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1)  Single side Limit of the Derivative
导数的单侧极限
1.
Single side Derivative and the Single side Limit of the Derivative are the two important concepts in calculus.
单侧导数与导数的单侧极限是微积分中两个重要概念,在求分段函数的导数,付里叶级数中都有其广泛的应用,本文讨论了这两个概念的关
2)  limits of derivatives
导数的极限
3)  limit from the left(or right)
单侧极限
1.
The relation between limit from the left(or right) and Schwarz derivative are obtained,and an inequation is built with Schwarz derivative.
研究Schwarz导数,在已有成果基础上给出了在一点单侧极限与Schwarz导数的关系,以及一定条件下,由Schwarz导数构成的不等式。
4)  unilateral derivative
单侧导数
1.
Unilateral Derivative and Its Effects on the Property of Function;
单侧导数及其对函数性态的影响
2.
The generalized Law of Mean with unilateral derivative and its asymptotic features of the “centred dot” are studied.
本文研究了单侧导数的广义中值定理及其“中间点”的渐近性质 ,进而获得了更广泛的结果。
3.
By means of the unilateral derivative being a little less than conditions,not derivative,it is dicussed that the monotonously of function is differented.
讨论了不用导数 ,而用较弱的条件单侧导数也能判别函数的单调性问
5)  one-sided derivative
单侧导数
1.
The decision methods that the function is derivable in the origin and the simple methods to find a functionl one-sided derivative are given in this paper.
给出了函数在原点可导的判定方法及求函数单侧导数的简便方法,并给出了这些方法的应用例子。
2.
It associates one-sided derivative with symmetric derivative to discuss the functional convex, whose condition is weaker than present reference.
把单侧导数与对称导数结合起来,以更弱的条件讨论函数的凸性,给出了凸函数的一个充要条件。
6)  Single Side Derivative
单侧导数
1.
Single side Derivative and the Single side Limit of the Derivative are the two important concepts in calculus.
单侧导数与导数的单侧极限是微积分中两个重要概念,在求分段函数的导数,付里叶级数中都有其广泛的应用,本文讨论了这两个概念的关
补充资料:单侧极限


单侧极限
one-sided limit

  单侧极限[姗浦山月玩血;0皿oc功poHH浦nPe床JI] 函数在一点处的左侧或右侧极限(h而t).设f是从有序集x(例如位于实直线上的集合)到拓扑空间Y中的一个映射,X看作具有给定的序关系生成的拓扑的拓扑空间,并设x。〔X.f关于任一区间(a,x。)={x:x‘X,“x。的选取).如果点x。同时是函数f定义域的左极限点和右极限点,则关于x。的去心邻域的通常极限 煞。f(x)(此时为与单侧极限相对,也称此极限为双侧极限)存在当且仅当点x。处左侧和右侧极限都存在且两者相等.几.八.Ky月p.B毋.撰[补注]也用符号恤:一,。*,腼:;、。(对应地,lim,一:。一,腼二,:。)代替腼二一:。十。(对应地,腼:一,。一。)· 沈永欢译
  
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