Mathorama

Summer Topic: Domains

noreply@blogger.com (Chris Thiel) — Wed, 12 Jul 2023 14:24:00 +0000

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

noreply@blogger.com (Chris Thiel) — Fri, 05 Aug 2022 16:55:00 +0000

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.

noreply@blogger.com (Chris Thiel) — Sat, 19 Feb 2022 19:40:00 +0000

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

noreply@blogger.com (Chris Thiel) — Sat, 19 Feb 2022 17:38:00 +0000

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)

noreply@blogger.com (Chris Thiel) — Thu, 02 Dec 2021 19:40:00 +0000

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

noreply@blogger.com (Chris Thiel) — Fri, 26 Nov 2021 21:46:00 +0000

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

noreply@blogger.com (Chris Thiel) — Sun, 17 Oct 2021 17:41:00 +0000

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

noreply@blogger.com (Chris Thiel) — Thu, 04 Feb 2021 03:01:00 +0000

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

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

noreply@blogger.com (Chris Thiel) — Thu, 04 Feb 2021 01:27:00 +0000

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

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

noreply@blogger.com (Chris Thiel) — Thu, 04 Feb 2021 00:06:00 +0000

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

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

noreply@blogger.com (Chris Thiel) — Wed, 03 Feb 2021 22:40:00 +0000

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

Elliptical Orbit in a Polar Form (10.6 p745 #59)

noreply@blogger.com (Chris Thiel) — Tue, 02 Feb 2021 05:16:00 +0000

Elliptical Orbit in a Polar Form (10.6 p745 #59)

Not only do we answer the question at hand, we derive the polar form of a conic section.

If you want to skip ahead:

Minute 5:45 Finding the distance between the surface of Earth and Explorer 18 when the angle is 60 degrees

Minute 12:53 Proof that e = c/a = 2c/2a=(distance between focii/major axis)

Definite Integral with arcsine (5.8 p387 #33)

noreply@blogger.com (Chris Thiel) — Tue, 02 Feb 2021 04:56:00 +0000

Definite Integral with arcsine (5.8 p387 #33)

Finding a Tangent Line Implicitly on a function with e^x (5.4 p348 #65)

noreply@blogger.com (Chris Thiel) — Tue, 02 Feb 2021 04:42:00 +0000

Finding a Tangent Line Implicitly on a function with e^x (5.4 p348 #65)

Implicit Differentiation with e^x (5.4 p 348 #63)

noreply@blogger.com (Chris Thiel) — Mon, 01 Feb 2021 18:00:00 +0000

Implicit Differentiation with e^x (5.4 p 348 #63)

Verifying a Differential Equation involoving e^x (5.4 p349 #69)

noreply@blogger.com (Chris Thiel) — Mon, 01 Feb 2021 17:44:00 +0000

Verifying a Differential Equation involoving e^x (5.4 p349 #69)

A Bounded Area (def Int) with log base 4 (5.5 p359 #81)

noreply@blogger.com (Chris Thiel) — Mon, 01 Feb 2021 03:03:00 +0000

A Bounded Area (def Int) with log base 4 (5.5 p359 #81)

This one has u substitution a a conversion from base 4 to bas e, confirming with the TI-84

An Indefinite Integral with Exponents (5.5 p 359 #76)

noreply@blogger.com (Chris Thiel) — Mon, 01 Feb 2021 00:08:00 +0000

An Indefinite Integral with Exponents (5.5 p 359 #76)

This includes u-substitution, and an exponential function in base 2

Derivative of a Log in base 2 (5.5 p358 #55)

noreply@blogger.com (Chris Thiel) — Sun, 31 Jan 2021 23:53:00 +0000

Derivative of a Log in base 2 (5.5 p358 #55)

Proving an old Compounded Interest Formula with L'Hôpital's Rule (5.6 p371 #90)

noreply@blogger.com (Chris Thiel) — Sun, 31 Jan 2021 23:40:00 +0000

Proving an old Compounded Interest Formula with L'Hôpital's Rule (5.6 p371 #90)

We demonstrate the ln technique as well as makeing a product into a ratio so you can use L'Hôpital's Rule.

Implicit Diff with arctan (5.7 p 380 #71)

noreply@blogger.com (Chris Thiel) — Sun, 31 Jan 2021 22:49:00 +0000

Implicit Diff with arctan (5.7 p 380 #71)

Here we find a tangent line of a function using implicit differentiation, the product rule, the chain rule, and some careful algebra.

Derivatives of Inverse Functions on the TI-84 (5.3 p 340 #71)

noreply@blogger.com (Chris Thiel) — Sun, 31 Jan 2021 22:01:00 +0000

Derivatives of Inverse Functions on the TI-84 (5.3 p 340 #71)

The Derivative of an Inverse Function (5.3 p340 #67)

noreply@blogger.com (Chris Thiel) — Sun, 31 Jan 2021 21:38:00 +0000

The Derivative of an Inverse Function (5.3 p340 #67)

The derivative of a inverse function is the reciprocal of the derivative of the inverse function. Be mindful of the exchange of values (x,y) to (y,x) with inverse functions

Intersections of Polar Curves (10.5 p 735 #29)

noreply@blogger.com (Chris Thiel) — Sun, 31 Jan 2021 21:17:00 +0000

Intersections of Polar Curves (10.5 p 735 #29)

Limiting the Domain of a Absolute Value Function so it would have an inverse (5.3 p340 #57)

noreply@blogger.com (Chris Thiel) — Mon, 25 Jan 2021 03:33:00 +0000

Limiting the Domain of a Absolute Value Function so it would have an inverse (5.3 p340 #57)