矢性函数的拉格朗日微分中值研究

Research on Specific Property of Vector Function Mean Value

一元数量函数的拉格朗日中值定理在微积分中具有重要的地位,正因为如此,众多学者把它推广到矢性(向量)函数中,得到了一系列结论.但是,很少有人注意到从数量函数到矢性函数拉格朗日中值定理的差异,微分中值的不统一性.经研究发现,对一般三维空间中的矢性函数A(t),微积分中的拉格朗日中值定理不再成立.但是,当是A(t)三维空间中的平面曲线时,有类似于拉格朗日中值定理的结论.最后给出空间曲线相应的结论的充要条件.

Lagrange Mean -- Value theorem of a single variable function has an important position in the calculus, and because of that, many scholars tried to generalize it into vector functions, obtaining a series of conclusions. But, very few people notice the differences from number function to the vector function of Lagrange theorem;Differential median inconsistencies. This paper points out that for the general vector functionA（t） in R3 , the Lagrange theorem is no longer valid. However, as long as A（t） is a plane curve in R3 , an analogous Lagrange theorem holds. This paper also gives a sufficient and necessary＇condition of the space curve for which the analogous Lagrange theorem holds.