The trouble with the error estimates is that it is often very diffi-cult to compute four

Chapter 7, Problem 23

(choose chapter or problem)

The trouble with the error estimates is that it is often very diffi-cult to compute four derivatives and obtain a good upper boundfor by hand. But computer algebra systems have no problem computing and graphing it, so we can easily find a value for from a machine graph. This exercise deals with approximations to the integral , where . (a) Use a graph to get a good upper bound for . (b) Use to approximate . (c) Use part (a) to estimate the error in part (b). (d) Use the built-in numerical integration capability of your CAS to approximate . (e) How does the actual error compare with the error estimate in part (c)? (f) Use a graph to get a good upper bound for . (g) Use to approximate . (h) Use part (f) to estimate the error in part (g). (i) How does the actual error compare with the error estimate in part (h)? (j) How large should be to guarantee that the size of the error in using is less than ?