求lim(x->1)[(3x-3)tan((π/2)x]

题目

求lim(x->1)[(3x-3)tan((π/2)x]

答案

lim(x->1)[(3x-3)tan((π/2)x]
=lim(x->1)[(3x-3)/cot((π/2)x]
分子分母求导数
3/[-1/sin²((π/2)x）* (π/2）]
=-3/[(π/2)/sin²((π/2)x]
=-3/(π/2)
=-6/π