求函数的极限lim((x→x/2)cosx)/(cos(x/2)-sin(x/2))
问题描述：
求函数的极限lim((x→x/2)cosx)/(cos(x/2)-sin(x/2))
答
x->π/2吧对分子cosx=sin(π/2-x)因为π/2-x ->0所以sin(π/2-x)~(π/2-x)对分母cos(x/2)-sin(x/2)=√2[((√2)/2)cos(x/2)-((√2)/2)sin(x/2)]=√2[sin(π/4)cos(x/2)-cos(π/4)sin(x/2)]=√2 sin(π/4-x/2)=√2 sin...