Limit of a Constant Function at a Cluster Point

This example uses an interactive graph to illustrate how a constant function behaves around a cluster point: as the input approaches the accumulation point, the function values stay equal to the same constant. It is designed to build intuition for the formal definition of limits in a neighborhood of a cluster point. The key mathematical concepts include the limit of a function, one-sided limit behavior (via LimitBelow/Limit), and the graphical meaning that a constant function’s limit equals its constant value. Construction-wise, the applet creates geometric primitives such as points and segments (Point, Segment), introduces the relevant neighborhood/approach point (ClusterPoint), and computes/labels the limiting value using Limit and LimitBelow (including objects like leftlimit and Limit). Visual/text objects (texto1–texto3) and supporting function/trace objects (e.g., g, h, and related points) are used to display the approach direction and confirm the constant limit. Suitable for calculus lessons and for students learning the first intuition of limits from function graphs.