Example 3.  Plot the absolute error    over the interval  ,  and estimate the maximum absolute error over the interval.
3 (a).  Compute the error bound    and observe that    over  .  
3 (b).  Since the function f[x] and its derivative is well known, and we have the graph for ,  we can observe that the maximum error on the given interval occurs at x=0.  Thus we can do better that "theory", we see that   over  .

Solution 3.

3 (a).  Compute the error bound    and observe that    over  .  

3 (b).  Since we the function f[x] and its derivative is well known, and we have the graph for ,  we can observe that the maximum error on the given interval occurs at x=0.  Thus we can do better that "theory", we see that   over  .

(c) John H. Mathews 2004