Unit route
Study lessons in order, complete the pathway selected by diagnostic evidence, conduct the investigation, then demonstrate mastery. Reassessment follows correction and reflection.
Weeks 4, 5, 6 · 8 detailed lessons
Limits: Numerical, Graphical & Algebraic Reasoning
How can values near an input reveal behavior at that input—even when direct substitution fails?
Pathways
Lesson 01 · Week 4
Approaching a Value: Tables, Graphs & Language
A limit describes the output behavior produced by inputs approaching a target. The value at the target may agree with the limit, differ from it, or be undefined. Numerical, graphical, and al…
Lesson 02 · Week 4One-Sided Limits and Two-Sided Agreement
A limit describes the output behavior produced by inputs approaching a target. The value at the target may agree with the limit, differ from it, or be undefined. Numerical, graphical, and al…
Lesson 03 · Week 4Limits from Graphs with Holes and Jumps
A limit describes the output behavior produced by inputs approaching a target. The value at the target may agree with the limit, differ from it, or be undefined. Numerical, graphical, and al…
Lesson 04 · Week 5Limit Laws and Direct Substitution
A limit describes the output behavior produced by inputs approaching a target. The value at the target may agree with the limit, differ from it, or be undefined. Numerical, graphical, and al…
Lesson 05 · Week 5Indeterminate Forms and Algebraic Simplification
A limit describes the output behavior produced by inputs approaching a target. The value at the target may agree with the limit, differ from it, or be undefined. Numerical, graphical, and al…
Lesson 06 · Week 5Rationalization and Radical Limits
A limit describes the output behavior produced by inputs approaching a target. The value at the target may agree with the limit, differ from it, or be undefined. Numerical, graphical, and al…
Lesson 07 · Week 6Infinite Limits and Vertical Asymptotes
Infinite limits and limits at infinity distinguish local unbounded behavior from long-run behavior. Vertical asymptotes arise near finite inputs; horizontal or slant behavior describes what …
Lesson 08 · Week 6Limits at Infinity and End Behavior
Infinite limits and limits at infinity distinguish local unbounded behavior from long-run behavior. Vertical asymptotes arise near finite inputs; horizontal or slant behavior describes what …