x->0
分子
xsinx = x^2 +o(x^2)
(1+xsinx)^(1/3)
=(1+x^2+o(x^2))^(1/3)
=1 +(1/3)x^2 +o(x^2)
(1+xsinx)^(1/3) -1 =(1/3)x^2 +o(x^2)
分母
cosx = 1-(1/2)x^2 +o(x^2)
lncosx = -(1/2)x^2 +o(x^2)
//
lim(x->0) [(1+xsinx)^(1/3) -1]/lncosx
=lim(x->0) (1/3)x^2/[-(1/2)x^2]
=-2/3