AP Calc: Graphical Limits (Geometric Intuition for Limits)

This GeoGebra applet demonstrates limits graphically by showing how a function’s behavior approaches a target value as the input moves closer to a particular point. It builds intuition for the limit concept using geometric constructions rather than only symbolic computation. The core ideas are limit as a “trending value” (based on approach), the local behavior of a function near special points, and how inequalities/constraints can be visualized alongside the graph. Construction-wise, it uses the GeoGebra commands Point and Vector to define key points (A, B, C, D) and direction/placement vectors (u, v), along with a function object f to represent the function whose limit is being studied. Additional derived points (C_1, B_1, B_2, B_3, B_4) capture intermediate or approaching positions, while text1 labels and contextualizes the plotted scenario. Suitable for AP Calculus and early undergraduate calculus courses as a classroom demonstration or self-study tool for understanding limits visually.