We proved the intermediate value theorem for continuous function at closed interval by constructing auxiliary sequence ingeniously and applying compact theorem as well as Cauchy convergence criterion.
通过巧妙地构造辅助数列，应用致密性定理、柯西收敛准则来证明闭区间上连续函数的介值性定理。
The continuity and derivative of the intermediate point in the Taylor mean value theorem are discussed, and some of their sufficient conditions are presented.
讨论泰勒中值定理中中值点的连续性及可导性问题，给出泰勒中值定理中中值点连续及可导的充分条件，同时给出计算其导数的公式。
This paper is devoted to studying the asymptotic behavior of the intermediate point in the mean value theorem for first form curve integrals. A general result is obtained.
讨论了第一类曲线积分中值定理“中间点”的渐近性质，得到了更具一般性的新结果。
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