当x无限趋向于零时,cos2x-cos3x/x^2的极限给力吧!
问题描述：
当x无限趋向于零时,cos2x-cos3x/x^2的极限给力吧!
答
cos2x - cos3x = 2 sin(5x/2) sin(x/2)原式= lim(x->0) 2 sin(5x/2) sin(x/2) / x² 等价无穷小代换 sin(5x/2) 5x/2 sin(x/2) x/2= lim(x->0) 2 (5x/2) (x/2) / x²= 5/2