limx->0 (1/x-1/(cosx-1))

limx->0 (1/x-1/(cosx-1))
limx->0 (1/x-1/(cosx-1))

limx->0 (1/x-1/(cosx-1))
x->0lim[ (1/x)-1/(cosx-1)]
原式=x→0lim[(cosx-x-1)/x(cosx-1)]=x→0lim[(-sinx-1)/(cosx-1-xsinx)]=-∞

解法一：lim(x->0)[(1-cosx)/x ]=lim(x->0)[2sin (x/2)/x ] (应用半角公式) =lim(x->0)[(1/2)sin (x/2)/(x/2) ] =(1/2)*