Exercise 1.44.  The idea of smoothing a function is an important concept in 
signal processing. If f is a function and dx is some small number, then the 
smoothed version of f is the function whose value at a point x is the average 
of f(x - dx), f(x), and f(x + dx). Write a procedure smooth that takes as input 
a procedure that computes f and returns a procedure that computes the smoothed 
f. 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. 
Show how to generate the n-fold smoothed function of any given function using 
smooth and repeated from exercise 1.43.

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(define dx 0.00001)

(define (smooth f)
  (lambda (x) (/ (+ (f (+ x dx)) (f x) (f (- x dx)))
                 3)))

; 4-fold smoothed function f can be written as:

((repeated smooth 4) f)