e^x - 1 = t
e^x = t + 1
x = ln (t+1)
x-->0
t-->0
Thus:
[ (e^x - 1)/x ] = t / ln (t + 1)
x-->0 t-->0

(1 + 1/x)^x = e
x-> Inf
(1 + x)^(1/x) = e
x-> 0
ln (1+x)/x = 1
x-> 0