exponential function and e

f'(e^x) = e^x, rate of change at any x = e^x
integration(1/x) = ln(x), i.e. area under the curve from x = 1 to x =
k is ln(k), for k = e, area is 1.
slope at x=0 of e^x is 1
compound interest, (1 + 1/n)^n = e as n approaches infinity
e = sigma(1/fact(n))
e^x = sigma(similar)