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AP®︎ Calculus AB content aligned to standards

This page lists every piece of AP Calculus AB content once and shows all the standards covered by that content. So, standards may appear more than once in this view. If you would like to quickly see all of the course content aligned to a particular standard, the Standards aligned to content page may be better suited.

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Each of our units is listed with a table of its contents, with the course content on the left side (Lessons ☰, Articles 📝, Videos 📺, and Exercises ✅) and the covered standards on the right side.
Place your cursor over a standard to reveal its description. Click a piece of course content to visit that Unit, Lesson, Article, Video, or Exercise.
If you’re looking for all of the AP Calculus AB content that’s aligned with a particular standard, you can use the “Find” feature of your browser to search for the standard or use the Standards aligned to content page.
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ContentStandards
Defining limits and using limit notation
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📺 Limits intro
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📝 Limits intro
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Limits intro
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Estimating limit values from graphs
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📺 Estimating limit values from graphs
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📺 Unbounded limits
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📝 Estimating limit values from graphs
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Estimating limit values from graphs
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📺 One-sided limits from graphs
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📺 One-sided limits from graphs: asymptote
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One-sided limits from graphs
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📺 Connecting limits and graphical behavior
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Connecting limits and graphical behavior
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Estimating limit values from tables
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📺 Approximating limits using tables
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📺 Estimating limits from tables
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📝 Using tables to approximate limit values
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Creating tables for approximating limits
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Estimating limits from tables
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📺 One-sided limits from tables
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One-sided limits from tables
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Determining limits using algebraic properties of limits: limit properties
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📺 Limit properties
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📺 Limits of combined functions
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📺 Limits of combined functions: piecewise functions
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Limits of combined functions: sums and differences
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Limits of combined functions: products and quotients
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📺 Limits of composite functions
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Limits of composite functions
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Determining limits using algebraic properties of limits: direct substitution
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📺 Limits by direct substitution
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Limits by direct substitution
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📺 Undefined limits by direct substitution
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Direct substitution with limits that don't exist
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📺 Limits of trigonometric functions
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Limits of trigonometric functions
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📺 Limits of piecewise functions
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Limits of piecewise functions
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📺 Limits of piecewise functions: absolute value
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Determining limits using algebraic manipulation
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📺 Limits by factoring
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Limits by factoring
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📺 Limits by rationalizing
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Limits using conjugates
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📺 Trig limit using Pythagorean identity
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📺 Trig limit using double angle identity
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Limits using trig identities
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Selecting procedures for determining limits
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📺 Strategy in finding limits
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📝 Strategy in finding limits
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Conclusions from direct substitution (finding limits)
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Next steps after indeterminate form (finding limits)
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Strategy in finding limits
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Determining limits using the squeeze theorem
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📺 Squeeze theorem intro
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Squeeze theorem
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📺 Limit of sin(x)/x as x approaches 0
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📺 Limit of (1-cos(x))/x as x approaches 0
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Exploring types of discontinuities
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📺 Types of discontinuities
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Classify discontinuities
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Defining continuity at a point
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📺 Continuity at a point
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📺 Worked example: Continuity at a point (graphical)
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Continuity at a point (graphical)
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📺 Worked example: point where a function is continuous
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📺 Worked example: point where a function isn't continuous
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Continuity at a point (algebraic)
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Confirming continuity over an interval
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📺 Continuity over an interval
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Continuity over an interval
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📺 Functions continuous on all real numbers
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📺 Functions continuous at specific x-values
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Continuity and common functions
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Removing discontinuities
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📺 Removing discontinuities (factoring)
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📺 Removing discontinuities (rationalization)
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Removable discontinuities
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Connecting infinite limits and vertical asymptotes
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📺 Introduction to infinite limits
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📺 Infinite limits and asymptotes
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Infinite limits: graphical
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📺 Analyzing unbounded limits: rational function
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📺 Analyzing unbounded limits: mixed function
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Infinite limits: algebraic
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Connecting limits at infinity and horizontal asymptotes
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📺 Introduction to limits at infinity
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📺 Functions with same limit at infinity
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Limits at infinity: graphical
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📺 Limits at infinity of quotients (Part 1)
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📺 Limits at infinity of quotients (Part 2)
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Limits at infinity of quotients
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📺 Limits at infinity of quotients with square roots (odd power)
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📺 Limits at infinity of quotients with square roots (even power)
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Limits at infinity of quotients with square roots
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Working with the intermediate value theorem
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📺 Intermediate value theorem
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📺 Worked example: using the intermediate value theorem
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Using the intermediate value theorem
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📺 Justification with the intermediate value theorem: table
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📺 Justification with the intermediate value theorem: equation
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Justification with the intermediate value theorem
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📝 Intermediate value theorem review
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Optional videos
📺 Formal definition of limits Part 1: intuition review
📺 Formal definition of limits Part 2: building the idea
📺 Formal definition of limits Part 3: the definition
📺 Formal definition of limits Part 4: using the definition
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ContentStandards
Defining average and instantaneous rates of change at a point
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📺 Newton, Leibniz, and Usain Bolt
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📺 Derivative as a concept
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📺 Secant lines & average rate of change
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Secant lines & average rate of change
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📝 Derivative notation review
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📺 Derivative as slope of curve
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Derivative as slope of curve
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📺 The derivative & tangent line equations
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The derivative & tangent line equations
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Defining the derivative of a function and using derivative notation
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📺 Formal definition of the derivative as a limit
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📺 Formal and alternate form of the derivative
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📺 Worked example: Derivative as a limit
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📺 Worked example: Derivative from limit expression
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Derivative as a limit
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📺 The derivative of x² at x=3 using the formal definition
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📺 The derivative of x² at any point using the formal definition
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📝 Finding tangent line equations using the formal definition of a limit
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Estimating derivatives of a function at a point
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📺 Estimating derivatives
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Estimate derivatives
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Connecting differentiability and continuity: determining when derivatives do and do not exist
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📺 Differentiability and continuity
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📺 Differentiability at a point: graphical
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Differentiability at a point: graphical
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📺 Differentiability at a point: algebraic (function is differentiable)
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📺 Differentiability at a point: algebraic (function isn't differentiable)
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Differentiability at a point: algebraic
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📝 Proof: Differentiability implies continuity
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Applying the power rule
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📺 Power rule
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Power rule (positive integer powers)
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Power rule (negative & fractional powers)
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📺 Power rule (with rewriting the expression)
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Power rule (with rewriting the expression)
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📝 Justifying the power rule
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Derivative rules: constant, sum, difference, and constant multiple: introduction
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📺 Basic derivative rules
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📺 Basic derivative rules: find the error
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Basic derivative rules: find the error
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📺 Basic derivative rules: table
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Basic derivative rules: table
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📝 Justifying the basic derivative rules
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Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule
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📺 Differentiating polynomials
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Differentiate polynomials
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📺 Differentiating integer powers (mixed positive and negative)
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Differentiate integer powers (mixed positive and negative)
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📺 Tangents of polynomials
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Tangents of polynomials
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Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)
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📺 Derivatives of sin(x) and cos(x)
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📺 Worked example: Derivatives of sin(x) and cos(x)
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Derivatives of sin(x) and cos(x)
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📝 Proving the derivatives of sin(x) and cos(x)
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📺 Derivative of 𝑒ˣ
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📺 Derivative of ln(x)
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Derivatives of 𝑒ˣ and ln(x)
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📝 Proof: The derivative of 𝑒ˣ is 𝑒ˣ
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📝 Proof: the derivative of ln(x) is 1/x
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The product rule
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📺 Product rule
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📺 Differentiating products
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Differentiate products
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📺 Worked example: Product rule with table
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📺 Worked example: Product rule with mixed implicit & explicit
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Product rule with tables
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📝 Proving the product rule
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📝 Product rule review
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The quotient rule
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📺 Quotient rule
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Differentiate quotients
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📺 Worked example: Quotient rule with table
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Quotient rule with tables
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📺 Differentiating rational functions
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Differentiate rational functions
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📝 Quotient rule review
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Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions
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📺 Derivatives of tan(x) and cot(x)
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📺 Derivatives of sec(x) and csc(x)
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Derivatives of tan(x), cot(x), sec(x), and csc(x)
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Optional videos
📺 Proof: Differentiability implies continuity
📺 Justifying the power rule
📺 Proof of power rule for positive integer powers
📺 Proof of power rule for square root function
📺 Limit of sin(x)/x as x approaches 0
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📺 Limit of (1-cos(x))/x as x approaches 0
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📺 Proof of the derivative of sin(x)
📺 Proof of the derivative of cos(x)
📺 Product rule proof
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ContentStandards
The chain rule: introduction
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📺 Chain rule
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📺 Common chain rule misunderstandings
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📝 Chain rule
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📺 Identifying composite functions
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Identify composite functions
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📺 Worked example: Derivative of cos³(x) using the chain rule
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📺 Worked example: Derivative of √(3x²-x) using the chain rule
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📺 Worked example: Derivative of ln(√x) using the chain rule
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Chain rule intro
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The chain rule: further practice
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📺 Worked example: Chain rule with table
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Chain rule with tables
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📺 Derivative of aˣ (for any positive base a)
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📺 Derivative of logₐx (for any positive base a≠1)
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Derivatives of aˣ and logₐx
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📺 Worked example: Derivative of 7^(x²-x) using the chain rule
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📺 Worked example: Derivative of log₄(x²+x) using the chain rule
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📺 Worked example: Derivative of sec(3π/2-x) using the chain rule
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📺 Worked example: Derivative of ∜(x³+4x²+7) using the chain rule
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Chain rule capstone
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📝 Proving the chain rule
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📝 Derivative rules review
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Implicit differentiation
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📺 Implicit differentiation
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📺 Worked example: Implicit differentiation
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📺 Worked example: Evaluating derivative with implicit differentiation
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Implicit differentiation
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📺 Showing explicit and implicit differentiation give same result
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📝 Implicit differentiation review
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Differentiating inverse functions
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📺 Derivatives of inverse functions
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📺 Derivatives of inverse functions: from equation
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📺 Derivatives of inverse functions: from table
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Derivatives of inverse functions
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Differentiating inverse trigonometric functions
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📺 Derivative of inverse sine
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📺 Derivative of inverse cosine
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📺 Derivative of inverse tangent
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Derivatives of inverse trigonometric functions
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📝 Differentiating inverse trig functions review
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Selecting procedures for calculating derivatives: strategy
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📺 Differentiating functions: Find the error
📺 Manipulating functions before differentiation
📝 Strategy in differentiating functions
Differentiating functions: Find the error
Manipulating functions before differentiation
Selecting procedures for calculating derivatives: multiple rules
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📺 Differentiating using multiple rules: strategy
Differentiating using multiple rules: strategy
📺 Applying the chain rule and product rule
📺 Applying the chain rule twice
📺 Derivative of eᶜᵒˢˣ⋅cos(eˣ)
📺 Derivative of sin(ln(x²))
Differentiating using multiple rules
Calculating higher-order derivatives
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📺 Second derivatives
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Second derivatives
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📺 Second derivatives (implicit equations): find expression
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📺 Second derivatives (implicit equations): evaluate derivative
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Second derivatives (implicit equations)
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📝 Second derivatives review
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Further practice connecting derivatives and limits
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📺 Disguised derivatives
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Disguised derivatives
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Optional videos
📺 Proof: Differentiability implies continuity
📺 If function u is continuous at x, then Δu→0 as Δx→0
📺 Chain rule proof
📺 Quotient rule from product & chain rules
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ContentStandards
Interpreting the meaning of the derivative in context
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📺 Interpreting the meaning of the derivative in context
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📝 Analyzing problems involving rates of change in applied contexts
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Interpreting the meaning of the derivative in context
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Straight-line motion: connecting position, velocity, and acceleration
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📺 Introduction to one-dimensional motion with calculus
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📺 Interpreting direction of motion from position-time graph
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📺 Interpreting direction of motion from velocity-time graph
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📺 Interpreting change in speed from velocity-time graph
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Interpret motion graphs
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📺 Worked example: Motion problems with derivatives
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Motion problems (differential calc)
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Rates of change in other applied contexts (non-motion problems)
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📺 Applied rate of change: forgetfulness
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Rates of change in other applied contexts (non-motion problems)
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📺 Marginal cost & differential calculus
Introduction to related rates
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📺 Related rates intro
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📝 Analyzing problems involving related rates
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📺 Analyzing related rates problems: expressions
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Analyzing related rates problems: expressions
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📺 Analyzing related rates problems: equations (Pythagoras)
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📺 Analyzing related rates problems: equations (trig)
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Analyzing related rates problems: equations
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📺 Differentiating related functions intro
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📺 Worked example: Differentiating related functions
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Differentiate related functions
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Solving related rates problems
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Related rates intro
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Related rates (multiple rates)
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📺 Related rates: Approaching cars
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📺 Related rates: Falling ladder
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Related rates (Pythagorean theorem)
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📺 Related rates: water pouring into a cone
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Related rates (advanced)
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📺 Related rates: shadow
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📺 Related rates: balloon
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Approximating values of a function using local linearity and linearization
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📺 Local linearity
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📺 Local linearity and differentiability
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📺 Worked example: Approximation with local linearity
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Approximation with local linearity
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📺 Linear approximation of a rational function
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Using L’Hôpital’s rule for finding limits of indeterminate forms
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📺 L'Hôpital's rule introduction
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📺 L'Hôpital's rule: limit at 0 example
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L'Hôpital's rule: 0/0
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📺 L'Hôpital's rule: limit at infinity example
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L'Hôpital's rule: ∞/∞
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📝 Proof of special case of l'Hôpital's rule
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Optional videos
📺 Proof of special case of l'Hôpital's rule
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ContentStandards
Using the mean value theorem
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📺 Mean value theorem
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📺 Mean value theorem example: polynomial
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📺 Mean value theorem example: square root function
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Using the mean value theorem
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📺 Justification with the mean value theorem: table
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📺 Justification with the mean value theorem: equation
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📝 Establishing differentiability for MVT
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Justification with the mean value theorem
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📺 Mean value theorem application
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📝 Mean value theorem review
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Extreme value theorem, global versus local extrema, and critical points
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📺 Extreme value theorem
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📺 Critical points introduction
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📺 Finding critical points
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Find critical points
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Determining intervals on which a function is increasing or decreasing
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📺 Finding decreasing interval given the function
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📺 Finding increasing interval given the derivative
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Increasing & decreasing intervals
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📝 Increasing & decreasing intervals review
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Using the first derivative test to find relative (local) extrema
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📺 Introduction to minimum and maximum points
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📺 Finding relative extrema (first derivative test)
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📺 Worked example: finding relative extrema
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📺 Analyzing mistakes when finding extrema (example 1)
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📺 Analyzing mistakes when finding extrema (example 2)
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📝 Finding relative extrema (first derivative test)
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Relative minima & maxima
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📝 Relative minima & maxima review
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Using the candidates test to find absolute (global) extrema
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📺 Finding absolute extrema on a closed interval
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Absolute minima & maxima (closed intervals)
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📺 Absolute minima & maxima (entire domain)
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Absolute minima & maxima (entire domain)
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📝 Absolute minima & maxima review
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Determining concavity of intervals and finding points of inflection: graphical
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📺 Concavity introduction
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📺 Analyzing concavity (graphical)
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Concavity intro
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📺 Inflection points introduction
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📺 Inflection points (graphical)
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Inflection points intro
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Determining concavity of intervals and finding points of inflection: algebraic
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📺 Analyzing concavity (algebraic)
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📺 Inflection points (algebraic)
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📺 Mistakes when finding inflection points: second derivative undefined
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📺 Mistakes when finding inflection points: not checking candidates
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📝 Analyzing the second derivative to find inflection points
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Analyze concavity
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Find inflection points
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📝 Concavity review
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📝 Inflection points review
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Using the second derivative test to find extrema
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📺 Second derivative test
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Second derivative test
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Sketching curves of functions and their derivatives
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📺 Curve sketching with calculus: polynomial
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📺 Curve sketching with calculus: logarithm
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📺 Analyzing a function with its derivative
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Connecting a function, its first derivative, and its second derivative
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📺 Calculus based justification for function increasing
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📺 Justification using first derivative
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📝 Justification using first derivative
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Justification using first derivative
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📺 Inflection points from graphs of function & derivatives
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📺 Justification using second derivative: inflection point
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📺 Justification using second derivative: maximum point
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📝 Justification using second derivative
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Justification using second derivative
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📺 Connecting f, f', and f'' graphically
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📺 Connecting f, f', and f'' graphically (another example)
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Connecting f, f', and f'' graphically
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Solving optimization problems
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📺 Optimization: sum of squares
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📺 Optimization: box volume (Part 1)
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📺 Optimization: box volume (Part 2)
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📺 Optimization: profit
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📺 Optimization: cost of materials
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📺 Optimization: area of triangle & square (Part 1)
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📺 Optimization: area of triangle & square (Part 2)
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Optimization
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📺 Motion problems: finding the maximum acceleration
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Exploring behaviors of implicit relations
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📺 Horizontal tangent to implicit curve
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Tangents to graphs of implicit relations
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Calculator-active practice
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Analyze functions (calculator-active)
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ContentStandards
Exploring accumulations of change
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📺 Introduction to integral calculus
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📺 Definite integrals intro
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📝 Exploring accumulation of change
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📺 Worked example: accumulation of change
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Accumulation of change
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Approximating areas with Riemann sums
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📺 Riemann approximation introduction
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📺 Over- and under-estimation of Riemann sums
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📝 Left & right Riemann sums
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📺 Worked example: finding a Riemann sum using a table
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Left & right Riemann sums
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📺 Worked example: over- and under-estimation of Riemann sums
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Over- and under-estimation of Riemann sums
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📺 Midpoint sums
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📺 Trapezoidal sums
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📝 Understanding the trapezoidal rule
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Midpoint & trapezoidal sums
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📝 Riemann sums review
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Riemann sums, summation notation, and definite integral notation
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📺 Summation notation
📝 Summation notation
📺 Worked examples: Summation notation
Summation notation
📺 Riemann sums in summation notation
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,
📝 Riemann sums in summation notation
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,
📺 Worked example: Riemann sums in summation notation
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Riemann sums in summation notation
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,
📺 Definite integral as the limit of a Riemann sum
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📝 Definite integral as the limit of a Riemann sum
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📺 Worked example: Rewriting definite integral as limit of Riemann sum
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📺 Worked example: Rewriting limit of Riemann sum as definite integral
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Definite integral as the limit of a Riemann sum
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The fundamental theorem of calculus and accumulation functions
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📺 The fundamental theorem of calculus and accumulation functions
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📺 Functions defined by definite integrals (accumulation functions)
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Functions defined by definite integrals (accumulation functions)
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📺 Worked example: Finding derivative with fundamental theorem of calculus
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Finding derivative with fundamental theorem of calculus
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Finding derivative with fundamental theorem of calculus: chain rule
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Interpreting the behavior of accumulation functions involving area
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📺 Interpreting the behavior of accumulation functions
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📝 Interpreting the behavior of accumulation functions
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,
Interpreting the behavior of accumulation functions
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Applying properties of definite integrals
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📺 Negative definite integrals
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📺 Finding definite integrals using area formulas
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Finding definite integrals using area formulas
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📺 Definite integral over a single point
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📺 Integrating scaled version of function
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📺 Switching bounds of definite integral
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📺 Integrating sums of functions
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📺 Worked examples: Finding definite integrals using algebraic properties
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Finding definite integrals using algebraic properties
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📺 Definite integrals on adjacent intervals
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📺 Worked example: Breaking up the integral's interval
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📺 Worked example: Merging definite integrals over adjacent intervals
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Definite integrals over adjacent intervals
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📺 Functions defined by integrals: switched interval
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📺 Finding derivative with fundamental theorem of calculus: x is on lower bound
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📺 Finding derivative with fundamental theorem of calculus: x is on both bounds
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📝 Definite integrals properties review
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The fundamental theorem of calculus and definite integrals
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📺 The fundamental theorem of calculus and definite integrals
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The fundamental theorem of calculus and definite integrals
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📺 Antiderivatives and indefinite integrals
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,
Antiderivatives and indefinite integrals
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📝 Proof of fundamental theorem of calculus
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,
Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule
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📺 Reverse power rule
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Reverse power rule
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Reverse power rule: negative and fractional powers
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📺 Indefinite integrals: sums & multiples
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,
Reverse power rule: sums & multiples
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,
📺 Rewriting before integrating
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,
Reverse power rule: rewriting before integrating
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,
📝 Reverse power rule review
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,
Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals
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📺 Indefinite integral of 1/x
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📺 Indefinite integrals of sin(x), cos(x), and eˣ
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Indefinite integrals: eˣ & 1/x
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Indefinite integrals: sin & cos
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,
📝 Common integrals review
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,
Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals
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,
📺 Definite integrals: reverse power rule
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,
Definite integrals: reverse power rule
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,
📺 Definite integral of rational function
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,
📺 Definite integral of radical function
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📺 Definite integral of trig function
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📺 Definite integral involving natural log
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,
Definite integrals: common functions
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📺 Definite integral of piecewise function
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,
📺 Definite integral of absolute value function
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,
Definite integrals of piecewise functions
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,
Integrating using substitution
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,
📺 𝘶-substitution intro
,
,
📺 𝘶-substitution: multiplying by a constant
,
,
📺 𝘶-substitution: defining 𝘶
,
,
📺 𝘶-substitution: defining 𝘶 (more examples)
,
,
📝 𝘶-substitution
,
,
𝘶-substitution: defining 𝘶
,
,
📺 𝘶-substitution: rational function
,
,
📺 𝘶-substitution: logarithmic function
,
,
📝 𝘶-substitution warmup
,
,
𝘶-substitution: indefinite integrals
,
,
📺 𝘶-substitution: definite integrals
,
,
,
📝 𝘶-substitution with definite integrals
,
,
,
𝘶-substitution: definite integrals
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,
,
📺 𝘶-substitution: definite integral of exponential function
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,
,
Integrating functions using long division and completing the square
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,
📺 Integration using long division
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,
Integration using long division
,
,
📺 Integration using completing the square and the derivative of arctan(x)
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,
Integration using completing the square
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,
Optional videos
📺 Proof of fundamental theorem of calculus
📺 Intuition for second part of fundamental theorem of calculus
,
ContentStandards
Modeling situations with differential equations
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📺 Differential equations introduction
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📺 Writing a differential equation
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Write differential equations
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Verifying solutions for differential equations
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📺 Verifying solutions to differential equations
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Verify solutions to differential equations
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Sketching slope fields
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📺 Slope fields introduction
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,
📺 Worked example: equation from slope field
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,
📺 Worked example: slope field from equation
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,
📺 Worked example: forming a slope field
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,
Slope fields & equations
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,
Reasoning using slope fields
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📺 Approximating solution curves in slope fields
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,
📺 Worked example: range of solution curve from slope field
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Reasoning using slope fields
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,
Finding general solutions using separation of variables
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,
📺 Separable equations introduction
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,
📺 Addressing treating differentials algebraically
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,
📝 Separable differential equations
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,
Separable differential equations: find the error
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,
📺 Worked example: separable differential equations
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Separable differential equations
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,
📺 Worked example: identifying separable equations
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📝 Identifying separable equations
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,
Identify separable equations
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,
Finding particular solutions using initial conditions and separation of variables
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,
,
📺 Particular solutions to differential equations: rational function
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,
📺 Particular solutions to differential equations: exponential function
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,
Particular solutions to differential equations
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,
📺 Worked example: finding a specific solution to a separable equation
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,
📺 Worked example: separable equation with an implicit solution
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,
Particular solutions to separable differential equations
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,
Exponential models with differential equations
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📺 Exponential models & differential equations (Part 1)
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📺 Exponential models & differential equations (Part 2)
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,
📺 Worked example: exponential solution to differential equation
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,
Differential equations: exponential model equations
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,
Differential equations: exponential model word problems
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,
ContentStandards
Finding the average value of a function on an interval
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,
📺 Average value over a closed interval
,
,
📺 Calculating average value of function over interval
,
,
Average value of a function
,
,
📺 Mean value theorem for integrals
,
,
Connecting position, velocity, and acceleration functions using integrals
,
,
,
📺 Motion problems with integrals: displacement vs. distance
,
,
📺 Analyzing motion problems: position
,
,
📺 Analyzing motion problems: total distance traveled
,
,
📝 Motion problems (with definite integrals)
,
,
Analyzing motion problems (integral calculus)
,
,
📺 Worked example: motion problems (with definite integrals)
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,
Motion problems (with integrals)
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,
📺 Average acceleration over interval
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,
Using accumulation functions and definite integrals in applied contexts
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,
,
📺 Area under rate function gives the net change
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,
,
,
📺 Interpreting definite integral as net change
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,
📺 Worked examples: interpreting definite integrals in context
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Interpreting definite integrals in context
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📺 Analyzing problems involving definite integrals
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📝 Analyzing problems involving definite integrals
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Analyzing problems involving definite integrals
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,
📺 Worked example: problem involving definite integral (algebraic)
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Problems involving definite integrals (algebraic)
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,
,
Finding the area between curves expressed as functions of x
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,
📺 Area between a curve and the x-axis
,
,
📺 Area between a curve and the x-axis: negative area
,
,
Area between a curve and the x-axis
,
,
📺 Area between curves
,
,
📺 Worked example: area between curves
,
,
Area between two curves given end points
,
,
Area between two curves
,
,
📺 Composite area between curves
,
,
Finding the area between curves expressed as functions of y
,
,
,
📺 Area between a curve and the 𝘺-axis
,
,
📺 Horizontal area between curves
,
,
Horizontal areas between curves
,
,
Finding the area between curves that intersect at more than two points
,
,
,
Area between curves that intersect at more than two points (calculator-active)
,
,
Volumes with cross sections: squares and rectangles
,
,
,
📺 Volume with cross sections: intro
,
,
Volumes with cross sections: squares and rectangles (intro)
,
,
📺 Volume with cross sections: squares and rectangles (no graph)
,
,
📺 Volume with cross sections perpendicular to y-axis
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,
Volumes with cross sections: squares and rectangles
,
,
Volumes with cross sections: triangles and semicircles
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,
📺 Volume with cross sections: semicircle
,
,
📺 Volume with cross sections: triangle
,
,
Volumes with cross sections: triangles and semicircles
,
,
,
Volume with disc method: revolving around x- or y-axis
,
,
,
📺 Disc method around x-axis
,
,
📺 Generalizing disc method around x-axis
,
,
📺 Disc method around y-axis
,
,
Disc method: revolving around x- or y-axis
,
,
Volume with disc method: revolving around other axes
,
,
,
📺 Disc method rotation around horizontal line
,
,
📺 Disc method rotating around vertical line
,
,
📺 Calculating integral disc around vertical line
,
,
Disc method: revolving around other axes
,
,
Volume with washer method: revolving around x- or y-axis
,
,
,
📺 Solid of revolution between two functions (leading up to the washer method)
,
,
📺 Generalizing the washer method
,
,
Washer method: revolving around x- or y-axis
,
,
Volume with washer method: revolving around other axes
,
,
,
📺 Washer method rotating around horizontal line (not x-axis), part 1
,
,
📺 Washer method rotating around horizontal line (not x-axis), part 2
,
,
📺 Washer method rotating around vertical line (not y-axis), part 1
,
,
📺 Washer method rotating around vertical line (not y-axis), part 2
,
,
Washer method: revolving around other axes
,
,
Calculator-active practice
,
,
,
,
Contextual and analytical applications of integration (calculator-active)
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