- CALCULUS 1 and 2: RESOURCES !!!
- Preliminary Review Topics
- Limits & Continuity
- Derivatives: Introduction & Intuition
- Derivatives of Special Functions & Differentiation Techniques
- Related Rates & Linearization of Functions
- Closed Interval Method & Optimization Problems
- Riemann Sums; Indefinite and Definite Integrals
- Areas and Volumes; Solids of Revolution & Non-Revolution
- Average Value and Arc Length
- Integration Techniques
- Differential Equations
- Sequences & Series
- Parametric Equations
- Polar Coordinates
- Multivariable Calculus Topics

# CALCULUS 1 and 2: RESOURCES !!!

- Author:
- Aedamar Frawley, Tim Brzezinski

**This GeoGebra book contains applets that can be used to foster active, student-centered, discovery-based learning, provide meaningful remediation, enhance opportunities for differentiation of instruction, and serve as a source of ongoing formative assessment. These GeoGebra books display the amazing work from several esteemed members of the GeoGebra community. I am truly humbled and amazed by their talents. These comprehensive resources would not have been possible without their contributions. I would like to express a BIG THANK YOU to Steve Phelps (https://www.geogebra.org/stevephelps) Dr. Ted Coe (https://www.geogebra.org/tedcoe) Kevin Hopkins (https://www.geogebra.org/dochopatsbu) John Golden (https://www.geogebra.org/goldenj) Irena Boyadzhiev (https://www.geogebra.org/irinaboyadzhiev) Terry Lee Lindenmuth (https://www.geogebra.org/tlindy) Doug Kuhlmann (https://www.geogebra.org/dkuhlmann) rockyroer_1 (https://www.geogebra.org/rockyroer_1) More dynamic worksheets will continue to be added to this volume over time. Teachers: It is my hope that these resources help empower your students to actively (and meaningfully) discover these calculus concepts. Students: It is my hope that these resources help you discover & help reinforce these calculus concepts in a way that makes sense to you. For questions, suggestions, and/or comments, feel free to e-mail me at any time. I wish you much success in your journey of teaching and/or learning mathematics! Best, Tim Brzezinski (www.geogebra.org/tbrzezinski) Independent Mathematics Education Consultant Adjunct Instructor of Mathematical Sciences (Central Connecticut State University) E-Mail: dynamicmathsolutions@gmail.com Twitter: @dynamic_math (https://twitter.com/dynamic_math)**

## Table of Contents

### Preliminary Review Topics

### Limits & Continuity

### Derivatives: Introduction & Intuition

- Average Velocity
- Average to Instantaneous (Intro)
- Sketch the Derivative (Warm Up)
- Drawing Derivatives
- Constructing Graphs of Derivative Functions (Intuitively)
- Average Rate of Change Intervals
- Average Rate of Change of a Function: Dynamic Illustration
- Average to Instantaneous (Rate of Change)
- Average Rate of Change vs. Instantaneous Rate of Change
- Derivative Function: Without Words
- Derivatives (Intro)-1
- Derivatives (Intro)-2
- Graphing The Derivative of a Function
- 3-Way Color-Changing Derivative Grapher
- When does f'(x) = f(x)?
- Mean Value Theorem
- Mean Value Theorem (Without Words)

### Derivatives of Special Functions & Differentiation Techniques

- Derivative of a Product
- Important Trig Limits
- Derivative of Sine & Cosine Functions (Quick Investigation)
- Derivative of Tangent Function (Investigation)
- Implicit Differentiation: Intro
- Folium of Descartes
- Implicit Differentiation (Quick Check)
- Derivative of Arcsine Function
- Derivative of Arccosine Function
- Derivative of Arctangent Function
- Derivatives of Inverse Functions
- Derivative of Natural Log Function

### Related Rates & Linearization of Functions

- Related Rates (1)
- Related Rates (2)
- Falling Ladder !!!
- Related Rates (3)
- Related Rates: Adjustable Cone with dh/dt Constant
- Filling a Cone: dV/dt Constant versus dh/dt Constant
- Related Rates (Rolling Carts Problem)
- Linearization Illustrator (Calculus)
- Linearization Checker (Calculus)
- Newton's Method: Illustrated

### Closed Interval Method & Optimization Problems

- Critical Numbers & Critical Points of Functions (Intro)
- The Closed Interval Method (Application Problem)
- Optimization: Area of a Rectangle
- Distance From Point to Graph
- Marginal Revenue, Cost, Profit: Analysis Problem 1
- Minimizing the Area of a Triangle
- Optimization Problem: Isosceles Triangle Circumscribed about a Circle
- Optimization - Box
- Maximizing Trapezoid Area
- Optimization Challenge 1
- Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
- Honeybee Population (Growth Rate Question)
- Oil Pipeline Optimization Problem
- Cylinder Inscribed Inside Sphere
- Cylinder Inscribed In Cone
- Sphere Inscribed Inside a Right Circular Cone

### Riemann Sums; Indefinite and Definite Integrals

### Areas and Volumes; Solids of Revolution & Non-Revolution

- U-Substitution (Definite Integrals)
- Areas Between Curves (Intro)
- Area Between Curves
- Area Between 2 Curves
- Visualizing Volumes of Rotation
- Volume of Solid of Revolution about x-axis
- Disc Action!!!
- Solids of Revolution (Discs)
- Custom Made Solid of Revolution
- Washer Action!!! (1)
- Washer Action !!! (2) - Calculus
- Cylindrical Shell Action!!! (1)
- Cylindrical Shell Action!!! (2)
- Custom Surface of REV From 2 Functions (Calculus): Template
- Arc Length to Surface of Revolution: Calculus
- Parabola Around y-Axis
- Parabola Rotated Around y-Axis Wireframe
- Parabola Rotated Around x-Axis
- Parabola Rotated Around x-Axis
- Solids of Revolution: Around the x-Axis
- Solids of Revolution: Around the y-Axis
- Solids of Revolution: Around y=6
- Calculus Solids
- Solids Formed From Certain Cross Sections
- V. of Solid NOT of Revolution
- Cross-Sections Perpendicular to x-Axis: Squares
- Cross-Sections Perpendicular to x-Axis: Equilateral Triangle
- Cross-Sections Perpendicular to x-Axis: Right Triangles
- Cross-Sections Perpendicular to x-Axis: Rectangles
- Areas & Volumes: Culminating Activity

### Average Value and Arc Length

### Integration Techniques

### Differential Equations

### Sequences & Series

### Parametric Equations

### Polar Coordinates

- Trig Function Values (30 Degrees)
- Trig Function Values (45 Degrees)
- Trig Function Values (60 Degrees)
- Special Angles in Standard Position: Intro (V1)
- Special Angles in Standard Position: Intro (V2)
- Special Angles in Standard Position: Intro (V3)
- Polar Coordinates! (Intro)
- Writing Equivalent Polar Coordinates: Quiz
- Polar Function Graphing
- Derivatives in Polar Coordintes
- Areas with Polar Coordinates
- Area Between 2 Polar Graphs
- Arc Length in Polar Coordintes

### Multivariable Calculus Topics

- Plotting Points in 3D: Dynamic Illustrator
- Cylindrical Coordinates: Dynamic Illustrator
- Spherical Coordinates: Dynamic Illustrator
- Partial Derivatives: Graphical Illustrator
- Sphere Investigation
- Circular Paraboloid of Revolution
- Animation 111
- Special Spheroid Action: Locus Illustration
- Animation 112
- Special Hyperboloid of 1 Sheet as a Locus
- Special Hyperboloid of 2 Sheets as a Locus
- Catenoid