Intuitive Idea of a Limit

A limit describes what value a function is approaching as the input gets close to a certain point. The key idea is that we care about nearby behavior, not necessarily what happens at the point itself. Instead of asking “What is the value here?”, limits ask “What happens as we get closer?” By examining values from both sides and looking at trends, we can predict behavior even when a function is undefined or behaves strangely at a point.