求极限limx→∞[(3x-1)/(3x+4)]^(x+1)=?..

问题描述:

求极限limx→∞[(3x-1)/(3x+4)]^(x+1)=?..

limx→∞[(3x-1)/(3x+4)]^(x+1)=limx→∞[1-5/(3x+4)]^(x+1)=1

limx→∞[(3x-1)/(3x+4)]^(x+1)
=limx→∞[1-5/(3x+4)]^[(3x+4)/5*5/3+1/3]
=limx→∞[1-5/(3x+4)]^[-(3x+4)/5]^[-5/3]
=e^(-5/3)