The sequences (ar) and (gr) satisfy a, >= g, for all n >= 1, and converge to the same limit which we use AGM(x, y) and call the arithmetic- geometric mean of x and y. Express a function agm(x, y) which returns an approximation to the arithmetic-geometric mean of two positive real numbers x and y. Your function should do this by generating the sequences (ar) and (gr) defined above, and returning the first value of an such that a, - g < 0.0001. The function is required to return a number according to the instructions above. It should not print anything out. You can assume that the inputs x and y are positive real numbers with x >= y, and your function must work for all such values of x and y.