求极限limx→∞[(3x-1)/(3x+4)]^(x+1)=?..
问题描述:
求极限limx→∞[(3x-1)/(3x+4)]^(x+1)=?..
答
limx→∞[(3x-1)/(3x+4)]^(x+1)=limx→∞[1-5/(3x+4)]^(x+1)=1
答
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)