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…

Sequences

This is a BC topic. SEQUENCES Everyday series (1-17-2017) The most familiar series: Numbers Amortization (2-9-2015) An important use of a (finite) series – Find you mortgage payment without calculus. Convergence Test List A summary of the tests. Download and copy for your students (and yourself) Which Convergence Test Should I Use? Part 1 (2-9-2018)…

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…

Good Question 14

Good Question 14 – The Integral Test I have no criteria for what constitutes a “Good Question” for this series of occasional posts. They are just questions that I found interesting, or that seem more than usually instructive, or that I learn something from. I cannot quote this question (2016 BC 92) since it is…