Summer Topic: Domains

Not all functions can take any number. The set of numbers that the function can accept is called a domain.  Here we review how to analyze a function to find its domain.

Some Algebra of Calculus

 Some Algebra of Calculus

Before Calculus you used Algebra to solve for x.  Now in Calculus we use Algebra to manipulate an expression to make for easy Calculus!

Volume of a Solid (Washer method) Example.

 

How to use a TI-84 to find the volume of a hollow solid (which is ofter referred to "the washer" method since our circular cross-sections will have a hole in them.  Others prefer the name "annular disk" or "ring"

SFHS students can follow this link: https://www.deltamath.com/app/assignment/15468561

Everyone can download a pdf at mathorama.com

Intro to Volumes of Revolution: Disk Method

An introduction to finding the Volume of a solid generated by rotating an area around a line. 

Everyone can download a pdf at mathorama.com

 

More definite Integrals and Area under a Curve (4.4 p 293 # 62)

 More Definite Integrals and the Area Under a Curve (4.4 p 293 # 62)

With just a little information about the area of some regions, we can use the properties of integrals to figure out 6 different things!

MVT for Integrals, 1st FTC, and 2nd FTC Proofs

MVT for Integrals, 1st FTC, and 2nd FTC Proofs 

Section 4.4 is chock full of gold.  There is a lot there, so the video lets you take it in.

Here are the Subjects by Time:

 0:00 - The MVT for integrals (Average Value Thm)  & AVERAGE VALUEs

 4:20 - An example with f(x) =6 and a curious observation

 6:24 -The First Fundamental Theorem Proof

11:16 - An Example of FTC1 

12:51 - "Net Change Theorem" version of FTC1 with a "word problem" example

15:27 -The Second Fundamental Theorem of Calculus with for examples

19:05 - The End

Related Rated Samples

 Related Rates Example Problems

Here are 7 examples of  Related Rates problems.

Using L'Hôpital's Rule on an e^x Function

Using L'Hôpital's Rule on an e^x Function

 

Inverse Functions Have Reciprocal Slopes (5.R p 400 #39)

 Inverse Functions Have Reciprocal Slopes (5.R p 400 #39)

A u-sub for arctan (5-R p. 400 #109)

 A u-sub for arctan (5-R p. 400 #109)

A Hybrid Parametric Area with d(theta) (10-R p.747 #57)

 A Hybrid Parametric Area with d(theta) (10-R p.747 #57)