求证定积分limx→0 ∫0到sinx √tanxdx/∫0到tanx √sinxdx =1？

Question

有两题，麻烦大家了

Answer 1

(3)
∫(x^2->0) tan(t^2) dt / (tanx)^6
=∫(x^2->0) tan(t^2) dt / x^6 (0/0分子分母分别求导)
=-2x.tan(x^4) / (6x^5)

=-2x.(x^4) / (6x^5)
=-1/3
(2)
lim(x->0+) ∫(0->sinx) √tant dt / ∫(0->tanx) √sint dt (0/0分子分母分别求导)
=lim(x->0+) cosx. √tan(sinx) / [(secx)^2 .√sin(tanx) ]
=lim(x->0+) √tan(sinx) / √sin(tanx)
=lim(x->0+) √x / √x
=1