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This problem is intended to demonstrate some problems that can arise from the finite precision of numerical calculations performed with computers. We will do this by approximating the derivative of a function. The definition of the derivative of the unction f(x) is:
We can approximate this with the computer by allowing ?x to be a finite number. Thus, the numerical approximation to the derivative of the function can be determined from:
The error between the actual derivative and its approximation is dependent upon both x and ?x:
Write a program to calculate and plot the error in the numerical estimate of the derivative according to equation (3), for the function
(You may find the logspace command useful.)
Use logarithmic scales on both the x-axis and y-axis of your plot (you may find the MATLAB command loglog helpful). Create a Microsoft Word document named homework8.doc and paste into it your plot of error vs. ?x. Also in your MS Word document, comment on your results - especially relative to the behavior of the error as ?x increases.
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