language: Scheme 

Code provided:

(define (cubert x)

(define (cube y)(* y y y))

(define (good-enough? guess x)

(< (abs (- (cube guess) x)) 0.001))

(define (improve x y)

(/ (+ (/ x (* y y))(* 2 y)) 3))

(define (cubert-iter guess x)

(if (good-enough? guess x)

guess

(cubert-iter (improve x guess) x)))

(cubert-iter 1.0 x))

a. Modify the algorithm in order to allow a user-defined procedure for good-enough? to be passed in as an argument and used in the algorithm. The user-defined procedure should be passed into the outer cube-root-finding procedure. E.g. (cbrt my-good-enough1 27). Demonstrate in your test cases that you can calculate the cube root of 27 using differing 'good-enough?' functions that vary the accuracy of the result (you will need to define these various good-enough functions yourself.

b. Using the new-if procedure as shown below. Replace the use of if in cbrt-iter with new-if. Does the new version work? Explain why or why not.

(define (new-if predicate consequent alternate) (cond (predicate consequent) (else alternate)))