Introduction:

The necessecity to approximate certain functions as sums of other functions has wide applications in engineering. This arises because sometimes we cannot perform certain computations easily on a given function and must resort to expressing that function in terms of more elementary functions. For example, suppose we wish to evaluate the integral shown below:

There is no elementary antiderivative for the integrand function but we can create an infinite power series representation for

this integral and then integrate term-by-term to obtain a series solution for the antiderivative.

This lab is designed to help you visualize the convergence of Taylor Polynomials and a few applications of their usage.