The function sqrt from the header file can be used to find the square root of a nonnegative real number. Using Newtons method, you can also write an algorithm to find the square root of a nonnegative real number within a given tolerance as follows: Suppose x is a nonnegative real number, a is the approximate square root of x, and epsilon is the tolerance. Start with a = x.

a. If |a² - x| epsilon, then a is the square root of x within the tolerance; otherwise:

b. Replace a with (a² + x) / (2a) and repeat Step a in which |a² - x| denotes the absolute value of a² - x. Write a recursive function to implement this algorithm to find the square root of a nonnegative real number. Also, write a program to test your function.

Turn in your source code file and one or more screen shots showing the results of your testing.

After completing this project you will show that you can

Identify the base case(s) and general case in a recursive algorithm

Utilize tail recursion in the construction of a recursive algorithm

Construct a recursive algorithm that does not use global variables