 ### AP数学极限常用运算公式

Oct 09, 2013  From：Original  Author：吴老师
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。

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.

1. 2.If And ，Then 3.If And ，Then 4.If And ，Then (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 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.

Rule No.1: (x is in radians,not degrees)

Rule No.2: Rule No.3: Rule No.4: 