Question

cosπ/2(1-x)x→0

求：limx→0,[(2/π)(cos π/2)(1-x)]/x=?
我知道了
原式=limx→0，(2/π)[cos(π/2-πx/2)]=(2/π·sinπx/2)/(πx/2)·(π/2)=1

Answer 1

limx→0 [(2/π) cos[ π/2(1-x)] / x
= limx→0 [(2/π) sin(πx /2) / x
= limu→0 sinu / u 令 u= πx /2
=1