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Link: http://codepad.org/BnT4Yi4g    [ raw code | output | fork ]

C++, pasted on Oct 19:
#include <stdio.h>
//#include <conio.h>
#include <math.h>
 
double f(double x, double eps)
{
    double v, sum = x;
    long n = 1;
    double fn = pow(x,3)/6.0;
    while(eps < fabs(fn))
    {
        sum += fn;
        n   += 1;
        fn *= (2*n - 1)*(2*n - 1)*x*x;
        fn /= 2*n*(2*n + 1);
    }
    return sum;
}
 
int main()
{
    char sign[] = " ";
    double x, fx, dx = 0, xn = 0, xk = 0, eps = 0;
    printf("Enter xn : ");/*scanf("%lf",&xn)*/ xn = 0;
    printf("Enter xk : ");/*scanf("%lf",&xk)*/ xk = 1;
    printf("Enter dx : ");/*scanf("%lf",&dx)*/ dx = 0.1;
    printf("Enter eps: ");/*scanf("%lf",&eps)*/eps= 1E-3;
    printf("|-----------------------------------|\n");
    printf("|    x   |  f(x)  |  asin |(sin-f)/f|\n");
    printf("|-----------------------------------|\n");
    for(x = xn; x <= xk; x += dx)
    {
        fx = f(x,eps);
        if(x < 0)
            sign[0] = '\0';
        else
            sign[0] = ' ';
        printf("|%s%.4f |%s%.4f |%s%.4f|%s%.4f  |\n",
            sign,x,sign,fx,sign,asin(fx),sign,(sin(x) != 0 ? fabs(sin(x) - fx)/sin(x) : 0));
    }
    printf("|-----------------------------------|\n");
    printf("Press any key to continue\n");
    getchar();
    return 0;
}


Output:
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Enter xn : Enter xk : Enter dx : Enter eps: |-----------------------------------|
|    x   |  f(x)  |  asin |(sin-f)/f|
|-----------------------------------|
| 0.0000 | 0.0000 | 0.0000| 0.0000  |
| 0.1000 | 0.1000 | 0.1002| 0.0017  |
| 0.2000 | 0.2013 | 0.2027| 0.0134  |
| 0.3000 | 0.3045 | 0.3094| 0.0304  |
| 0.4000 | 0.4107 | 0.4232| 0.0546  |
| 0.5000 | 0.5232 | 0.5506| 0.0913  |
| 0.6000 | 0.6431 | 0.6985| 0.1389  |
| 0.7000 | 0.7747 | 0.8862| 0.2025  |
| 0.8000 | 0.9253 | 1.1817| 0.2898  |
| 0.9000 | 1.1165 | nan| 0.4253  |
| 1.0000 | 1.4847 | nan| 0.7644  |
|-----------------------------------|
Press any key to continue


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