Section Summary

In this section we have seen that we can approximate a non-polynomial function by polynomials whose coefficients can be calculated by matching derivative values with the original function at a particular reference point, `x = 0`. We have computed these approximating polynomials explicitly for the exponential and sine functions — in the exercises you will extend these ideas and computations to several other functions. We find that our approximations, even for low degree, are quite good near the reference point, but they seem to deteriorate as we move away from the reference point. On the other hand, it appears that we can extend the interval of close approximation by taking higher-degree approximations. That will be our point of departure in the next section.