Expii

Example of the Substitution Rule for Limits - Expii

Intuitively, the limit describes the behavior of a function as we approach a certain point from both sides. If the function is defined at the point we choose (and the function doesn't oscillate wildly or anything), then the function approaches the limit and happens to equal it at the point at which the limit is taken. This intuition can be made more precise using the substitution description of continuity.