Function Calculation Accuracy

#include <iostream>
using namespace std;

double power(double base, int n) {
    double result = 1.0;
    if (n == 0) {
        return 1;
    }
    for (int i = 1; i <= n; i++) {
        result = result * base;
    }
    return result;

}
double fact(int n) {
    if (n == 0) {
        return 1.0;
    } else {
        return (double)n * fact(n - 1);
    }
}
double exponent(double epsilon, double x) {
    int n = 1;
    double current = 1.0;
    double result = current;
    while (abs(current) >= epsilon) {
        current = power(x, n) / fact(n);
        result = result + current;
        n++;
    }
    return result;
}
double merkator(double epsilon, double x) {
    int n = 2;
    double current = x;
    double result = current;
    while (abs(current) >= epsilon) {
        current = (power(-1, n - 1) * power(x, n)) / n;
        result = result + current;
        n++;
    }
    return result;
}
double cosine(double epsilon, double x) {
    int n = 1;
    double current = 1.0;
    double result = current;
    while (abs(current) >= epsilon) {
        current = power(-1, n) * (power(x, 2 * n) / fact(2*n));
        result = result + current;
        n++;
    }
    return result;
}
double arctg(double epsilon, double x) {
    int n = 2;
    double current = x;
    double result = current;
    while (abs(current) >= epsilon) {
        current = (power(-1, n - 1) / (2 * n - 1)) * power(x, 2 * n - 1);
        result = result + current;
        n++;
    }
    return result;
}



int main()
{
    setlocale(LC_ALL, "Russian");
    int n;
    double x;
    double accuracy;

    cout << "1 - e^x" << endl << "2 - ln(1+x)" << endl << "3 - cos(x)" << endl << "4 - arctg(x)" << endl;
    cout << "Введите номер функции > "; cin >> n; cout << endl;
    cout << "Введите точность > "; cin >> accuracy; cout << endl;

    double result;
    switch (n)
    {
    case 1:
        cout << "Введите x > "; cin >> x; cout << endl;
        result = exponent(accuracy, x);
        break;
    case 2:
        while (true) {
            cout << "Введите x > "; cin >> x; cout << endl;
            if (x > -1 && x <= 1) {
                break;
            }
            else {
                cout << "Ошибка: х должен быть в пределах (-1; 1]" << endl;
            }
        }
        result = merkator(accuracy, x);
        break;
    case 3:
        cout << "Введите x > "; cin >> x; cout << endl;
        result = cosine(accuracy, x);
        break;
    case 4:
        while (true) {
            cout << "Введите x > "; cin >> x; cout << endl;
            if (x >= -1 && x <= 1) {
                break;
            }
            else {
                cout << "Ошибка: х должен быть в пределах [-1; 1]" << endl;
            }
        }
        result = arctg(accuracy, x);
        break;
    }
    cout << "Результат: " << result << endl;
    system("pause");
}