to continue.
Vérifions les égalités :
Nous avons vu que :
tanh(y) + tanh(x)
tanh(x+y) = ------------------
1 + tanh(y) tanh(x)
posons y = 2x :
tanh(2x) + tanh(x)
tanh(x+2x) = ------------------
1 + tanh(2x) tanh(x)
tanh(2x) + tanh(x) (a)
tanh(3x) = --------------------
1 + tanh(2x) tanh(x) (b)
a) ------------------------------------------
2*tanh(x)
tanh(2x) + tanh(x) = ------------ + tanh(x)
1+tanh(x)**2
2*tanh(x) tanh(x) (1+tanh(x)**2)
tanh(2x) + tanh(x) = ------------ + ----------------------
1+tanh(x)**2 1+tanh(x)**2
2*tanh(x) tanh(x)+tanh(x)**3
tanh(2x) + tanh(x) = ------------ + ------------------
1+tanh(x)**2 1+tanh(x)**2
3*tanh(x) + tanh(x)**3
tanh(2x) + tanh(x) = ----------------------
1+tanh(x)**2
b) ------------------------------------------
2*tanh(x)
1 + tanh(2x) tanh(x) = 1 + ------------ tan(x)
1+tanh(x)**2
1+tanh(x)**2 2*tanh(x)**2
1 + tanh(2x) tanh(x) = ------------ + ------------
1+tanh(x)**2 1+tanh(x)**2
1 + 3 tanh(x)**2
1 + tanh(2x) tanh(x) = ----------------
1+tanh(x)**2
a/b) ------------------------------------------
3*tanh(x) + tanh(x)**3
----------------------
1+tanh(x)**2
tanh(3x) = ------------
1 + 3 tanh(x)**2
----------------
1+tanh(x)**2
donc
3*tanh(x) + tanh(x)**3
tanh(3x) = ------------------
1 + 3 tanh(x)**2