sicp-all-tasks/sicp/1_002e44

Exercise 1.44: The idea of 
smoothing a
function is an important concept in signal processing.  If 
  f
 is a function
and 
  
    d
    x
  
 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
    −
    d
    x
    )
  
, 

  
    f
    (
    x
    )
  
, and 
  
    f
    (
    x
    +
    d
    x
    )
  
.  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 obtain 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.