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Exercise 5: An evaluation of the error in the computer implementation of the centered difference formula.

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?