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
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.