11.9: Representations of Functions as Power Series

If you are absent, check out the appropriate AP Classroom videos.

11.9 Notes.

Why should we care:

Series can be used to approximate functions by using a partial sum of the series
An infinite series = partial sum + the rest of the terms; therefore, (series) - (partial sum) = error
- we need to know where it is a good approximation of the function: whether and where it converges.
- we need to have a way of measuring how much error is left after we stop adding terms

Preview of coming attractions:

1. Watch the following and take notes: 3 Blue, 1 Brown: Taylor Series

2. Start memorizing the 5 Common Taylor Series ! (Note, I don't need you to have the Natural Log series memorized).

I will start quizzing on these after mid-winter break!

HW 11.9.1: #3-10; 13-17 odd, 16 & 23. Due after break.

Resources & Stuff you must know:

All the convergence tests & geometric series rules! Summary of Convergence Tests

AP Videos!!!