求极限 Lim(n趋于无穷)(n^(2/3) sinn^2)/(n-1)如题
问题描述:
求极限 Lim(n趋于无穷)(n^(2/3) sinn^2)/(n-1)
如题
答
lim(n→∞) (n^(2/3) sinn²)/(n-1)=lim(n→∞) [n^(2/3)/(n-1)]*sinn²∵lim(n→∞) [n^(2/3)/(n-1)]=lim(n→∞) {1/[n^(1/3)-1/n^(2/3)}=0-1≤sinn²≤1,sinn²有界∴lim(n→∞) [n^(2/3)/(n...