Mathc initiation/Fichiers c : c78hd2
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c01d.c |
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/* --------------------------------- */
/* save as c1d.c */
/* --------------------------------- */
#include "x_hfile.h"
#include "fd.h"
/* --------------------------------- */
int main(void)
{
double x = 1.2;
double y = 1.5;
clrscrn();
printf(" (x,y) = (%0.1f,%0.1f) \n\n\n",x,y);
printf(" %s \t\t\t= %0.8f\n", f1eq, f1(x,y));
printf(" %s \t= %0.8f \n\n\n", f2eq, f2(x,y));
stop();
return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */
Vérifions par le calcul :
(x,y) = (1.2,1.5)
cosh(x) - cosh(y) = -0.54175405
2 sinh( (x+y)/2 ) sinh( (x-y)/2 ) = -0.54175405
Press return to continue.
Vérifions les égalités :
cosh(x) - cosh(y) = 2 sinh( (x+y)/2 ) sinh( (x-y)/2 )
sinh( X ) = [e**X - e**(-X) ] / 2
sinh((x+y)/2) = [e**((x+y)/2) - e**(-(x+y)/2)] / 2
sinh((x-y)/2) = [e**((x-y)/2) - e**(-(x-y)/2)] / 2
cosh(x) - cosh(y) = 2 sinh( (x+y)/2 ) sinh( (x-y)/2 )
cosh(x) - cosh(y) = 2 [e**((x+y)/2)-e**(-(x+y)/2)] / 2 [e**((x-y)/2)-e**(-(x-y)/2)] / 2
2[cosh(x) - cosh(y)] = [e**((x+y)/2)-e**(-(x+y)/2)] [e**((x-y)/2)-e**(-(x-y)/2)]
(x+y)/2 + (x-y)/2 = x
(x+y)/2 + (-(x-y)/2)) = y
-(x+y)/2) + (x-y)/2 = -y
-(x+y)/2) + (-(x-y)/2) = -x
2[cosh(x) - cosh(y)] = e**x-e**y-e**(-y)+e**(-x)
2[cosh(x) - cosh(y)] = e**x+e**(-x) - e**y-e**(-y)
2[cosh(x) - cosh(y)] = e**x+e**(-x) - (e**y+e**(-y))
cosh(x) - cosh(y) = (e**x+e**(-x))/2 - (e**y+e**(-y))/2
cosh(x) - cosh(y) = cosh(x) - cosh(y)