(x+2)/(x-3) = 1 + 5/(x-3)let1/y = 5/(x-3)lim(x->∞) [(x+2)/(x-3)]^x=lim(y->∞) (1+ 1/y)^(5y+3)=lim(y->∞) (1+ 1/y)^(5y)=e^5
设t=x-3→∞，原式→(1+5/t)^(t+3)→[(1+5/t)^(t/5)]^5→e^5.
