If a variable takes values which are more and more close to a finite number , then we say that approaches written as ).
- If values of come closer to but are always greater than , then we say that approaches form right ().
- If values of come closer to but are always less than , then approaches from left () .
The concept of a limit may apply to:
If , then can approach to '2' from two sides:
- From right side: In notation we write means is coming closer to '2' from right i.e. it is more than '2'.
- From left side: In notation we write mean is coming closer to 2 from left i.e. it is less than '2'.
Meaning of a limiting value
Let be function of . If the expression comes close to as approaches then we say that is the limit of as approaches .
In notation, it is written as .
Right Hand Limit
If approaches as approaches from the right, then is called as the right hand limit of .
Right hand limit can be expressed in two ways:-
Left Hand Limit
If approaches from the left, then is called the left hand limit of . The left hand limit can be expressed in two ways:-
Note that is a positive real number, that we let approach 0..
Existence of Limit
For existence of limit at
Illustrating the concept
If , then evaluate .
L.H.L. = i.e. is coming closer to 2 but it is less than '2'. So, observe the situation in table below:
|Coming closer to 2 but less than 2||Coming closer to 4 but less than 4|