Tangent as a Limit Demonstration

This example dynamically demonstrates how the secant line AB approaches its limiting position as point A gets closer to point B on the curve, visually illustrating the definition of a tangent line. It involves core mathematical concepts such as derivatives, quadratic functions, cosine, differential calculus, piecewise functions, etc. The construction uses GeoGebra commands like Line, Tangent, and objects like Δx, f, x_a, B, A, a, b, T2, T3, T5, T4, T7, c, d, T1, T6 to build the graph and animation. It is suitable for high school and above students learning calculus and analytical geometry, understanding the relationship between limits and derivatives.