## Wednesday, February 3, 2021

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

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

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

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

## 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)

### 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

### 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

## Sunday, January 24, 2021

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

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

### Inverse Functions (5.3 p 340 #53)

Inverse Functions (5.3 p 340 #53)

We have more than just the horizontal line test now, if a function is strictly monotonic, it will have an inverse.

### Celsius/Fahrenheit Inverse Functions (5/3 p 340 #50)

Celsius/Fahrenheit Inverse Functions (5/3 p 340 #50)

### The Area of a Region That Involves a Secant Function (5.2 p331 #71)

The Area of a Region That Involves a Secant Function (5.2 p331 #71)

## Saturday, January 23, 2021

### Another Definite Integral without u-Substitution (5.2 p 331 #65)

Another Definite Integral without u-Substitution (5.2 p 331 #65)

### A Definite Integral Requiring u-Substitution (5.2 p 330 #51)

A Definite Integral Requiring u-Substitution (5.2 p 330 #51)

## Wednesday, January 20, 2021

### Another Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)

Another  Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)

### Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)

Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)

A slope field and a diffyQ checked with the TI-84

### A u-Sub Involving Natural Log ln x (5-2 p330 #49)

A u-Sub Involving Natural Log ln x (5-2 p330 #49)

## Tuesday, January 19, 2021

### Long Division AND u-Substitution help this Integral (5-2 p330 #21)

Long Division AND u-Substitution help this Integral (5-2 p330 #21)

### Long Division Before Integrating (5-2 p330 #17)

Long Division Before Integrating (5-2 p330 #17)

This one looks like a difficult u-sub, but turns out to be easy after long division!

### Differentiating Using Logarithms Instead of the Quotient Rule (5-1 p322 #79)

Differentiating Using Logarithms  Instead of the Quotient Rule (5-1 p322 #79)

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

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