taylor series: f(a) + f^n(a) * (x-a)^n/n!.
solving infinite series: lim n->infinty |(an+1)/an| = lim n -> inf | (an+1) * (1/an)|
ratio test: lim < 1
finding function for series: n=0 E inf: f(x)^n = 1/(1-f(x))
convergence: |f(x)| < 1
e^x = n=0 E inf (x^n)/n!
cos^2(theta) = 1/2 (1 + cos2(theta))
cartesian: r^2 = 2r sin(theta) + 2r cos(theta)
x = r cos(theta) y = r sin(theta) and r^2 = x^2 + y^2
x^2 + y^2 = 2y + 2x
limacon: integral 0->2pi f(x)^2