Intuitive Notion of Limits 1: Dynamic Approach to a Function

①This example dynamically illustrates the intuitive concept of a limit by showing how function values approach a target value as the input approaches a point, using sliders and graphs. ②Core mathematical concept: limit, including the behavior of a function near a point, neighborhoods, and the delta-epsilon idea, visualized through left and right approaches on the graph. ③Construction: Built with GeoGebra commands such as Point, Segment, Locus, and Function, creating objects like function f, moving points P and Q, limit point A, delta segment δseg, dashed lines dashLeft/dashRight, range, auxiliary shapes g, c, poly1, and text labels text1/text2; a slider controls δ to animate the approach. ④Suitable for high school seniors or early college calculus students to build intuition about limits, and useful for classroom demonstrations.