lim趋于0((tanx-x)/(x-sinx))^(cotx-1/x)

底数和指数分开求：
底数：
lim tanx-x / x-sinx (0/0形式,求导)
=lim 1/cos^2(x)-1 / 1-cosx (0/0形式,再求导)
=lim 2sinx/cos^3(x) / sinx = 2/sinx * sinx/cos^3(x) = 2/cos^3(x) = 2
指数：
lim cotx-1/x = lim (xcosx - sinx)/(xsinx) (0/0形式,求导)
=lim (cosx - xsinx - cosx)/(sinx + xcosx) (0/0)
=lim -(sinx + xcosx)/(2cosx - xsinx) = 0/2 = 0
所以lim=2^0=1

底数和指数分开求：

底数：
lim tanx-x / x-sinx (0/0形式,求导)

=lim 1/cos^2(x)-1 / 1-cosx (0/0形式，再求导)

=lim 2sinx/cos^3(x) / sinx = 2/sinx * sinx/cos^3(x) = 2/cos^3(x) = 2