Calculus I · Limits and Continuity · review
Finite Limits Review
Review Finite Limits Review with a concise concept summary, common errors, and links to targeted practice.
Where this chapter fits
Chapter 3: Trigonometric limits
Use squeezing, the fundamental sine limit, identities, and scaling to make trigonometric behavior predictable.
Reading lens: Can the expression be rewritten around a known small-angle limit, with every scaling factor accounted for? Keep that question in view while reading Finite Limits Review; the worked mathematics is evidence for the idea, not a substitute for it.
This page connects Finite Limit Decision Tree to The Squeeze Theorem. Read the explanation first, predict each example’s next move, and only then compare the written solution.
Chapter 2 Summary
• Direct substitution is the correct first move, not an unsophisticated shortcut. • A legal real substitution result usually finishes the problem. • is indeterminate; it tells you to transform the expression. • Factor polynomial forms, rationalize radicals, combine complex fractions, and use one-sided rules for absolute values. • Cancellation is legal in a limit when it is performed for nearby non-target inputs where the cancelled factor is nonzero.
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.