class limit	{
	public static void main (String[] args)	{
		double res = limit( 2 );
		System.out.println(" O limite é : " + res );
	}
	public static double f (double x)
	{
		return ( x / ( x*x + 1) );
		//return 4 * ( ((x*x) - 4 ) / (x - 2));
	}
	public static double poslimit( double a )	{
		int a_n = (int) Math.round(a * 1000);
		double minn = 999999;
		for(int x=a_n+20;x>a_n;x--)	{
			minn = Math.min(minn, f(x/1000.0));
		}
		System.out.println("LimPos: " + minn );
		return minn;
	}
	public static double neglimit( double a )	{
		int a_n = (int) Math.round(a * 1000);
		double maxn = -999999;
		for(int x=a_n-20;x<a_n;x++)	{
			maxn = Math.max(maxn, f(x/1000.0));
		}
		System.out.println("LimNeg: " + maxn );
		return maxn;
	}
	public static double limit( double a )		{
		double neg = Math.round(neglimit(a)*100)/100.0;
		double pos = Math.round(poslimit(a)*100)/100.0;
		return ( neg==pos ) ? neg : Double.NaN;
	}
}