Mathematics: Analysis and Approaches · Topic 5: Calculus

AHL5.12 — Limits and differentiation from first principles

Mathematics: Analysis and Approaches · SL / HL · syllabus-mapped notes

1. Continuity and differentiability

   Informal understanding of continuity and differentiability of a function at a point.

2. Limits: convergence and divergence

   Understanding of limits, and convergence versus divergence (polynomials only).

3. Derivative from first principles

   The formal definition of the derivative as a limit.

4. Higher derivatives and notation

   Second and higher derivatives, and the standard notations.