lim(x->0+)(cos√x)^pi/x
问题描述:
lim(x->0+)(cos√x)^pi/x
答
=lim(x->0+)[1-﹙1-cos√x﹚]^﹛[1/﹙1-cos√x﹚][π﹙1-cos√x﹚/x]﹜
∵lim[π﹙1-cos√x﹚/x]=π/2
∴原式极限=e^﹙﹣π/2﹚