Friday, August 5, 2022

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!



Saturday, February 19, 2022

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



 

Thursday, December 2, 2021

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!


Friday, November 26, 2021

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

Sunday, October 17, 2021

Related Rated Samples

 Related Rates Example Problems



Here are 7 examples of  Related Rates problems.

Monday, February 1, 2021

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

 

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)

 Definite Integral with arcsine (5.8 p387 #33)





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

 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)

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



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

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




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 m...