We will discuss in class the method for finding roots of equations called the Newton-Raphson method. Your programming assignment is to write a simple program which will implement this method for finding roots of numbers. The iterative formula in the Newton-Raphson method is

1. Prompt the user to input two real numbers, a and b.

2. Verify that these numbers are greater than 1. Your program should inform the user they have made an error if they attempt to input a number smaller than or equal to 1.

3. Prompt the user for a tolerance, tol.

4. Implement the Newton-Raphson method to find the b^th root of a with a tolerance of tol.

The numbers a, b, and the result of the program, i.e. the b^th root of a, and the tolerance tol identifying each to the user. Do not worry at this point about how many decimal points are printed out. We will discuss later ways of formatting output.