Having now finished all of our technical preliminaries (that is, proofs of the needed facts about the real numbers, limits and continuity), we are finally ready for what this text is really about, which is an advanced look at the core material taught in a singlevariable calculus course. It has taken us this long to get to material from calculus because limits are at the heart of what makes calculus work, even in theorems that do not explicitly mention limits, and to make limits work, we needed the properties of the real numbers.
KeywordsOpen Interval Product Rule Tangent Line Chain Rule Global Maximum
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