double eps = 0.00001; //точность вычисления
double sum = 0;
double temp = x;
int i = 1;
while (abs(temp) >= eps)
{
    sum += temp;
    temp = temp * (x*x) / ((2 * i + 1) * (2 * i));
    i++;
}
cout << "x = " << x << "ty = " << 2 * x + sum << endl;

double calc(double x, int i)
{
    if (i > 1000) return 1;  // Критерий останова рекурсии
    return 1+x*x/(2*i+1)/(2*i)*calc(x,i+1);
}

double Sinh(double x)
{
    return x*calc(x,1);
}

int main(int argc, const char * argv[])
{
    for(double x = 0; x < 2; x += 0.1)
    {
        cout << setw(4) << x << setw(15) << Sinh(x) << setw(15) << sinh(x) << endl;
    }
}

double calc(double x, int i, double term)
{
    double fact = x*x/(2*i+1)/(2*i);
    term *= fact;
    if (fact < 1e-8) return 1;  // Критерий останова рекурсии
    return 1+fact*calc(x,i+1, term);
}

double Sinh(double x)
{
    return x*calc(x,1,abs(x));
}

double exp2(double x, int e1, int e2, int &i)
    {
        if(e1 == i || e2 == i) return 1 + x * x / e1 * e2;
        return 1 + x * x / (e1 * e2) * exp2(x, e1 + 2, e2 + 2, i);
}
void recurs_gorner(double x, int &i)
{
    clock_t t0 = clock();
    cout << "x = " << x << "ty = " << 2 * x + exp2(x,2,3,i) << endl;
    for (int i = 0; i < 50000000; i++);
    clock_t t1 = clock();
    cout << "Время (рекурсия): " << (double)(t1 - t0) / CLOCKS_PER_SEC << endl;
}
int main()
{
    setlocale(LC_ALL, "rus");
    double x = 3.0;
    int i = 1;
    recurs_gorner(x, i);
    _getch();
    return 0;
}