import java.lang.Math;
public class analise{
  public static int iterations = 0;
  public static void main(String[] args) {
    double x0 = 1.7; //a
    double epsilon = epsilon_value(); //erro para alinea a
    System.out.println("Alinea a");
    System.out.println("Valor aproximado da raiz com erro epsilon: " + newton(x0,epsilon));
    System.out.println("iterações: "+ iterations);
    System.out.println();
    System.out.println("Alinea d");
    System.out.println("Valor aproximado da raiz com erro 5*10^-12: " + newton(x0,5.0*Math.pow(10,-12)));
    System.out.println("iterações: "+ iterations);
    System.out.println();
    System.out.println("Alinea e");
    System.out.println("Valor aproximado da raiz com erro 5*10^-14: " + newton(x0,5.0*Math.pow(10,-14)));
    System.out.println("iterações: "+ iterations);
  }

  public static double f(double x) {
    return Math.cosh(x)-Math.cos(x)-3;
  }
  public static double fdev(double x){
    return Math.sinh(x)+Math.sin(x);
  }
  public static float epsilon_value(){
    float eps = 1;
    while((eps+1)>1){
      eps = eps/2;
    }
    eps = eps*2;
    return eps;
  }
    //a)
    public static double newton(double x0,double epsilon){
      iterations = 0;
      double x1 = x0 - f(x0)/fdev(x0);
      while(Math.abs(x1 - x0) > epsilon){
        x1 = x0 - f(x0)/fdev(x0);
        x0 = x1;
        iterations++;
      }

    return x0;
    }
}