求极限lim(X趋向于0)(根号(4-x^2)-2)/(1-cos2X)
问题描述:
求极限lim(X趋向于0)(根号(4-x^2)-2)/(1-cos2X)
答
lim(X→0)2(√(1-(x/2)^2)-1)/(1-cos2X) (用等价无穷小代换)
=lim(X→0)2*1/2*[-(x/2)^2]/[1/2*(2x)^2]
=-1/82(√(1-(x/2)^2)-1)是怎么化出来的?