Sum of infinite geometric series in form ar^(n-1)
a/(1-r)

Length of curve, cartesian
integral of sqrt(1+(dy/dx)^2)

Length of curve, parametric
integral of sqrt((dx/dt)^2 + (dy/dt)^2)

Integral of this
arccos x

Integral of this
arcsin x

Integral of this
arctan x

Derivative of sec x
sec x tan x

Derivative of cosec x
-cosec x cot x

Derivative of cot x
-cosec^2 x

Derivative of tan x
sec^2 x

sin(2x) is
2sin(x)cos(x)

cos(2x) is
cos^2(x) - sin^2(x)
2cos^2(x) - 1
1 - 2sin^2(x)

Maclaurin series for e^x
1+x+x^2/2!+...

Maclaurin series for ln(1+x)
x-x^2/2!+x^3/3!-...

Maclaurin series for sinx
x-x^3/3!+x^5/5!-...

Maclaurin series for cosx
1-x^2/2!+x^4/4!-...

Maclaurin series for arctan x
x-x^3/3+x^5/5-...

What is mean value theorem basically saying (know what is a, b, and c)
slope

Radius of convergence where each term is a_n (use inf for infinity)
lim n->inf |a_n+1/a_n| < 1

How do you know if the series diverges 
lim n-> inf a_n = inf

How to test convergence if the radius is 1
integral from 0 to inf

For 1/(n^p) what values of p mean it converges
p > 1

For alternating series e.g. (-1)^n * a_n when does it converge
lim n -> inf a_n = 0

Integral for polar curves
1/2 integral of r^2 dtheta

Integration by parts (where original func is uv')
uv - integral of u'v

Does sum of geometric series also work for alternating series/harmonic series
yes

Polar derivative formula (just say f(theta) is r, theta is "0")
r'sin(0) + rcos(0)/r'cos(0) - rsin(0)

What is error bound for alternating series up to N terms (where a_n is the nth term)
a_n+1

Trapezoidal sum formula, where h is step size, include y_0, y_1, y_2, y_n
1/2h(y_0 + 2(y_1 + y_2 + ...) + y_n)

Integrating factor: equation is of form `form`, you multiply both sides by integrating factor I(x) and realize left side is product rule, I(x) = `integrating factor`
form: dy/dx + P(x)y = Q(x)
integrating factor: e^integral of P(x)

In homogeneous diff eq, it follows format `format` and you just sub in `sub` and differentiate y with that and plug it into y in original eq
format: dy/dx = f(y/x)
sub: y = vx

Does summation of 1/n diverge or converge
diverge

What is 1/n series called
harmonic series

How to calculate mean of function from a to b
integral from a to by / (b-a)