What does limit does not exist mean?

Question

Cameron Alexander · Accepted Answer

For the definition, please see below.

#lim_(xrarra)f(x)# does not exist The idea is that there is no number that #f(x)# gets arbitrarily close to for #x# sufficiently close to #a#. For a function #f# defined in some open interval that contains #a#, except possibly at #a#, #lim_(xrarra)f(x)# does not exist if and only if there is no number #L# such that for every #epsilon > 0#, there is a #delta > 0# with: for all #x#, if #0 < abs(x-a) < delta#, then #abs(f(x)-L) < epsilon# equivalently for every #L# there is some #epsilon > 0# such that for every #delta > 0# there is some #x# with #0 < abs(x-a) < delta#, and #abs(f(x)-L) >= epsilon#

Evelyn Agard · Answer

undefined "Limit does not exist" means that the limit of a function does not have a finite value or does not exist at a particular point. This can occur if the function approaches different values from the left and right sides of the point, or if the function oscillates or diverges as it approaches the point.