Limits Example 1: A Two-Sided Approach

①This example dynamically illustrates the fundamental condition for a function limit to exist at a point: the left-hand limit and right-hand limit must be equal, emphasizing that 'it takes two sides to have a limit'. ②Core mathematical concepts include the two-sided definition of a limit, one-sided limits, and the visualization of discontinuities or piecewise behavior. ③Construction highlights: using GeoGebra commands Point and Segment, the construction involves objects such as function f, points C, D, E, and texts text1 and text2, with a slider t controlling the approach; segments c, d, e and points F, a, b help depict the left and right approaching paths. ④This resource is suitable for high school seniors or early university students learning calculus, serving as an interactive demonstration for teachers or a self-exploration tool for students to grasp the rigorous concept of limits.