求当n趋向于无穷时,lim[cos(θ/n)])^n)^n=?
问题描述：
求当n趋向于无穷时,lim[cos(θ/n)])^n)^n=?
答
lim { [cos(θ/n)]^n }^n=lim [cos(θ/n)]^(n^2)=lim {1+[cos(θ/n)-1]}^(n^2)=lim {{1+[cos(θ/n)-1]}^[1/(cos(θ/n)-1) }^ {[cos(θ/n)-1]*(n^2)}∵lim {{1+[cos(θ/n)-1]}^[1/(cos(θ/n)-1)] = elim [cos(θ/n)-1...