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Calculus I (Notes) / Extras   [Notes]
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 Extras

In this chapter material that didn’t fit into other sections for a variety of reasons.  Also, in order to not obscure the mechanics of actually working problems, most of the proofs of various facts and formulas are in this chapter as opposed to being in the section with the fact/formula.

 

This chapter contains those topics.

 

Proof of Various Limit Properties  In this section we prove several of the limit properties and facts that were given in various sections of the Limits chapter.

 

Proof of Various Derivative Facts/Formulas/Properties  In this section we give the proof for several of the rules/formulas/properties of derivatives that we saw in Derivatives Chapter.  Included are multiple proofs of the Power Rule, Product Rule, Quotient Rule and Chain Rule.

 

Proof of Trig Limits  Here we give proofs for the two limits that are needed to find the derivative of the sine and cosine functions.

 

Proofs of Derivative Applications Facts/Formulas  We’ll give proofs of many of the facts that we saw in the Applications of Derivatives chapter.

 

Proof of Various Integral Facts/Formulas/Properties  Here we will give the proofs of some of the facts and formulas from the Integral Chapter as well as a couple from the Applications of Integrals chapter.

 

Area and Volume Formulas  Here is the derivation of the formulas for finding area between two curves and finding the volume of a solid of revolution.

 

Types of Infinity  This is a discussion on the types of infinity and how these affect certain limits.

 

Summation Notation  Here is a quick review of summation notation.

 

Constant of Integration  This is a discussion on a couple of subtleties involving constants of integration that many students don’t think about.

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