>>342
log(1+x) = x - (x^2/2) + O(x^3)
(1/x)log(1+x) = 1 - x/2 + O(x^2)
(1+x)^(1/x) = e^(1-x/2+O(x^2)) = e*(1-x/2+O(x^2))
{(1+x)^(1/x) - e}/x = -(e/2) + O(x)