你要知道一个等价无穷小
x->0,(1+x)^a~ax
而(2x-x^2)^(1/3)=[1-(x-1)^2]^(1/3)~(-1/3)(x-1)^2
设x-1=t
原式变为lim t->0, [ln(1+t)-sint]/[(-1/3)t^2]
=lim t->0 [t-t^2/2+o(t^2)-t+o(t^2)]/[(-1/3)t^2]
=lim t->0,[(-1/2)t^2+o(t^2)]/[(-1/3)t^2]
=3/2