The proof of the generalized cauchy mean - value theorem with method of interpolation 利用插值法证明推广的柯西中值定理
Based on the rolle mid - value theorem , by using determinant method , the lagrange mid - value theorem and cauchy mid - value theorem are obtained , and some new results are discovered 本文从罗尔中值定理出发,这用行列式理论,不仅证明了拉格朗日中值定理和柯西中值定理,还发现了一些新的结论。
Lagrange and cauchy differential mean value theorem on open interval are obtained based on generalized roll ' s theorem , which make it more expedient to study general character of function defined on open interval by means of derivative 摘要基于推广的罗尔中值定理,得到有限开区间上的拉格朗日中值定理及柯西中值定理,使得利用导数研究开区间上函数的整体性态更为方便。
柯: stalk or branch axe-handle; ...西: west中: hit; fit exactly值: price; value定理: theorem西中值定理: cauchy柯西中值: cauchy mean中值定理: intermediate value theorem; law of the mean; mean value theorem; theorem of mean第二中值定理: second mean-value theorem; secondmean-valuetheorem第一中值定理: first law of the mean; mean value theorem广义中值定理: extended theorem of mean value积分中值定理: mean value theorem of integrals泰勒中值定理: taylor's theorem微分中值定理: mean value theorem柯西的平均值定理: cauchy's mean theorem拉格朗日中值定理: mean value theorem中值定理的一个新证明: a new method of proving lagrange value theorem中值定律: law of the mean边(界)值定理: boundary value theorem边值定理: boundary value theorem初值定理: initial value theorem; initial-value theorem单值定理: monodromy theorem赋值定理: axiom of assignment介值定理: intermediate value theorem; lacation principle均值定理: mean value theorem