Question

大哥们大哥们，小弟不会呀？

Answer 1

t->0
分子
(tant)^2 = t^2 +o(t^2)
∫(0->x^2/2) (tant)^2 dt
=∫(0->x^2/2) [t^2 +o(t^2) ] dt
=[ (1/3)t^3 +o(t^3) ]]|(0->x^2/2)
=(1/24)x^6 +o(x^6)
分母
t-sint = (1/6)t^3+o(t^3)
t^2.(t-sint) =(1/6)t^5+o(t^5)
∫(x->0) t^2.(t-sint) dt
=∫(x->0) [(1/6)t^5+o(t^5)] dt
=[(1/36)t^6+o(t^6)]|(x->0)
=-(1/36)x^6+o(x^6)
//
lim(x->0) ∫(0->x^2/2) (tant)^2 dt /∫(x->0) t^2.(t-sint) dt

=lim(x->0) (1/24)x^6 / [-(1/36)x^6]
=-3/2

Answer 2

过程与结果如图所示