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Calculus AB - Concept Videos
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All Topics
10:00
Interpreting Accumulation Functions in Context
10:00
Understanding Graphical Implications of Area Accumulation
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Relating Accumulation Functions to Graphical Areas
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Linearity and Additivity of Integrals
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Using Symmetry Properties of Integrals
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Splitting Integrals for Complex Domains
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Connecting Antiderivatives to Definite Integrals
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Solving Problems Using the Fundamental Theorem of Calculus
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Applying the Fundamental Theorem to Real-World Contexts
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Understanding Basic Rules and Notation for Indefinite Integrals
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Finding Antiderivatives of Polynomial, Exponential, and Trigonometric Functions
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Verifying Antiderivative Solutions
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Recognizing Patterns for u-Substitution
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Adjusting Bounds During Substitution
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Verifying Substitution Results Using Differentiation
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Simplifying Functions Using Long Division for Integration
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Completing the Square for Complex Denominators
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Solving Rational Integrals Using These Techniques
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Choosing Appropriate Techniques Based on Function Type
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Combining Multiple Techniques in Complex Problems
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Verifying Solutions to Antiderivative Problems
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Understanding Accumulations of Change in Context
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Interpreting Integrals as Accumulated Changes
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Exploring Applications of Accumulated Change
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Estimating Areas Using Left, Right and Midpoint Reimann Sums
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Using Trapezoidal Approximations
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Connecting Riemann Sums to Definite Integrals
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Expressing Riemann Sums Using Summation Notation
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Transitioning from Riemann Sums to Definite Integral Notation
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Writing and Interpreting Definite Integrals
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Statement and Proof of the Fundamental Theorem of Calculus
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Connecting Definite Integrals to Accumulation Functions
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Understanding the Behavior of Accumulation Functions
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Comparing Volumes with Disc and Washer Approaches
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Disc Method: Revolving Around the x- or y-Axis
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Washer Method: Solving Problems with Inner and Outer Radii
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Calculating the Average Value of a Function on an Interval
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Relating Average Value to the Mean Value Theorem for Integrals
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Understanding Position, Velocity, and Acceleration Through Integration
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Applying Definite Integrals to Motion Problems
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Solving Accumulated Change Problems
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Defining and Interpreting Accumulation Functions
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Using Accumulation Functions in Real-World Scenarios
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Connecting Accumulation Functions to Graphical Representations
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Setting Up Integrals for Curves Expressed as Functions of x
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Setting Up Integrals for Curves Expressed as Functions of y
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Solving Problems with Curves That Intersect at Multiple Points
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Establishing Volumes with Square and Rectangular Cross-Sections
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Using Triangular and Semicircular Cross-Sections for Volumes
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Setting Up Volumes with General Cross-Sections
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Inverse Trigonometric Functions
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Selecting Procedures for Calculating Derivatives
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Sketching and Interpreting Results
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Understanding and Applying the Chain Rule
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Differentiating Implicitly Defined Functions
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Interpreting the Meaning of Derivatives in Context
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Straight-Line Motion: Position, Velocity and Acceleration
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Rates of Change in Applied Contexts Other Than Motion
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Introduction to Related Rates
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Solving Related Rates Problems
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Approximating Function Values Using Linearization
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Using L’Hopital’s Rule for Indeterminate Forms
10:00
Statement and Proof of the Mean Value Theorem
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Verifying Conditions for the Mean Value Theorem
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Applying the Mean Value Theorem to Motion and Contextual Problems
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Understanding the Extreme Value Theorem
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Identifying Global and Local Extrema
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Finding and Classifying Critical Points
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Using the First Derivative to Determine Intervals of Increase or Decrease
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Interpreting First Derivative Sign Charts
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Applying the First Derivative Test to Find Relative Extrema
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Justifying Local Maxima and Minima Using Sign Changes in the First Derivative
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Understanding the Candidates Test
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Applying the Candidates Test to Determine Absolute Extrema on a Closed Interval
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Using the Second Derivative to Determine Concavity
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Classifying Functions as Concave Up or Concave Down
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Applying the Second Derivative Test to Classify Critical Points
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Connecting the Second Derivative Test to Concavity and Extrema
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Sketching Functions Based on Their Derivatives
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Analyzing the Graphical Relationship Between a Function and Its First and Second Derivatives
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Understanding the Interplay Between a Function and Its Derivatives
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Predicting Behaviors Based on First and Second Derivative Information
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Analyzing Implicitly Defined Relations Using Derivatives
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Understanding the Graphical Implications of Implicit Differentiation
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Can Change Occur at an Instant?
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Defining Limits and Using Limit Notation
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Estimating Limit Values from Graphs
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Estimating Limit Values from Tables
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Determining Limits Using Algebraic Properties of Limits
10:00
Determining Limits Using Algebraic Manipulation
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Determining Limits Using the Squeeze Theorem
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Exploring Types of Discontinuities
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Defining Continuity at a Point
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Confirming Continuity over an Interval
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Removing Discontinuities
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Connecting Infinite Limits and Vertical Asymptotes
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Connecting Limits at Infinity and Horizontal Asymptotes
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Working with the Intermediate Value Theorem (IVT)
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Understanding the Role of Slope Fields
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Sketching and Interpreting Slope Fields
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Matching Differential Equations to Slope Fields
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Separating Variables in Differential Equations
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Solving Exponential Growth and Decay Problems
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Solving Logistic Growth Models
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Verifying Solutions to Differential Equations
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Constructing Differential Equations from Contexts
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Interpreting Differential Equations in Motion and Population Models
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Defining Average and Instantaneous Rates of Change at a Point
10:00
Defining the Derivative of a Function and Using Derivative Notation
10:00
Estimating Derivatives of a Function at a Point
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Connecting Differentiability and Continuity
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Applying the Power Rule
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Derivative Rules: Constant, Sum, Difference and Constant Multiple
10:00
Derivatives of cos(x), sin(x), e^x and ln(x)
10:00
The Product Rule and Quotient Rule
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