Taylor Flashcards
1
Q
General equation
A
(F^n(a)(x-a)^n)/n!
2
Q
1/(1-x)
A
1+x+x^2….x^n
3
Q
E^x
A
1+x+x^2/2!+x^3/3!…x^n/n!
4
Q
sin(x)
A
X-x^3/3!+x^5/5!-x^7/7!….(-1)^n(x^(2n+1))/(2n+1)!
5
Q
cos(x)
A
1-x^2/2!+x^4/4!-x^6/6!…(-1)^n(x^2n)/(2n)!
6
Q
ln(1+x)
A
x-x^2/2+x^3/3-x^4/4…..(-1)(x^(n+1))/(n+1)
7
Q
1/(1+x)
A
1-x+x^2-x^3……(-1)(x^n)
8
Q
ln(1-x)
A
-x-x^2/2-x^3/3….(-x^n)/(n)
9
Q
Radius of convergence
A
|x-a|<1 solve |x-a|
10
Q
Interval of convergence
A
-R<R
11
Q
Lagrange error bound
A
|Rn(x)|_<(M/(n+1)!)|x-a|^(n+1)
