Example 7.  Plot the absolute error    over the interval  ,  and estimate the maximum absolute error over the interval.  
7 (a).  Compute the error bound    and observe that    over  .  
7 (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 7.

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

7 (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  .  Usually we can do better that "theory", with   over  . However, the two bounds are nearly the same for this example.

Remark. Is there a difference between the error bound and minimal error bound?  It looks different i the 10 decimal place to me.  It was hard to get it too.

(c) John H. Mathews 2004