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