合聚咖

合聚咖

请问这个的极限是什么

admin

当x→0时分子sin(x^n)=x^n,sin(x)^m=x^m,所以limsin(x^n)/sin(x)^m=limx^(n-m)所以

n=m时,limsin(x^n)/sin(x)^m=limx^(n-m)=1

n>m时,limsin(x^n)/sin(x)^m=limx^(n-m)=0

n<m时,limsin(x^n)/sin(x)^m=limx^(n-m)=∞