AP数学极限常用运算公式
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.
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.If
And
，Then
3.If And，Then
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.If And，Then
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 
，the limit，technically，does not exist
(3) If k is a positive constant,then 
、
，and 
does not exist.
(4) If k is a positive constant, then 
、
，and 
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 
，and
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:
(x is in radians,not degrees)
Rule No.2:
Rule No.3:
Rule No.4:
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！
