This lab is an exploration of some of the problems that come up when you approximate a function with a finite Taylor polynomial.
WARNING: THIS LAB IS NOT COMPLETE YET. I AM PUTTING IT UP FOR COMMENTS AND FOR MY OWN AMUSEMENT. I WILL EVENTUALLY POLISH THIS UP AND FINISH THE COMMENTARY, BUT THIS IS ALL THERE IS FOR NOW. YOU HAVE BEEN WARNED...
In this section, we will examine the situation where we want to approximate our function with a given degree Taylor polynomial. We thus need to find out what domain this polynomial is guaranteed to fall within our error tolerence.
In this section, we will examine the situation where we want to approximate our function over a given interval. We thus need to find out how many terms we need to take to guarantee our error is small enough.