Interactive Infinite Limits and Limits at Infinity

This GeoGebra applet dynamically demonstrates how outputs behave as inputs approach critical values or move toward positive/negative infinity, illustrating infinite limits and limits at infinity. It focuses on the core ideas of divergence to ±∞ and the interpretation of lim_{x→±∞} in an intuitive, geometric way. The construction uses GeoGebra primitives from the provided build summary: Point to define key positions (e.g., H, K, L, M, N and other auxiliary points), Polygon to build a visual geometric setup (e.g., poly1 and related polygonal elements), and Vector to encode direction and proportional relationships in the diagram (e.g., vector-like objects such as u, v and related constructs). Additional helper objects (k, l, m, n, f, a, b, A, B, g, and labels like text1 and other annotated text elements) support the visualization and interpretation of the current input-to-output behavior. Suitable for calculus instruction, especially for introducing limit concepts through interactive visualization and student exploration.