Good Question 16

I had an email last week from a teacher asking, how come I can use a substitution to find a power series for  , and for  , but not for  ? The answer is that you can. Substituting (2x) in to the cosine’s series give you a Taylor series centered at x = 0, a…

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…

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…