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)




Sunday, January 31, 2021

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

 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)

 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)

 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)

 


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)

 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)

 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 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)

 Intersections of Polar Curves (10.5 p 735 #29)




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

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