Oct 09, 2013 From:Original Author:吴老师


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.




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


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



(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


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.


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