10.5-10.6 Flashcards
1
Q
What are the three cases for I, R?
A
- x=a, R=0 I={a}
- converge for all x, R=inf I={-inf,inf}
- -R+a
2
Q
What is the process for finding R,I?
A
- Do ratio test.
- set n to infinity
- |x-a|
3
Q
How to test end points in a power series?
A
- plug ends of (I) into original series.
- If divergent, leave out
- If convergent, put in
4
Q
n! = ?
A
n(n-1)!
5
Q
What is the form you’re shooting for in power series via geometric series?
A
Series((x)^n) = 1/(1-x)
6
Q
What is the form of a power series? What are I and R?
A
- c(x-a)
* center is x=a
7
Q
When taking derivatives of power series’ what must be done.
A
- nx^n-1, keep constants (n) the same
* GO TO n=1 (means add (n+1) if n was 0)
8
Q
How to find integrals of power series’?
A
- x^n+1/n+1, keep constants same.
* +C
9
Q
What to do if degree on bottom that needs to be a power series is high?
A
Integrate
10
Q
How to approximate error of power series.
A
- Convert to power series, integrate
- plug n+1 for n
- plug in different n’s till you find right one.
