Calculus I · Limits and Continuity · review
Infinite Limits and Asymptotes Review
Review Infinite Limits and Asymptotes Review with a concise concept summary, common errors, and links to targeted practice.
Where this chapter fits
Chapter 5: Continuity
Connect limits to function values, classify discontinuities, repair piecewise definitions, and use the Intermediate Value Theorem.
Reading lens: Do the limit, the function value, and the surrounding domain fit together at the point or across the interval? Keep that question in view while reading Infinite Limits and Asymptotes Review; the worked mathematics is evidence for the idea, not a substitute for it.
This page connects Complete Rational Function Asymptote Analysis to Continuity at a Point. Read the explanation first, predict each example’s next move, and only then compare the written solution.
Chapter 4 Summary
• Infinite limits describe unbounded behavior; infinity is not a real number. • Remaining denominator zeros after cancellation give vertical asymptote candidates. • Sign charts determine versus on each side. • Rational end behavior is controlled by degrees and leading coefficients. • If the degree difference is one, polynomial division may reveal a slant asymptote. • At negative infinity, never replace by ; use .
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.