拉格朗日中值定理中参数θ的估计

Estimation of the Parameters in Lagrange′s Therom

拉格朗日中值定理告诉我们 ,若函数f(x)在x =x0 的某δ邻域Uδ(x0 )内有连续的导数 ,那么当h满足x0 ±h∈Uδ(x0 )时 ,有f(x0 +h) =f(x0 ) +f′(x0 +θh)·h,其中 0 <θ<1 本文就f(x)在x0 附近的特点 ,得到当h→

The Lagrange′s therom tells us,if the function f(x) is continuously differentiable in U δ(x 0) for a certain δ>0,and when x 0±h belongs to U δ(x 0),we then have the equation f(x 0+h)=f(x 0)+f′(x 0+θh)h which θ satisfies 0<θ<1.In this paper,I get the limit value of θ when h comes to zero according to the higher derivative of the function f(x) at x 0.This conclusion can be used in the calculation of approximate value.