Why would a limit not exist?

In short, the limit does not exist if there is a lack of continuity in the neighbourhood about the value of interest. … Most limits DNE when limx→a−f(x)≠limx→a+f(x) , that is, the left-side limit does not match the right-side limit. This typically occurs in piecewise or step functions (such as round, floor, and ceiling).

When a limit does not exist example?

One example is when the right and left limits are different. So in that particular point the limit doesn’t exist. You can have a limit for p approaching 100 torr from the left ( =0.8l ) or right ( 0.3l ) but not in p=100 torr. So: limp→100V= doesn’t exist.