Conclusion: The Arc of Rigor

From Zeno's paradoxes to Weierstrass's epsilon-delta—you have traversed the intellectual journey of calculus.

What You've Learned

2.1
Tangent Lines & Rates
Limit of the difference quotient
2.2
Limit Definition
Rule of Three: Numerical, Graphical, Algebraic
2.3
One-Sided Limits
Left/right limits must agree for existence
2.4
Computing Limits
Factoring, conjugates, Squeeze Theorem
2.5
Limits at Infinity
Horizontal asymptotes, degree dominance
2.6
Continuity
IVT and taxonomy of discontinuities
2.7
Epsilon-Delta
The rigorous foundation of limits
The Narrative Structure

This unit moved you through the full intellectual arc of calculus:

  1. 1.Concrete problems of tangents and velocity
  2. 2.Procedural toolkit of algebraic limits
  3. 3.Profound implications of continuity and infinite behavior
  4. 4.Rigorous foundation of the epsilon-delta definition
Final Pedagogical Insight

Frame your understanding as a historical narrative:

  • • Start with Zeno's paradoxes to create the "need" for limits
  • • Use Newton and Leibniz to show the power of the tool
  • • Use Berkeley's "ghosts" to show the logical holes
  • • Use Cauchy and Weierstrass (Epsilon-Delta) to provide the resolution

This narrative structure turns abstract mathematics into an intellectual drama, significantly improving conceptual retention.

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