Recursion: sqrt(x) revisited

Numerous algorithms exist for determining the square root of a non-negative real number. An interesting one that can be derived from Newton's Method, involves starting with an initial guess followed by successive improvements.

For example, suppose the square root of a number, n, is sought. An initial guess, g₀,  might be taken as n/g. If g² is not sufficiently close enough to n, (say, |n-g|< 0.001), we could use the average of g₀ and n/g, call it  g₁, and try again.  As a result, our feedback strategy should reveal a sequences of closer approximations to the square root of n.

Program: Write a recursive function,

double sqrt(double n, double g)

that will return an approximation to the square root of n accurate to 0.001.  Write a main program to test your function for a variety of well-chosen values for n.

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