Here goes our smoothing function:
1 2 3 4 5 6 (define (smooth f) (define (average a b c) (/ (+ a b c) 2) ) (lambda (x) (average (f (- x dx)) (f x) (f (+ x dx)) )) )
Procedure for nth-smoothing:
1 2 3 (define (nth-smooth f n) ((repeated smooth n) f) )
Note that it we may also think of doing nth-smoothing instead in the following way:
1 2 3 (define (smooth-nth f n) (repeated (smooth f) n) )
I think it is not correct as this is repeating
(smooth f) n times. As to quote from the exercise:
It is sometimes valuable to repeatedly smooth a function (that is, smooth the smoothed function, and so on) to obtained the n-fold smoothed function.
We need to do smoothing of the smoothed function n times.