Infinite Limits and Limits at Infinity

① This applet dynamically demonstrates the behavior of a function as the input approaches a specific point or infinity, showing outputs that tend to infinity or to finite values. ② Core mathematical concepts include infinite limits, limits at infinity, vertical and horizontal asymptotes, and the divergence of functions near special points. ③ Construction details: Based on the summary, the applet uses GeoGebra commands such as Point, Polygon, and Vector, creating objects H, K, L, M, N, poly1, lines k, l, m, n, f, a, b, A, B, g, u, v, text1, c, d, e, h, i. A red dot can be dragged along the x-axis to show various inputs and outputs, with text labels indicating limit values. ④ Suitable for high school seniors or early college calculus students, this applet serves as an intuitive visual aid for understanding limits, and is also useful for teachers to illustrate the difference between unbounded behavior at a point and convergence at infinity.