Unit: Limits & Continuity (AP Calc AB Unit 1)
Topics: Limits, Convergence, Continuity, Intermediate Value Theorem & Squeeze Theorem
In this worksheet, students trace the historical development of calculus through Augustin-Louis Cauchy’s original definitions from his 1821 Cours d’analyse, connecting his original language in the book to more modern definitions. They compute terms of sequences to explore convergence, use the Squeeze Theorem to evaluate limits of bounded functions, classify jump and infinite discontinuities in piecewise functions using Cauchy’s definitions, and apply the Intermediate Value Theorem to guarantee the existence of roots.