∵ lnx ,∴ x->+∞
lim(x->+∞) (1+1/2x)^(3x+lnx)
=lim(x->+∞) [(1+1/2x)^2x]^[(3x+lnx)/2x]
∵ lim(x->+∞) [(1+1/2x)^2x] = e
lim(x->+∞) [(3x+lnx)/2x] = lim(x->+∞) [3/2 + lnx/2x] = 3/2 ,故：
= e^(3/2)