lim(x→∞) (1+2/x)^(x+3)
lim(x→∞)(1+2/x)^[(x/2)*2(x+3)/x]
=lim(x→∞) [(1+2/x)^(x/2)]^(2(x+3)/x)
=e^(lim(x→∞) (2(x+3)/x)
=e^2