Suppose that we wish to evaluate the function f (x) = (x − sin x)/x3 for values of x close to zero.
a. Write a routine for this function. Evaluate f (x)16 times. Initially, let x ← 1, and then let x ← 1/10 x 15 times. Explain the results.
Note: L’Hˆopital’s Rule indicates that f (x) should tend to 1/6 . Test this code.
b. Write a function procedure that produces more accurate values of f (x) for all values of x. Test this code.
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