π from Collisions

  One of my sons sent me the link to the videos below. They show a very unusual way to find the digits of π. The problems and its two solutions show the connections and the interplay between mathematics and physics. The quality of the illustrations and the verbal explanations are excellent. Here are the…

Power Series 2

This is a BC topic Good Question 16 (11-30-2018) What you get when you substitute. Geometric Series – Far Out (2-14-2017) A very interesting and instructive mistake Synthetic Summer Fun (7-10-2017) Finding the Taylor series coefficients without differentiating Error Bounds (2-22-2013) The alternating series error bound, and the Lagrange error bound The Lagrange Highway (5-20-15)…

Power Series 1

This is a BC topic POWER SERIES (Maclaurin series and Taylor series) Introducing Power Series 1 (2-8-2013) Making better approximations Introducing Power Series 2 (2-11-2013) Graphing and seeing the interval of convergence Introducing Power Series 3 (2-13-2013) Questions pointing the way to power series Graphing Taylor Polynomials (2-7-2017) Using a graphing calculator to graphs Taylor…

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…