Lagrange型余项中θ极限问题的进一步研究

Further Research on θ Limit of Lagrange Remainder

利用Taylor公式对Lagrange及Taylor中值定理中Lagrange型余项的θ极限问题进行了定量研究.通过对f(x)在x=x0点的某个邻域内低阶可导情形的研究推广到n阶连续可导的情形,进而得到一般性的结论.

The quantitative research on θ limit of Lagrange remainder in Lagrange mean value theorem and Taylor mean value theorem has been carried out by using Taylor formula. The research of low-order differentiable within a neighbourhood on f （x） at x=x0 is extended to n order continuously differentiable,and then a general conclusion has been obtained.