求极限(1-x )tan (πx /2) x →1要过程喔如题
问题描述：
求极限(1-x )tan (πx /2) x →1要过程喔如题
答
∵lim(x->1)[(1-x)/cos(πx/2)]=lim(x->1){(-1)/[(-π/2)sin(πx/2)]} (0/0型极限,应用罗比达法则) =(2/π)lim(x->1)[1/sin(πx/2)] =2/π ∴lim(x->1)[(1-x)tan(πx/2)]=lim(x->1)[(1-x)sin(πx/2)/cos(πx/2)] =lim(x->1)sin(πx/2)*lim(x->1)[(1-x)/cos(πx/2)] =1*(2/π) =2/π.