题目

求lim(x->1)(1-X)tan(πx/2)的极限
因为当x→1时,cot(πx/2)=tan(π/2-πx/2)=tan[(1-x)π/2]～(1-x)π/2
所以lim(1-x)tan(πx/2)=lim(1-x)/cot(πx/2)
=lim(1-x)/[(1-x)π/2]=2/π
解释下这个cot(πx/2)=tan(π/2-πx/2)=tan[(1-x)π/2]～(1-x)π/2
洛必达法则还没有学

提问时间：2020-06-13

答案

lim(x->1)(1-x)tan(πx/2) =lim(y->0)[y*tan(π/2-πy/2)] (用y=1-x代换) =lim(y->0)[y*ctan(πy/2)] =lim(y->0)[y*cos(πy/2)/sin(πy/2)] =lim(y->0){[(πy/2)/sin(πy/2)]*[(2/...