How do you know a limit does not exist? In short, the limit does not exist if there is a lack of continuity in the neighbourhood about the value of interest. Recall that there doesn't need to be continuity at the value of interest, just the neighbourhood is required.
To determine if the limit of 5S ( 5e ) at 5e = 5N exists, we check three things:
1
if the left limit of 5S ( 5e ) at 5e = 5N exists,
2
if the right limit of 5S ( 5e ) at 5e = 5N exists,
3
if these two limits are equal.
