x趋向于1极限(x-1)tan派x/2

问题描述:

x趋向于1极限(x-1)tan派x/2

(x-1)tanπx/2
=[(x-1)sinπx/2]/cosπx/2
=[(x-1)sinπx/2]'/(cosπx/2)'
=[sinπx/2+(x-1)cosπx/2*π/2]/[-sinπx/2*π/2]
=-2/π ,x-->1