Mathorama

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

 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/15468561Everyone can download a pdf at mathorama.com

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 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 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 Proof11:16 - An Example of FTC1 12:51 - "Net Change Theorem" version of FTC1 with a "word problem" example15:27 -The Second Fundamental Theorem of Calculus with for examples19:05 - The End

 Related Rates Example ProblemsHere are 7 examples of  Related Rates problems.

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

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

 A u-sub for arctan (5-R p. 400 #109)

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

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

 Definite Integral with arcsine (5.8 p387 #33)

 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)

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

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

 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)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)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)

 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)

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