AP微积分辅导

AP数学极限常用运算公式

Oct 09, 2013 From:Original Author:吴老师
Abstract:AP数学极限常用运算公式,包含极限(limit)的四则运算法则、极限(limit)的四条判定法则、极限(limit)的四种常见运算结果(公式)和极限(limit)的四条重要公式,希望同学们可以好好参详参详。

极限(limit)是AP数学最基础的知识,今天,吴老师带领同学们回顾一下“AP数学极限常用运算公式”。大家先阅读一下以下的关于极限(limit)的说明。

In order to understand calculus,you need to know what a “limit” is.A limit is the value a function(which usually is written “f(x)” on the AP exam) approaches as the variable within that function(usually ”x”)gets nearer and nearer to a particular value. In other words, when x is very close to a certain number, what is f(x) very close to? As far as the AB test is concerned, that’s all you have to know about eavaluating limits. There is a more technical method that you BC students have to learn, but we won’t discuss it until we have to – at the end of this chapter.

极限(limit)的四则运算法则

1.极限乘常数法则

运用技巧:函数的极限和常数项相乘,不影响极限的存在性,并且常数项可以自由“游动”于函数极限的内部和外部,是极限乘以常数法则的本质特点,利用这个特性,在求解极限的时候,可以根据需要任意“凑”上需要的常数项。

2.Iff(x)在a点的极限 Andg(x)在a点的极限,Then极限的加法公式

3.Iff(x)在a点的极限 Andg(x)在a点的极限,Then极限的减法公式

运用技巧:极限的加法和减法法则的实质是函数的点极限可以被拆分成两个或者多个极限来运算,也可以把多个极限组合成一个极限来运算。这种“化整为零”或者“把部分组合成一个整体的”思路体现了数学运算的灵活。

4.Iff(x)在a点的极限 Andg(x)在a点的极限,Then极限的乘法公式

运用技巧:极限的乘法运算公式使得一个复杂的函数可以化为部分相乘的形式去计算,也使得部分相乘的极限化为整体运算成为可能。

极限(limit)的四条判定法则

(1) If the left-hand limit of a function is not equal to the right-hand limit of the function,then the limit does not exist.

(2) A limit equal to infinity is not the same as a limit that does not exist,but sometimes you will see the expression "no limit",which serves both purpose.If 无限极限,the limit,technically,does not exist

(3) If k is a positive constant,then 趋于0的左极限趋于0的右极限,and 趋于0的极限 does not exist.

(4) If k is a positive constant, then x平方趋于0的左极限x平方趋于0的右极限,and x平方趋于0的极限

极限(limit)的四种常见运算结果(公式)

1). If k and n are constants,|x|>1,and n>0,then x次幂趋于正无穷的极限,andx次幂趋于负无穷的极限

2).If the hightest power of x in a rational expression is in the numerator,then the limit as x approaches infinity is infinity.

3). If the hightest power of x in a rational expression is in the denominator,then the limit as x approaches infinity is zero.

4). If the hightest power of x in a rational expression is the same in both the numerator and denominator,then the limit as x approaches infinity is the coefficient of the hightest term in the numerator divided by the coefficient of the heightest term in the denominator.

极限(limit)的四条重要公式

Rule No.1:sinx/x趋于0的极限(x is in radians,not degrees)

Rule No.2:(cosx-1)/x趋于0的极限

Rule No.3:sinax/x趋于0的极限

Rule No.4:sinax/sinbx趋于0的极限

极限部分是AP微积分课程的基础,直接影响到入门的感觉和学习AP微积分的兴趣,所以值得注意!

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