原式=lim(x->∞){[(2x+3-2)/(2x+3)]^(x+1)}
=lim(x->∞){[(1+(-2)/(2x+3))^((2x+3)/(-2))]^[-2(x+1)/(2x+3)]}
=e^{lim(x->∞)[-2(x+1)/(2x+3)]} (應(yīng)用重要極限lim(z->0)[(1+z)^(1/z)]=e)
=e^{lim(x->∞)[-2(1+1/x)/(2+3/x)]}
=e^[-2(1+0)/(2+0)]
=e^(-1)
=1/e.=lim(x->∞){[(1+(-2)/(2x+3))^((2x+3)/(-2))]^[-2(x+1)/(2x+3)]}這步怎么來的？好暈…