![]() Topic 21.: Proper notation and multiple-representations of limits. Topic 1.1: Suggests an introduction to calculus to give students a hint of what’s coming. See Getting Started #2) Topics 1.1 – 1.9: Limits (As a general technique, rather than starting the year with a week or three of review – which the students need but will immediately forget again – be ready to review topics as they come up during the year as they are needed – you will have to do that anyway. As you go through this unit, you may want to quickly review these terms and concepts as they come up. They should know the names of the types of discontinuities – jump, removable, infinite, etc. Students should have plenty of experience in their math courses before calculus with functions that are and are not continuous. Only later was it pulled out as a separate concept and then returned to the definition of continuity as a previously defined term. But their formulation did not use the word “limit”, rather the use was part of their definition of continuity. It was in the early 1800’s that the epsilon-delta definition of limit was first given by Bolzano (whose work was overlooked) and then by Cauchy and Weierstrass. Newton and Leibnitz did not have the concept of limit the way we use it today. Practically and historically, continuity comes first. Logically, limits come before continuity since limit is used to define continuity. ![]() These topics account for about 10 – 12% of questions on the AB exam and 4 – 7% of the BC questions. ![]() Unit 1 contains topics on Limits and Continuity. This is the first of a series of blog posts that I plan to write over the next few months, staying a little ahead of where you are so you can use anything you find useful in your planning.
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