Outline

# BC Calculus

Some activities to support class discussions.

## Table of Contents

### Chapter 1 - Limits

### Chapter 2 - The Derivative

### Chapter 3 - Derivatives of Elementary Functions

- Derivatives of Inverse Functions
- Graphing The Derivative of a Function
- Derivative of Sine & Cosine Functions (Quick Investigation)
- Derivative of a Product
- Derivative of Tangent Function (Investigation)
- Implicit Differentiation: Intro
- Implicit Differentiation (Quick Check)
- Derivative of Arcsine Function
- Derivative of Arccosine Function
- Derivative of Arctangent Function
- Derivative of Natural Log Function

### Chapter4 Applications of the Derivative

- Derivative Definition
- tangent and derivative
- Existence of Derivative
- The rate of change of a shadow
- Mean Value Theorem (Without Words)
- Critical Points
- Critical Points of a function -Example
- Critical Numbers & Critical Points of Functions (Intro)
- Maximum/Minimum Videos
- Relative Extrema Illustrator
- Extrema on a Closed Interval
- Investigating the derivative at a cusp.
- Constructing Graphs of Derivative Functions (Intuitively)
- Sketch the Derivative (Warm Up)
- Quiz: Writing Exponential Growth & Decay Functions
- Exponential Growth vs. Decay (Intro)
- Newton's Law of Cooling
- Logistic Growth Function

### Chapter 5 The Integral

### Chapters 6 Antiderivatives

### Chapters 7 & 8 - Applications of Integral

- Volume of Rotation - Disk Method Visual
- Visualizing Volumes of Rotation
- 3D volume by rotation of a function
- Parabola Around y-Axis
- Parabola Rotated Around y-Axis Wireframe
- Parabola Rotated Around x-Axis
- Parabola Rotated Around x-Axis
- Cross sections are semi-circles.
- Cross sections are squares with one side in base.
- Volume: Circ base cross section isos rt triangle hyp in base
- Volume of revolution, donut shape, cylindrical shell method.
- Cylindrical Shell Action!!! (1)
- Cylindrical Shell Action!!! (2)
- Volume by Cylindrical Shells: Illustrated
- Volume of a Solid - Washer Method
- illustration of volume as a set of nested cylinders
- Arc length: Quick Investigation
- Disc Action!!!
- Washer Action!!! (1)
- Washer Action !!! (2) - Calculus
- V. of Solid NOT of Revolution
- Areas & Volumes: Culminating Activity

### Chapter 9 - Techniques of Integration

### Chapter 10 - Improper Integrals

### Chapter 11 - Infinite Series

### Chapter 12 - Differential Equations

### Chapter 13 - Polar