构造辅助函数是利用微分中值定理解决问题的关键，构造辅助函数的方法较多。
Constructing auxiliary functions is the key in using differential mean value theorem to solve problems; there are many methods for constructing auxiliary functions.
第二个辅助构造函数只接受一个标签。
因为所有的辅助构造函数最终都会调用主构造函数，它主体中进行的逻辑检查和其它初始化工作会在所有实例被创建的时候执行。
Because all auxiliary constructors eventually invoke the primary constructor, logic checks and other initializations done in the body will be performed consistently for all instances created.
ButtonWithCallbacks定义了两个方便用户使用的辅助构造函数。
ButtonWithCallbacks defines two auxiliary constructors for the user's convenience.
为了避免无限递归，Scala要求每一个辅助构造函数调用在它之前定义的构造函数[ScalaSpec2009]。
In order to avoid infinite recursion, Scala requires each auxiliary constructor to invoke another constructor defined before it [ScalaSpec2009].
Traits不支持辅助构造函数，它们也不支持在主构造函数，trait的主体里的参数列表。
Traits don't support auxiliary constructors, nor do they accept an argument list for the primary constructor, the body of a trait.
Scala可以区分主构造函数和0个或多个辅助构造函数。
Scala distinguishes between a primary constructor and zero or more auxiliary constructors.
包含了用于VB语言构造的一些辅助函数的这个类库（译者注：这个类库即Microsoft.VisualBasic.dll，VB语言的很多基础功能都需要调用到这个类库），是作为.NET平台的一个基本功能共同发布的。
This library, which contains helper functions called by VB language constructs, is shipped with the baseline .NET platform.
子类的主构造函数必须调用父类的一个构造函数，无论是主构造函数或者是辅助构造函数。
The primary constructor in a derived class must invoke one of the parent class constructors, either the primary constructor or an auxiliary constructor.
被调用的构造函数可以是另外一个辅助构造函数或者主构造函数，而且它必须出现在辅助构造函数主体的第一句。
The constructor invoked may be either another auxiliary constructor or the primary constructor, and it must be the first statement in the auxiliary constructor's body.
第一个辅助构造函数接受一个标签和一个单独的回调函数。
The first auxiliary constructor accepts a label and a single callback.
在《第5章 -Scala 的基本面向对象编程》的“Scala 的构造函数”章节中，我们会看到如何定义辅助的构造函数。
We’ll see how to define auxiliary constructors in the section called “Constructors in Scala” in Chapter 5, Basic Object-Oriented Programming in Scala.
辅助函数的构造是高等数学教学中的重要内容之一，也是学生所要掌握的重要的解题方法之一。
The structure of auxiliary function is one of the important contents in the mathematics teaching, it is one of the important solution approaches that students should grasp too.
最后探讨了拉格朗日中值定理证明中辅助函数的构造方法，以此拓展对定理证明的思路。
Finally discusses the Lagrange mean value theorem proof method of constructing auxiliary function in order to expand on the idea of theorem proving.
其证明方法关键在于构造一个辅助函数，再应用罗尔中值定理推出拉格朗日中值定理的结论。
Its key proof is to construct an auxiliary function, which is used by Roll's theorem to reach a conclusion of Lagrange's theorem.
本文给出构造中值问题辅助函数的一种方法。
A method to construct auxiliary functions for intermediate value problems is given.
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。
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.
针对微分中值问题的结论的不同特征，本文归纳出了辅助函数的四种构造方法。
According to different features of conclusion about middle value questions in differential calculus, four kinds of methods about the auxiliary function structures will be concluded.
研究了复合迭代函数方程所代表的一类不变曲线的解析解，通过构造辅助方程的幂级数解，从而获得原方程的解析解。
This paper is concerned with an analytic invariant curves on a planar mapping of the iterative functional equation.
研究了复合迭代函数方程所代表的一类不变曲线的解析解，通过构造辅助方程的幂级数解，从而获得原方程的解析解。
This paper is concerned with an analytic invariant curves on a planar mapping of the iterative functional equation.
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