When the limit of function Doesnot exist and when is it infinity or -infinity

Here we need to use 3+. which means x is little more than 3. Example 3.000001 or 3.001 or 3.02 or a number close to 3 but little larger than 3

Therefore, if we plug in x= 3.000001 in the function, we get 

and if we keep reducing the value of x but ensuring it is still larger than 3, we can observe that the final answer keeps increasing and getting really large or 

Examples of such values of x are:3.000000000000000000005 or 3.0000000000000000000001

You can plug in the above values and verify the result to be really large.

and hence the

Case2:

Here it is 3-, which means x is close to 3 but little less than 3

Try to think of such numbers!

Anyways, Examples of x are 2.99999 or 2.99998 and infinitely more.

Lets plug in one of such values of x in the expression which is close to 3 but less than 3,

Usin x=2.99999 in the expression

and if we keep increasing the value of x but ensuring it is still less than 3, we can observe that the final answer keeps decreasing and getting really small or

Examples of such numbers are x=2.9999999999999999 or 2.9999999999999999998765

You can plug in the above values and verify the result to be really small.

and hence 

Now the final question

what is the value of 

The conditions for limit to exist for a function at x=a

where a=3 in the above case is

1. 

2. 

3.  The value of #1 = #2

Since the conditions #1 is not met as

 and hence we need not verify #2 and #3.

Hence