求limx→∞[(3x+2)/(3x-1)]^2x-1
问题描述：
求limx→∞[(3x+2)/(3x-1)]^2x-1
答
运用重要极限 lim(x→0)(1+x)^(1/x)=e
lim(x→∞)[(3x+2)/(3x-1)]^2x-1
=lim(x→∞)[1+3/(3x-1)]^[(3x-1)/3]*[3*(2x-1)/(3x-1)]
=e^lim(x→∞)[3*(2x-1)/(3x-1)]
=e^2