limx→∞[(1-x)/(3-x)]^2x
=limx→∞[1+2/(x-3)]^{4[(x-3)/2]+6}
=limx→∞[1+2/(x-3)]^4[(x-3)/2]*=limx→∞[1+2/(x-3)]^6
=e^4*1^6=e^4