Dominance and Limits to Infinity: Interactive Function Comparison

① This interactive GeoGebra example demonstrates how different functions (e.g., polynomials, exponentials, logarithms) behave as x approaches infinity, highlighting the concept of dominance—which function grows faster and thus determines the limit. ② Core mathematical concepts include limits at infinity, comparison of growth rates, and asymptotic dominance (exponential > power > logarithmic). ③ Construction details: The applet uses text fields (Textfield, InputBox1/2/3) for users to input custom functions f and boundary parameters a, b, c, along with sliders zoom_x and zoom_y to control the viewing window. Objects lebm and rebm likely mark left/right endpoints, enabling dynamic visualization of the function's behavior as the domain extends. ④ Suitable for high school seniors or early university calculus students to build intuition about limits and growth orders, and for teachers as a classroom demonstration tool.