Limit of the Identity Function Near a Cluster Point

This example visualizes how the identity function’s values behave as the input approaches a cluster point. It emphasizes the idea of a limit as values get arbitrarily close to a target point, making the “approach and convergence” phenomenon easy to see. The key concepts include cluster points, (one-sided and general) limits, and an intuitive connection to continuity for simple linear functions. Construction-wise, it is built from GeoGebra primitives: Point and Segment to set up the geometric reference, and Limit / LimitBelow to compute and display the limiting behavior from the appropriate side. The function itself is represented by the object f, while additional labeled objects help present the inferred limit value. Suitable for late high school through early university calculus courses, especially for teaching limits via function graphs.