Limits Investigation: Visualizing Function Approach

① This example dynamically demonstrates the concept of a limit by showing how a function's value approaches a target as the input nears a specific point. ② Core mathematical concepts include limits, function graphing, points, vectors, and trigonometric functions, emphasizing the intuitive idea of convergence. ③ Construction details: The GeoGebra commands LaTeX and Point are used to create key points (A, B, C, D, E, G, H), while text objects (text1 to text6) label expressions, limit values, or hints; objects f, g, h are function curves, and a, b, c serve as auxiliary segments or vectors, allowing dynamic observation of the approach. ④ Suitable for high school or introductory college calculus students, this interactive tool aids classroom demonstrations or self-study, building an intuitive foundation for limits and preparing for derivatives and continuity.