2.5 The Precise Definition of a Limit

OpenStax Calculus Volume 1 — Section 2.5

Learning Objectives

  • State the epsilon-delta definition: \(\forall \varepsilon > 0, \exists \delta > 0\) such that \(0 < |x - a| < \delta \implies |f(x) - L| < \varepsilon\)

  • Prove simple limits rigorously using epsilon-delta (linear functions)

  • Prove limits of quadratic and rational functions using epsilon-delta

  • Understand why this rigorous foundation matters for all subsequent theorems

Key Concepts

To be filled during study.

Practice Problems

To be completed with textbook exercises.

Section Summary

To be written after completing the section.

Study Notes

Personal observations and connections to engineering work.