Introducing Power Series

The posts for the next several weeks will be on topics tested only on the BC Calculus exams. Continuing with some posts on introducing power series (the Taylor and Maclaurin series) Introducing Power Series 1 Two examples to lead off with. Introducing Power Series 2 Looking at the graph of a power series foreshadows the…

Infinite Series

The posts for the next several weeks will be on topics tested only on the BC Calculus exams. The first few weeks will be past posts on sequences and series. That will be followed, in February, by a discussion of Parametric and Vector functions, and Polar equation. We begin with series. Comparison Test Chart A table…

Synthetic Summer Fun

Today, for some summer fun, let’s look at synthetic division a/k/a synthetic substitution. I’ll assume you all know how to do that since it is a pretty common pre-calculus topic and even comes up again in calculus. Why Does Synthetic Division Work? An example: consider the polynomial . This can be written in nested form…

Graphing Taylor Polynomials

The seventh in the Graphing Calculator / Technology series Here are some hints for graphing Taylor polynomials using technology. (The illustrations are made using a TI-8x calculator. The  ideas are the same on other graphing calculators; the syntax may be slightly different.) Each successive term of a Taylor polynomial consists of all the previous terms…

Everyday Series

Our BC friends will soon be starting to teach series. Today, to emphasize that series are all around us, I would like to discuss series that we see every day: numbers. Long ago I was taught that no one has ever seen a “number.” Have you ever see a four? What we see are numerals, symbols or…