(Continuation) As we saw in the computer experiment First, the accuracy of a formula for...

(Continuation) As we saw in the computer experiment First, the accuracy of a formula for numerical differentiation may deteriorate as the step-size h decreases. Study the following central difference formula:

as h → 0. We learn in Section 4.3 that the truncation error for this formula is in the interval (x − h, x + h).

Modify and run the code for the experiment First so that approximate values for the rounding error and truncation error are computed. On the same graph, plot the rounding error, the truncation error, and the total error (sum of these two errors) using a log-scale; that is, the axes in the plot should be −log₁₀ |error| versus log₁₀ h. Analyze these results.