VISUALIZING CALCULUS: INFINITESIMALS VS. LIMITS

THE INFINITESIMAL APPROACH

Under a hyperreal microscope, the curve becomes perfectly straight.
dx and dy are non-zero, concrete numbers forming a fraction.

THE LIMIT APPROACH

Evaluating the secant line as h approaches 0.
The limit is a process, and dy/dx is treated as notation, not a fraction.

©2026 Chris Athanas

Link to source code:

https://github.com/realityexpander/Calculus_Infinitesimals_vs_Limit/