Question

微积分求极限

微积分求极限超级难！

Answer 1

知道洛必达法则，基本求导熟练，懂无穷近似值代换，都是很简单的基础题
(1)=lim(1/x)/nx^(n-1)=lim1/nx^n=0
(2)=lim(cosx/sinx)/(cos√x/sin√x*1/2√x)
=lim2sin√x*√x/sinx=2
(3)=lime^x/(1/x)=+∞
(4)=lim(e^x-1)/(e^x+1)=lime^x/e^x=1
(5)=limx*1/x=1
(6)=lim(xlnx-x+1)/(x-1)lnx
=lim(xlnx-x+1)/(x-1)²
=lim(lnx+1-1)/2(x-1)
=1/2
(7)=lim(1-sinx)/cosx=lim-cosx/-sinx=0
(8)=e^lim2lnsinx/(1+lnx)
=e^lim2(cosx/sinx)/(1/x)
=e^lim2x/tanx
=e^2

Answer 2

用洛必达法则可解。