Epsilon-Delta Visualization of Finite Limit and Continuity

This GeoGebra example provides an interactive visualization of the epsilon-delta definition of a finite limit and continuity of a function. It demonstrates that for any given positive epsilon, there exists a positive delta such that if the distance between x and the target point x_A is less than delta, then the distance between f(x) and the limit value is less than epsilon. The core concepts include the rigorous definition of limits, continuity, neighborhoods, and the epsilon-delta logic. The construction uses GeoGebra commands such as Point to create key points A, B, C, OrthogonalLine to draw perpendicular lines representing the epsilon and delta bands, and Intersect to find intersection points. Objects like epsilon, g, h, x_A, i, f, A, j, y_A, B, C, delta, eq1, eq2 are defined, allowing users to adjust epsilon and delta via sliders or inputs and observe how the function graph relates to the bands. This is suitable for university-level calculus or advanced high school mathematics, helping students grasp the formal definition of limits and continuity through dynamic exploration.