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Modules
A - Functions and Graphs Review
Introduction and Objectives
The Domain of a Function
General Rule
Example A
Example B
Example C
Basic Types of Functions
Linear and Quadratic Functions
Other Polynomial Functions
Power Functions
Sine and Cosine Functions
Operations on Functions
The Graph of f(x)±c
The Graph of f(x±c)
The Graph of -f(x)
The Graph of cf(x)
The Graph of f(-x)
The Graph of f(cx)
Example A
Example B
Example C
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
B - Trigonometry Review
Introduction and Objectives
Basics
Definitions of Sine and Cosine
Graphs of Sine and Cosine
Other Trigonometric Functions
Graph of the Tangent Function
Evaluating Trigonometric Functions
Triangle Trigonometry
Introduction
Evaluate Using Triangle Trigonometry
Identities
Pythagorean Identities
Example A
Example B
Example C
Summary
Self Evaluation
Problem 1
Problem 2
Worksheet
C - Logarithms Review
Introduction and Objectives
Logarithm Rules
Graphs of Logarithm Functions
The Natural Logarithm Function
Solving Equations
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
Problem 4
1 - Limits
Introduction and Objectives
Further Discussion
Examples: Limits from Data and Graphs
Example A
Example B
Example C
Example D
Example E
Evaluating Limits with Algebra
Examples: Evaluating Limits
Example A
Example B
Example C
Example D
Summary
Self Evaluation
Problem 1
Problem 2
Worksheet
Worksheet Answers
2 - Rates of Change and Derivatives
Introduction and Objectives
Average Rate of Change
Instantaneous Rate of Change
Examples: Rates of Change
Example A
Example B
Example C
Derivative of a Function
Examples: Derivatives
Example A
Example B
Example C
Example D
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
Worksheet
Worksheet Answers
3 - Calculating Derivatives
Introduction and Objectives
Interactive Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Worksheet
Worksheet Answers
4 - Derivatives of Trigonometric Functions
Introduction and Objectives
Outlining the Task
Applying the Definition
Two Important Limits
Limit Examples
Example 1
Example 2
Derivative Formulae
Derivative Examples
Example A
Example B
Example C
Summary
Self Evaluation
Problem 1
Problem 2
Worksheet
Worksheet Answers
5 - Using the Chain Rule
Introduction and Objectives
Interactive Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Worksheet
Worksheet Answers
6 - Related Rates
Introduction and Objectives
The Process
Implicit Differentiation Review
Steps for Solving
Examples
Example A(a)
Example A(b)
Example A(c)
Example B
Example C
Example D
Self Evaluation
Problem 1
Problem 2
Problem 3
Summary
Worksheet
Worksheet Answers
7 - Linear Approximations and Differentials
Introduction and Objectives
The Linear Approximation Formula
Examples
Example A
Example B
Example C
Example D
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
Worksheet
Worksheet Answers
8 - The Shape of a Function's Graph
Introduction and Objectives
Examples
Example A
Example B
Example C
Example D
Example E
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
Worksheet
9 - Curve Sketching
Introduction and Objectives
Symmetry
Brief Discussion
Example A
Example B
Periodicity
Brief Discussion
Example
Asymptotes
Brief Discussion
Example
Monotonicity and Concavity
Brief Discussion
Example
Examples
Example A
Example B
Example C
Worksheet
Worksheet Answers
10 - Newton's Method
Introduction and Objectives
The Basic Idea
Deriving the Formula
Examples
Example A
Example B
Example C
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
Worksheet
11 - Riemann Sums
Introduction and Objectives
Riemann Sums
A motivating example
Formulae for the area under a curve
One more example
The Definite Integral
Summary
Self Evaluation
Problem 1
Problem 2
Worksheet
12 - Integration by Substitution
Introduction and Objectives
Recognizing the Appropriate Substitution
Rewriting the Integral
Complete Problems
Worksheet
13 - Area Between Curves
Introduction and Objectives
Examples
Example A
Example B
Example C
Example D
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
Worksheet
14 - Volume I: Slices
Introduction and Objectives
The Three-Step Process
Examples
Example A
Example B
Example C
Summary
Self Evaluation
Worksheet
15 - Volume II: Solids of Revolution
Coming Soon
16 - Inverse Functions
Introduction and Objectives
Calculating a Rule for f
-1
The graph of f
-1
The derivative of f
-1
Further Examples
Calculating a Rule for f
-1
The graph of f
-1
The derivative of f
-1
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
Problem 4
Worksheet
17 - L'Hôpital's Rule
Introduction and Objectives
L'Hôpital's Rule
Examples
Example A
Example B
Example C
Example D
Example E
Example F
Summary
Self Evaluation
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Worksheet
