In an earlier lab, we observed how we could have a function that is undefined at some value (such as (sin x)/x at the point x=0), but could come arbitrarily close to it by successively evaluating smaller and smaller numbers (i.e. taking a limit). For example, we might evaluate at x=0.1, x=0.01, x=0.001, etc. until we have come very close to the value. Taking limits like this, numerically, is commonly done when functions are too complicated to evaluate analytically. You will write a program to compute a derivative as a numerical limit. This activity has a few parts:

You may reuse code from activity #1 if it is helpful.

Python Program

1. Evaluating a polynomial limit analytically

You should have learned by now the process for finding the derivative of a polynomial (as another polynomial). Write a program that will read in from the user a cubic polynomial f(x) (as a set of 4 coefficients), and use this to compute the derivative polynomial (i.e. compute the three coefficients of the derivative f(x)). Then, read in a value for x from a user, and evaluate the derivative polynomial at that x. Print out that value.