Question

求极限：x→0 lim sin(x^3)/(sinx)^3 麻烦写下步骤谢谢。

Answer 1

x→0 sin(x^3) ~ x^3, (sinx)^3 ~ x^3
等价无穷小代换
原式 = lim (x→0) x^3 / x^3 = 1

Answer 2

lim sin(x^3)/(sinx)^3
=lim[ sin(x^3)*x^3/x^3]/(sinx*x/x)^3
=limx^3/x^3
=1