Because I'm not allowed to promote diversity, equity and
inclusion anymore, I've decided to promote
censorship
childishness
conformity
oppression
propoganda
People afraid of ideas and words should not be running our
country.
Today's lab is designed to get a head start on one of primary
reasons that we talk about these series: we seek to
represent functions as series, where the terms are
themselves simple functions (powers, sines and cosines).
So today we're going to use one class of functions --
polynomials -- to approximate other functions (e.g. sines, and
a rational function).
Your final two lab exams will be problem solving exercises. For
that reason, you might attempt any of the "technology"
exercises I assign from the text for practice (and you could
try a few more on your own).
Today:
There are two parts to the lab:
We begin by generalizing the geometric series formula, and
use it (and a partial sum of polynomial terms) to
approximate a rational function.
We then use a partial sum of polynomial terms to
approximate the sine function so that you wouldn't know
the difference.
One common thread here is polynomials: those bunny rabbits of
the function zoo can do a lot of work for us. They are perfect
for computers, too, seeing as their evaluation only requires
multiplication and addition -- two things that computers do
really well.