Limits, Continuity, Differentiability
Standard limits, a routine for indeterminate forms, L'Hopital's rule with its exact conditions and a case where it is silent, the 1 to the power infinity shortcut, series expansions for limits, one-sided limits and when a limit exists, limits at infinity of rational functions, continuity and the four kinds of discontinuity, differentiability from one-sided derivatives with the standard counterexamples, fixing constants in piecewise functions, derivative rules and a solved past question on counting discontinuities.