Calculus I · Limits and Continuity · reference
Finite Limit Decision Tree
Use this Finite Limit Decision Tree reference to choose methods, review notation, and solve Calculus I limits and continuity problems.
Where this chapter fits
Chapter 2: Finite limits and algebra
Turn indeterminate forms into solvable expressions using substitution, limit laws, factoring, conjugates, and piecewise reasoning.
Reading lens: What did direct substitution reveal, and which algebraic move removes the obstacle without changing nearby behavior? Keep that question in view while reading Finite Limit Decision Tree; the worked mathematics is evidence for the idea, not a substitute for it.
This page connects Limits With Absolute Values and Piecewise Functions to The Squeeze Theorem. Read the explanation first, predict each example’s next move, and only then compare the written solution.
The Finite-Limit Decision Tree
A Repeatable Homework Procedure
For a finite target :
• Substitute . • If you get a real number, stop. • If you get , inspect the expression:
• factor polynomial expressions; • rationalize radical differences; • combine complex fractions; • split absolute values or piecewise functions into one-sided cases; • save trig limits for Chapter 3.
• Simplify only for nearby values where the original expression is defined. • Substitute again. • State why the method is valid, especially if one-sided limits are involved.
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.