Since computer arithmetic has finite precision, in addition to the truncation errors of Exercise 5, rounding and precision errors must be considered. Let , , and denote the rounding/precision errors associated with the evaluations of , , and , respectively. Show that in a computer implementation of the centered difference formula for the sum of the roundoff/precision error and the truncation error has the form
What does this formula for Error tell you about choosing a large value of h in a calculation? What does it tell you about choosing a very small value of h in a calculation?