Calculus I · Limits and Continuity · review
Continuity and IVT Review
Review Continuity and IVT Review with a concise concept summary, common errors, and links to targeted practice.
Where this chapter fits
Chapter 6: Formal limits
Translate the intuitive neighborhood picture into epsilon-delta language, constructive proofs, graph windows, and counterexamples.
Reading lens: How small must the input window be to force every allowed output into the requested tolerance band? Keep that question in view while reading Continuity and IVT Review; the worked mathematics is evidence for the idea, not a substitute for it.
This page connects Bisection Method After the IVT to Epsilon-Delta Definition: An Introduction. Read the explanation first, predict each example’s next move, and only then compare the written solution.
Chapter 5 Summary
• Continuity at requires a defined value, an existing limit, and equality between them. • At endpoints, use the one-sided limit from inside the interval. • Removable discontinuities can be repaired with one value; jumps and asymptotes cannot. • For piecewise continuity, set the left and right expressions equal at the join. • The Intermediate Value Theorem guarantees an attained value, not its exact location or uniqueness. • Bisection refines an IVT interval into a numerical approximation.
Source & rights
Original instruction with traceable references.
The exposition is original. No Active Calculus exercise is reproduced verbatim. Public-domain examples were modernized and recomposed when used as inspiration.
The verified handoff declares original composition and requires owner provenance review. BetterGrades-original material remains separate from public-domain references; no source textbook PDF is published here.