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Unit 1 – Limits and Continuity
1.1 Can Change Occur at an Instant?
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
1.4 Estimating Limit Values from Tables
1.5 Determining Limits Using Algebraic Properties
(1.5 includes piecewise functions involving limits)
1.6 Determining Limits Using Algebraic Manipulation
Finding Limits Using Difference of Cubes (video)
Finding Limits Using Difference of Cubes II (video)
Finding Limits Using Common Denominator (video)
Finding Limits Using Conjugates (video)
Finding Limits Involving Trig Functions I (video)
1.7 Selecting Procedures for Determining Limits
(1.7 includes rationalization, complex fractions, and absolute value)
1.8 Determining Limits Using the Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
Mid-Unit Review - Unit 1
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
1.12 Confirming Continuity Over an Interval
1.13 Removing Discontinuities
1.14 Infinite Limits and Vertical Asymptotes
1.15 Limits at Infinity and Horizontal Asymptotes
1.16 Intermediate Value Theorem (IVT)
Review - Unit 1
Unit 2 – Differentiation: Definition and Fundamental Properties
2.1 Defining Average and Instantaneous Rate of Change at a Point
2.2 Defining the Derivative of a Function and Using Derivative Notation
(2.2 includes equation of the tangent line)
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity
Derivatives Section 2.5 Through 3.1
GUIDED Notes to Follow videos (PDF)
Solutions to NOTES from videos (PDF)
Problems to try on your OWN (PDF)
2.5 Applying the Power Rule
Power rule
Example 1 (video)
Example 2 (video)
Example 3 (video)
Example 4 (video)
Example 5 (video)
Example 6 (video)
Example 7 (video)
Example 8 (video)
Example 9 (video)
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
(2.6 includes horizontal tangent lines, equation of the normal line, and differentiability of piecewise)
2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
2.8 The Product Rule
Product Rules
Example 1 (video)
Example 2 (video)
Example 3 (video)
Example 4 (video)
Example 5 (video)
Example 6 (video)
Example 7 (video)
Example 8 (video)
2.9 The Quotient Rule
Quotient Rule
Example 1 (video)
Example 2 (video)
Example 3 (video)
Example 4 (video)
Example 5 (video)
Example 6 (video)
Example 7 (video)
2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)
Derivatives of trigonometric functions
Review - Unit 2
Unit 3 – Differentiation: Composite, Implicit, and Inverse Functions
3.1 The Chain Rule
Chain Rule (Applied across all the rules)
Example 1 (video)
Example 2 (video)
Example 3 (video)
Example 4 (video)
Example 5 (video)
Example 6 (video)
Example 7 (video)
Example 8 (video)
Example 9 (video)
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher-Order Derivatives
Review - Unit 3
Unit 4 – Contextual Applications of Differentiation
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
4.3 Rates of Change in Applied Contexts Other Than Motion
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values of a Function Using Local Linearity and Linearization
4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms
Review - Unit 4
Unit 5 – Analytical Applications of Differentiation
5.1 Using the Mean Value Theorem
5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
5.3 Determining Intervals on Which a Function is Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative Local Extrema
5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
5.6 Determining Concavity of Functions over Their Domains
5.7 Using the Second Derivative Test to Determine Extrema
Mid-Unit Review - Unit 5
5.8 Sketching Graphs of Functions and Their Derivatives
5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
(5.9 includes a revisit of particle motion and determining if a particle is speeding up/down.)
5.10 Introduction to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Behaviors of Implicit Relations
Review - Unit 5
Unit 6 – Integration and Accumulation of Change
6.1 Exploring Accumulation of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
6.4 The Fundamental Theorem of Calculus and Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions Involving Area
Mid-Unit Review - Unit 6
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite Integrals
6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division and Completing the Square
6.14 Selecting Techniques for Anti-differentiation
Review - Unit 6
Unit 7 – Differential Equations
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.6 General Solutions Using Separation of Variables
7.7 Particular Solutions using Initial Conditions and Separation of Variables
7.8 Exponential Models with Differential Equations
Review - Unit 7
Unit 8 – Applications of Integration
8.1 Average Value of a Function on an Interval
Concept of Average Value of a Function (Video)
8.2 Position, Velocity, and Acceleration Using Integrals
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Area Between Curves (with respect to x)
Introduction and Concepts of Area Between Curves (Video)
Area Between Curves Example 1 (Video)
Area Between Curves Example 2 (Video)
Area Between Curves Example 3 (Video)
8.5 Area Between Curves (with respect to y)
8.6 Area Between Curves - More than Two Intersections
Mid-Unit Review - Unit 8
8.7 Cross Sections: Squares and Rectangles
Cross-Sections Introduction and Some Basic Formulas (video)
Examples of Cross-Sections Taken Perpendicular to x-axis (video)
Examples of Cross-Sections Taken Perpendicular to y-axis (video)
8.8 Cross Sections: Triangles and Semicircles
8.9 Disc Method: Revolving Around the x- or y- Axis
Introduction and Concept for Solids of Revolution: (Video)
Solids of Revolution: Disc Method Example 1 (Video)
Solids of Revolution: Disc Method Example 2 (Video)
Solids of Revolution: Disc Method Example 3 (Video)
Solids of Revolution: Disc Method Example 4 (Video)
Solids of Revolution: Disc Method Example 5 (Video)
8.10 Disc Method: Revolving Around Other Axes
8.11 Washer Method: Revolving Around the x- or y-Axis
Solids of Revolution: Washer Method Example 1 (Video)
Solids of Revolution: Washer Method Example 2 (Video)
Solids of Revolution: Washer Method Example 3 (Video)
Solids of Revolution: Washer Method Example 4 (Video)
Solids of Revolution: Washer Method Example 5 (Video)
8.12 Washer Method: Revolving Around Other Axes
8.13a Shell Method:
Solids of Revolution Review and Intro to Shell Method (Video)
Solids of Revolution Shell Method: Example 1 (Video)
Solids of Revolution Shell Method: Example 2 (Video)
Solids of Revolution Shell Method: Example 3 (Video)
Solids of Revolution Shell Method: Example 4 (Video)
Solids of Revolution Shell Method: Example 5 (Video)
8.13b Shell Method:
More of Shell Method Example 1 (video)
More of Shell Method Example 2 (video)
More of Shell Method Example 3 (video)
More of Shell Method Example 4 (video)
More of Shell Method Example 5 (video)
8.14 The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC topic)
Review - Unit 8