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-1)]*sinn²=0
∴lim(n→∞) (n^(2/3) sinn²)/(n-1)=0
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-1)]*sinn²=0
∴lim(n→∞) (n^(2/3) sinn²)/(n-1)=0