AP Calculus AB and BC glossary
Limit does not exist
A limit does not exist when the function fails to approach a single finite value. There are three standard causes: the left and right limits disagree, the function grows without bound, or the function oscillates infinitely often near the point.
Writing is a description of HOW the limit fails, not a claim that it exists. On the AP exam both statements can earn credit, but only if you say the limit does not exist and then describe the unbounded behavior.
The mistake
Concluding a limit fails because the function is undefined at the point. A removable discontinuity has no function value there and a perfectly good limit; the limit never looks at the point itself.
Appears in: Unit 1: Limits and Continuity