One Special Limit (V2) – Dynamic Exploration of Logarithmic Functions and Orthoc

This GeoGebra example dynamically demonstrates a special limit problem related to logarithmic functions, while ingeniously incorporating geometric elements such as the orthocenter, creating a cross-disciplinary visualization between algebra and geometry. Core mathematical concepts include limits, logarithmic functions, optimization problems, and properties of the orthocenter, with conditional probability and hyperbolas as background extensions. In terms of construction, the summary shows the use of the Point command to create key points, defining functions f and g, along with objects p, B, i, q, A, etc. Text objects (text1, text2, text3) and buttons (button1, button2) enable interactive control, with b serving as a parameter or dynamic object. This example is suitable for high school to early university students, helping them understand the intuitive meaning of limits, asymptotic behavior of logarithmic functions, and exploring relationships between mathematical objects through dynamic geometry. It also serves as a valuable resource for teachers in classroom demonstrations or for student self-directed inquiry.