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*** S.Gudder

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Limits 

The notion of limit  is one of the most basic and powerful concepts in all of mathematics. Differentiation and Integration, which comprise the core of study in calculus, are both products of the limit.  The concept of limit  is the foundation stone of calculus and as such is the basis of all that follows it. It is extremely important that you get a good understanding of the notion of limit of a function if you have a desire to fully understand calculus at the entry level. 

Limit of a function at a point

 Let be a function of x. Let a and l be constants such that as, as we have. In such a case we say that the limit of function as x approaches a is l. We write this as  .

 

Some Standard Results On Limits

1.     If f(x) = k, a constant function , then

2.    

3.       

4.    

5.    

6.     , provided

7.     , provided  is a real number.

8.     If n is any real number and a is any positive real number, then,

9.     If angleis measured in radians then,

10.If angleis measured in radians then,

11.If angleis measured in radians then,

12.If angleis measured in radians then,

13.If angleis measured in radians then,

14.

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18.