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📘 Limits

The foundation for everything that follows: continuity, derivatives, integrals. Build the limit before you build the things that use it.

Topics

📋 Introduction (Pretest)

Diagnostic: 15 problems covering the whole limits unit. Find your sharpest places first.

15 problems

📈 Graphical Limits

Reading limits off a graph — limits at infinity, asymptotes, and the "top wins / bottom wins" pattern.

2 problems

➗ Algebraic Limits

Computing limits symbolically — direct substitution, factoring, conjugates, rationalizing.

Coming when we start

🔗 Continuity

Three-condition continuity test, removable / jump / infinite discontinuities, IVT.

Coming when we start

∆ Difference Quotient

The 5-step dance: write the difference quotient, expand, subtract, factor, take the limit. The bridge from secant slopes to tangent slopes.

5 problems

🎯 Limit Definition of the Derivative

Name the thing we just derived: the limit of the difference quotient is the derivative. Formal definition, alt forms, worked examples.

In progress

✅ Conclusion (Posttest)

End-of-module assessment — covers all 7 topics. The "you finished Limits" gate.

Coming when we start
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