What is a Limit?
A limit describes the value that a function approaches as the input gets closer and closer to a particular value — without necessarily reaching it. We write: which reads "the limit of as approaches equals ".
Limits are the foundation on which all of calculus is built. They allow us to talk precisely about the behaviour of a function near a point, even if the function is undefined at that exact point.
Imagine walking towards a wall. A limit describes how close you get to the wall — it doesn't matter whether you actually touch it. The limit is about the journey, not the destination.
The limit of a function as approaches a point is not the same as the function's value at that point. We only care about what the function approaches — not what happens exactly at that point.