Limits - Chapter Revision Points

Sections in the Chapter

20.1 Informal approach to limit
20.2 Formal approach to limit
20.3 Evaluation of left hand and right hand limits
20.4 Difference between the value of a function at a point and the limit at a point
20.5 The algebra of limits
20.6 Evaluation of limits




We can approach a given number ‘a’ on the real line from its left hand side by increasing numbers which are less than ‘a’. It means starting from a- δ and increasing to reach a.

We can also approach a given number ‘a’ on the real line from its right hand side by decreasing numbers which are greater than ‘a’. It means starting from a+δ and decreasing to reach a.

Hence there are two types of limits – left hand limit and right hand limit.

For some functions both these limits are equal at a point and for some functions they are not equal.

If both are equal we say lim (x→a) f(x) exists. Otherwise it does not exist.


Updated 17 Jan 2016, 2 Dec 2008