Question

高数 定积分 求详解啊 如图

Answer 1

由罗比达法则：
=lim2xsinx^4/(-x)(ln(1+x^2))^2
=-2limx^4/(x^4+o(x^4)) (ln(1+x^2)=x^2+o(x^3), (ln(1+x^2))^2=x^4+o(x^4))
=-2

Answer 2

原式=lim(x->0)2xsinx^4/[-xln²(1+x²)]
=-2lim(x->0)sinx^4/[ln²(1+x²)]
=-2lim(x->0)x^4/[(x^4)]
=-2