1/2,可以洛必达,也可以代换1-cosx~1/2x^2,sinx~x
x→0时,运用等价无穷小,
即1-cosx~x^2/2(1-cosx等价于x^2/2,在乘除中可以直接替换)
sinx~x(同理,在乘除中可以直接替换)
于是原式=(x^2/2)/(x*x)
=1/2
lim(x->0)(1-cosx)/(xsinx) (0/0)
= lim(x->0)(sinx)/(xcosx+sinx) (0/0)
= lim(x->0)(cosx)/(-xsinx+2cosx)
= 1/2