#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define H 0.000002
#define INICIO -1
#define FIM 1

double fx(double x)  {
    return (1+ tanh(4*x))/2;
}

double calculaH (int k) {
    double h0=H;
    return h0/pow(2,k);
}

double calculaX0(double x0, int k) {

    double h= calculaH(k);


    return ((-3.0/2.0)*fx(x0)+2.0*fx(x0+h)-(1.0/2.0)*fx(x0+2*h))*(1/h);
}

double calculaX1(double x1, int k) {
     double h= calculaH(k);
    return ( (-1.0/2.0) * fx(x1-h) + (1.0/2.0) * fx(x1+h)) * (1.0 / h);
}

double calculaX2(double x2, int k) {
     double h= calculaH(k);
    return ( (1.0/2.0) * fx(x2-2*h) - 2.0 * fx(x2-h) + (3.0/2.0) * fx(x2) ) * (1.0/h);
}

int main()
{
    double x0=0, x1=0.1, x2=0.2,d;
    int k =4,i;
    double vetX0[k], vetX1[k],vetX2[k];

    for (i=0;i<=k;i++){

        vetX0[i]=calculaX0(x0,i);
        vetX1[i]=calculaX1(x1,i);
        vetX2[i]=calculaX2(x2,i);

        printf("\n\nk=%d : h=%.6lf\n",i,calculaH(i));
        printf("f'(x0)=%.20lf", vetX0[i]);
        printf("\nf'(x1)=%.20lf", vetX1[i]);
       printf("\nf'(x2)=%.20lf", vetX2[i]);
    }

    //calculando o erro relativo

    printf("\n\nErro relativo\n");
   /* for(i=1;i<k;i++){
        printf("\n\nK= %d\n",i);
       printf("dx0= %.20lf",(fabs(vetX0[i]-vetX0[i-1]))/fabs(vetX0[i]));


       // printf("\ndx1= %.6lf",(fabs(vetX1[i+1]-vetX1[i]))/fabs(vetX1[i]));
      //  printf("\ndx2= %.6lf",(fabs(vetX2[i+1]-vetX2[i]))/fabs(vetX2[i]));
    }*/
    for(i=1;i<k;i++){
        printf("\n\nPara k = %d\n",i);
        printf("Er f'(x0)=%.6e",( fabs(vetX0[i]-vetX0[i-1]) ) / fabs(vetX0[i]) );
       printf("\nEr f'(x1)=%.6e",(fabs(vetX1[i]-vetX1[i-1]))/fabs(vetX1[i]));
       printf("\nEr f'(x2)=%.6e",(fabs(vetX2[i]-vetX2[i-1]))/fabs(vetX2[i]));
    }
}