求助孩子真的看的眼花了

x->0
sinx ~ x-(1/6)x^3
sinsinx ~ [x-(1/6)x^3 ] -(1/6)[x-(1/6)x^3 ]^3 ~ x - (1/3)x^3
arctanx ~ x-(1/3)x^3
sinarctanx ~[x-(1/3)x^3] -(1/6)[x-(1/3)x^3]^3 ~ x- (1/2)x^3
sinsinx/sinarctanx
~ (x - (1/3)x^3)/[x- (1/2)x^3]
= (1 - (1/3)x^2)/[1- (1/2)x^2]
=1 + { (1/6)x^2/[1- (1/2)x^2]}
~ 1 +(1/6)x^2
lim(x->0) ( sinsinx/sinarctanx)^[1/(1-cosx)]
=lim(x->0) ( sinsinx/sinarctanx)^(2/x^2)
=lim(x->0) [1 +(1/6)x^2]^(2/x^2)
=e^(1/3)