Continuity of a Function

We now turn to the idea of continuity — a concept that captures, in precise mathematical language, the intuitive notion of a function whose graph can be drawn without lifting the pen. A function is continuous at a point if its value there matches the limit of its values as we approach that point. This simple condition, $\lim_{x \to a} f(x) = f(a)$, ties together everything we have learned about limits and la …