lim(x->0)[(e^x^3-1-e^3)/(sin^6)2x]请尽量详细些.题目抄错了不好意思，正确如下：lim(x->0)[(e^(x^3)-1-x^3)/(sin^6)2x]

Question

lim(x->0)[(e^x^3-1-e^3)/(sin^6)2x] 请尽量详细些.
题目抄错了不好意思，正确如下：lim(x->0)[(e^(x^3)-1-x^3)/(sin^6)2x]

Answer 1

x->0
e^x^3-1-e^3=1-1-e^3=-e^3
(sin^6)2x=0
所以
lim(x->0)[(e^x^3-1-e^3)/(sin^6)2x]
=-e^3/0
=-∞