Mathc initiation/Fichiers c : c30cd
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c2d.c |
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/* --------------------------------- */
/* save as c2d.c */
/* --------------------------------- */
#include "x_hfile.h"
#include "fd.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 = 7/3 = %.5f\n\n", feq, 7./3.);
stop();
return 0;
}
/* --------------------------------- */
On peut obtenir le même résultat en utilisant la Règle de L'Hôpital. [wikipedia].
(sin(7*x))'/(3*x)' = 7*cos(7*x)/3 et lim x->0 7*cos(7*x)/3 = 7*cos(7*0)/3 = 7/3 = 2,33333
(sin(A*x))'/(B*x)' = A*cos(A*x)/B et lim x->0 A*cos(A*x)/B = A*cos(A*0)/B = A/B
Exemple de sortie écran :
Does lim x->0 sin(7*x)/(3*x) exist ?
Substituing 0 for x gives 0/0.
Press return to continue.
Exemple de sortie écran :
f : x-> sin(7*x)/(3*x)
Approximate f(x) by the right,
for x near 0.
f(+1.0) = 0.219 || f(+0.10) = 2.147392 || f(+0.010) = 2.33142824
f(+0.9) = 0.006 || f(+0.09) = 2.182018 || f(+0.009) = 2.33179014
f(+0.8) = -0.263 || f(+0.08) = 2.213276 || f(+0.008) = 2.33211397
f(+0.7) = -0.468 || f(+0.07) = 2.241076 || f(+0.007) = 2.33239972
f(+0.6) = -0.484 || f(+0.06) = 2.265336 || f(+0.006) = 2.33264739
f(+0.5) = -0.234 || f(+0.05) = 2.285985 || f(+0.005) = 2.33285697
f(+0.4) = 0.279 || f(+0.04) = 2.302964 || f(+0.004) = 2.33302846
f(+0.3) = 0.959 || f(+0.03) = 2.316221 || f(+0.003) = 2.33316184
f(+0.2) = 1.642 || f(+0.02) = 2.325719 || f(+0.002) = 2.33325711
f(+0.1) = 2.147 || f(+0.01) = 2.331428 || f(+0.001) = 2.33331428
Press return to continue.
Exemple de sortie écran :
f : x-> sin(7*x)/(3*x)
Approximate f(x) by the left,
for x near 0.
f(-1.0) = 0.219 || f(-0.10) = 2.147392 || f(-0.010) = 2.33142824
f(-0.9) = 0.006 || f(-0.09) = 2.182018 || f(-0.009) = 2.33179014
f(-0.8) = -0.263 || f(-0.08) = 2.213276 || f(-0.008) = 2.33211397
f(-0.7) = -0.468 || f(-0.07) = 2.241076 || f(-0.007) = 2.33239972
f(-0.6) = -0.484 || f(-0.06) = 2.265336 || f(-0.006) = 2.33264739
f(-0.5) = -0.234 || f(-0.05) = 2.285985 || f(-0.005) = 2.33285697
f(-0.4) = 0.279 || f(-0.04) = 2.302964 || f(-0.004) = 2.33302846
f(-0.3) = 0.959 || f(-0.03) = 2.316221 || f(-0.003) = 2.33316184
f(-0.2) = 1.642 || f(-0.02) = 2.325719 || f(-0.002) = 2.33325711
f(-0.1) = 2.147 || f(-0.01) = 2.331428 || f(-0.001) = 2.33331428
Press return to continue.
Exemple de sortie écran :
With the table we arrive at the following conjecture.
lim x->0 sin(7*x)/(3*x) = 7/3 = 2.33333
Press return to continue.