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) 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)