求函数的极限lim((x→x/2)cosx)/(cos(x/2)-sin(x/2))_数学解答

求函数的极限lim((x→x/2)cosx)/(cos(x/2)-sin(x/2))

人气：388 ℃　时间：2019-08-20 20:01:46

解答

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...