Visualizing Limits: Left and Right Limits with Function Graphs

① This example dynamically demonstrates the concept of left-hand and right-hand limits at a point, visually showing how function values approach a target as the independent variable tends to that point. ② Core mathematical concepts include limits (LHL and RHL), continuity, trigonometric functions, hyperbolas, and 2D vectors in geometric constructions. ③ Construction details: Uses GeoGebra commands OrthogonalLine, Intersect, and Segment to build auxiliary lines, with LaTeX text objects (text1, text2, text3) labeling limit values; objects include functions f and h, points A, B, C, D, E, F, lines g, i, j, k, segment l, and point p, where the positions of LHL and RHL points illustrate the limiting behavior. ④ Suitable for high school to early college students, this serves as an interactive tool for grasping the intuitive definition of limits, distinguishing left vs. right limits, and analyzing discontinuities, ideal for introductory calculus instruction.