limx趋向于0,(1/sinx-1/x)=?

用泰勒公式吧sinx在x=0展开
sinx=x-x^3/3!+x^5/5!-...(-1)^(k-1)*x^(2k-1)/(2k-1)!+...
则sinx~x
所以原式=lim(x-sinx)/xsinx
=lim[x^3/3!-x^5/5!+...(-1)^k*x^(2k-1)/(2k-1)!+...]/x*x
=lim[x/3!-x^3/5!+...(-1)^k*x^(2k-3)/(2k-1)!+...]
=0