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Calculate rational and radical end behavior, retain domains and verify asymptotic lines. Prerequisites: limits at infinity, limit laws and conjugates. Learn to check each infinite direction independently.
Oct 27, 2026
Build and apply fundamental trigonometric limits using radian geometry, squeeze and identities. Prerequisites: unit-circle trigonometry and the squeeze theorem. Learn to retain scale factors and avoid circular foundations.
Oct 27, 2026
Use valid neighborhood inequalities to control oscillation and determine limits. Prerequisites: finite limit laws and nonexistence from persistent oscillation. Learn to check amplitude and inequality directions.
Oct 27, 2026
Practice sign cases, branch selection and matching one-sided limits. Prerequisites: finite limit laws and one-sided notation. Learn to distinguish nearby behavior from an assigned point value.
Oct 27, 2026
Classify removable, jump, unbounded, and bounded oscillatory failures. Decide whether a point assignment suffices or nearby branch behavior must change. Prerequisites: continuity at a point, factoring, and one-sided piecewise limits. Practice continuous extensions and parameter matching without derivative conditions.
Oct 27, 2026
Check continuity using a defined value, an appropriate finite limit, and equality. Identify intervals of continuity and use limits from inside included domain endpoints. Prerequisites: one-sided limits and direct substitution. Apply the checks to simple formulas, exact graph descriptions, and physical time intervals.
Oct 27, 2026
A retrieval checkpoint on elementary algebraic, squeeze, trigonometric, and end-behavior limit methods, with precision and quantifier interpretation. Use Chapter 02 methods and radian angles. Prerequisites: the preceding Calculating limits skills. Detailed feedback identifies invalid shortcuts and routes further practice.
Oct 27, 2026
Interpret arbitrary precision through tolerance bands, punctured neighborhoods, and the order of choices. Practice choosing valid input radii and judging measurement evidence. Prerequisites: one-sided limits and elementary limit laws. Formal proof construction is reserved for the optional proof chapter.
Oct 27, 2026
Review derivative definitions, local rates, graph evidence, differentiability, tangent and normal lines, and motion. Prerequisites: the seven derivative-meaning lessons. These twelve independent retrieval tasks introduce no differentiation shortcut rules.
Oct 27, 2026
Interpret position, velocity and acceleration on an oriented line, including units, speed and direction. Prerequisites: the derivative as a function and reading local graph slopes. Distinguish instantaneous rate data from location and travel history.
Oct 27, 2026
Construct tangent and normal lines through the correct function point, including horizontal and vertical special cases. Prerequisites: derivative meaning and elementary algebra. Verify contact, perpendicularity and the local meaning of tangency.
Oct 27, 2026
Test finite differentiability with one-sided difference quotients and distinguish corners, cusps, vertical tangents and discontinuities. Prerequisites: the derivative limit and continuity. Use an explicit endpoint convention and explain why differentiability implies continuity.
Oct 27, 2026
