Today's lab concerns Taylor Polynomials. In particular, we'll
learn about the error that we make in using one to approximate a
function on an interval.
Last time:
We explored some power series, and in particular learned
about their intervals and radii of convergent.
Often we use the ratio test to find the radii; and then we
have to test the endpoints specifically, to see if either of
those leaves the series convergent.
Then we began to explore Taylor series, which provide a
method for constructing series for arbitrary functions for
which all derivatives exist about the center.
We will then approximate these with partial sums, which are
called Taylor polynomials.
Today:
There are two parts to the lab:
Constructing series for various functions, and then
Estimating and visualizing the errors we make when using
these approximations.