求lim(x趋向于0)1/(x^3)∫(上限为x下限为0)sin(t^2)dt

题目

求lim(x趋向于0)1/(x^3)∫(上限为x下限为0)sin(t^2)dt

答案

用洛比达法则,得
=lim sin(x^2) / (3x^2)
=lim (x^2) / (3x^2) 【等价无穷小代换】
= 1/3