Amelionation of Taylor's Formula by Using the Asymptotic Behavior of the Intermediate Point of the Mean-Value Theorem

May one obtain a more better approximate formula about f(x) if onsubstitutes the approximate valu (x)/((n+1)) for intermediate point ξ? The problem isdiscussed and the error caused by using the approximate formula proves to be superior to that caused by using the homogeneous Taylor's polynomial and an expression is proved to be similatr to the remainder in Taylor's formula. Also asymptotic behavior of intermediate point of the error is studied and proved and, and the result is extended to Taylor's formula of a function of several variabls.