lab1

#define _USE_MATH_DEFINES

#include <cmath>
#include <cstdio>

double mysinh(double x, double eps, int &k, double &rn) {
    double s = 0;
    double u = x;
    k = 1;

    while (fabs(u) >= eps) {
        s += u;
        u = x * x / (2 * k * (2 * k + 1)) * u;
        k++;
    }

    rn = u;
    return s;
}

int main() {
    double a = -1.8;
    double b = 1.9;
    double x = (a + b) * 0.5;
    double h = (b - a) / 9.0;

    int n = 0;
    double rn = 0;

    printf("|  eps  | n  |  abs error  |   rem term   |\n");
    for (double eps = 1e-2; eps > 1e-14; eps *= 1e-2) {
        double y = mysinh(x, eps, n, rn);
        printf("| %.0e | %2i | %8.5e | %12.5e |\n", eps, n, fabs(sinh(x) - y), fabs(rn));
    }

    printf("\n|   xi   |  abs error  |   rem term   |\n");
    for (int i = 0; i < 10; i++) {
        double x = a + h * i;
        double y = mysinh(x, 1e-8, n, rn);
        printf("| %6.2f | %8.5e | %12.5e |\n", x, fabs(sinh(x) - y), fabs(rn));
    }
    return 0;
}