i think you meant and not also by "exists" you mean "being a finite number". to me if the limit is infinity, then it still exists. if the one sided limits are not equal,

then the limit doesn't exist. other cases that i'd say the limit doesn't exist, are limits like: or etc. enough about lecturing you! haha

to answer your question, we have it's clear now that the limit would be infinity unless and for the limit is -1.