Question

Difference between limit does not exist and infinity

Answer 1

exists if and only if it is equal to a number. Note that ∞ is not a number. For example limx→01x2=∞ so it doesn't exist. When a function approaches infinity, the limittechnically doesn't exist by the proper definition, that demands it work out to be a number.

Answer 2

See..if limit does not exist it because..left hand limit and right hand limit both are not equal..whereas in case of infinity..the value of a limit is infinity....and here limit is not existing because...left hand neighbourhood of the point is different value than right hand neighbourhood.
Hope u get it!