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 7, 8, 9 · 7 detailed lessons
Continuity & Asymptotic Behavior
How do continuity conditions connect local behavior, global guarantees, and model reliability?
Pathways
Lesson 01 · Week 7
Continuity at a Point and on an Interval
Continuity at an input requires an existing function value, an existing limit, and agreement between them. Continuity on an interval supports global conclusions such as the Intermediate Valu…
Lesson 02 · Week 7Classifying Discontinuities
Continuity at an input requires an existing function value, an existing limit, and agreement between them. Continuity on an interval supports global conclusions such as the Intermediate Valu…
Lesson 03 · Week 7Piecewise Functions and Continuity Conditions
Continuity at an input requires an existing function value, an existing limit, and agreement between them. Continuity on an interval supports global conclusions such as the Intermediate Valu…
Lesson 04 · Week 8The Intermediate Value Theorem
Continuity at an input requires an existing function value, an existing limit, and agreement between them. Continuity on an interval supports global conclusions such as the Intermediate Valu…
Lesson 05 · Week 8The Squeeze Theorem
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 9Continuity of Composite and Transcendental Functions
Continuity at an input requires an existing function value, an existing limit, and agreement between them. Continuity on an interval supports global conclusions such as the Intermediate Valu…
Lesson 07 · Week 9Continuity, Asymptotes & Model Reliability
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 …