求极限limx→0 [x^3/ln(1+x^3)]*arctan1/x

问题描述:

求极限limx→0 [x^3/ln(1+x^3)]*arctan1/x

limx→0 [x^3/ln(1+x^3)]*arctan1/x
=x^3/x^3 *π/2
=π/2
其中ln(1+x^3)=x^3 等价无穷小
arctan1/x=π/2