Question

Suppose f' is continuous on [a,b]. It can be shown that if K is greater than or equal to the maximum value of abs(f') on [a,b], then

Answer 1

\[E _{n}^{L}\le \frac{ K }{ 2n}(b-a)^{2} and E _{n}^{R}\le \frac{ K }{ 2n}(b-a)^{2}\]
The right sides of the inequalities are error bounds for the left sum and right sum, respectively.

Answer 2

Notice that they approach zero as n increases without bound. Find error bounds for the following.

a.

Answer 3

Do you know how to find the K in these error bounds?