KHAN ACADEMY VIDEOS
CHAPTER 1, 2, & 5
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CHAPTER 1:
LIMITS
§1.2: Introduction to Limits (Review)
YouTube: Limits Intro
YouTube: Approximating Limits
••••••
Practice Questions: Limits from Graphs
Practice Questions: Creating Tables for Approximating Limits
Practice Questions: Limits from Tables
§1.3: Properties of Limits
YouTube: Limits from Graphs
YouTube: Approximating Limits using Tables
YouTube: Estimating Limits from Tables
YouTube: Limit Properties
YouTube: Limits of Combined Functions
YouTube: Limits of Composite Functions
YouTube: Limits of Direct Substitution
YouTube: Undefined Limits by Direct Substitution
YouTube: Limits by Factoring
YouTube: Limits by Rationalizing
••••••
Practice Questions: Connecting Limits and Graphical Behavior
Practice Questions: Limits of Combine Functions
Practice Questions: Limits of Composite Functions
Practice Questions: Direct Substitution
Practice Questions: Direct Substitution that DNE
Practice Questions: Limits of Factoring
Practice Questions: Limits using Conjugates
§1.3A: Trig Limits
YouTube: Limits of Trig Functions
YouTube: Trig Limits Using Pythagorean Identity
YouTube: Trig Limits Using Double Angle Identity
YouTube: Limit of sin(x)/x
YouTube: Squeeze Theorem Intro
YouTube: Squeeze Theorem Example
••••••
Practice Questions: Limits of Trig Functions
Practice Questions: Limits of Trig Identities
Practice Questions: Squeeze Theorem
§1.4: One-Sided Limits
YouTube: One-Sided Limits from Graphs
YouTube: One-Sided Limits from Graphs: Asymptotes
YouTube: One-Sided Limits from Tables
YouTube: Connecting Limits and Graphical Behavior
••••••
Practice Questions: One-Sided Limits from Graphs
Practice Questions: One-Sided Limits from Tables
§1.4A: Continuity
YouTube: Continuity at a Point
YouTube: Worked Example of Continuity at a Point
YouTube: Continuity over an Interval
YouTube: Functions Continuous on all Real Numbers
YouTube: Functions Continuous at Specific x-values
YouTube: Types of Discontinuities
YouTube: Analyzing Functions of Discontinuities (Continuous)
YouTube: Analyzing Functions of Discontinuities (Discontinuous)
YouTube: Removing Discontinuities (Factoring)
YouTube: Removing Discontinuities (Rationalization)
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Practice Questions: Continuity at a Point
Practice Questions: Continuity at an Interval
Practice Questions: Continuity and Common Functions
Practice Questions: Classify Discontinuities
Practice Questions: Analyzing functions for discontinuities: algebraic
Practice Questions: Removable discontinuities
§1.4B: Intermediate Value Theorem
••••••
YouTube: IVT
YouTube: Conditions of IVT
YouTube: Conditions of IVT on a graph
YouTube: IVT Example
§1.5: Infinite Limits
YouTube: Infinite Limits
YouTube: Infinite Limit and Asymptotes
YouTube: Analyzing Unbounded Limits of Rational Functions
YouTube: Analyzing Unbounded Limits of Mixed Fractions
••••••
Practice Questions: Analyze Unbounded Limits
Practice Questions: Limits of Rational Functions
Practice Questions: Limits of Rational Functions: Radicals
Practice Questions: Limits of Rational Functions: Trig
§3.5: Limits at Infinity
YouTube: Functions with the Same Limit at Infinity
YouTube: Limits at Infinity of Rational Functions (Part 1)
YouTube: Limits at Infinity of Rational Functions (Part 2)
YouTube: Limits at Infinity of Rational Functions (Odd Powers)
YouTube: Limits at Infinity of Rational Functions (Even Powers)
YouTube: Limits at Infinity of Rational Functions (Trig)
YouTube: Limits at Infinity of Rational Functions (Trig: Limit DE)
••••••
Practice Questions: Infinite Limits and Graphs
YouTube: Limits Intro
YouTube: Approximating Limits
••••••
Practice Questions: Limits from Graphs
Practice Questions: Creating Tables for Approximating Limits
Practice Questions: Limits from Tables
§1.3: Properties of Limits
YouTube: Limits from Graphs
YouTube: Approximating Limits using Tables
YouTube: Estimating Limits from Tables
YouTube: Limit Properties
YouTube: Limits of Combined Functions
YouTube: Limits of Composite Functions
YouTube: Limits of Direct Substitution
YouTube: Undefined Limits by Direct Substitution
YouTube: Limits by Factoring
YouTube: Limits by Rationalizing
••••••
Practice Questions: Connecting Limits and Graphical Behavior
Practice Questions: Limits of Combine Functions
Practice Questions: Limits of Composite Functions
Practice Questions: Direct Substitution
Practice Questions: Direct Substitution that DNE
Practice Questions: Limits of Factoring
Practice Questions: Limits using Conjugates
§1.3A: Trig Limits
YouTube: Limits of Trig Functions
YouTube: Trig Limits Using Pythagorean Identity
YouTube: Trig Limits Using Double Angle Identity
YouTube: Limit of sin(x)/x
YouTube: Squeeze Theorem Intro
YouTube: Squeeze Theorem Example
••••••
Practice Questions: Limits of Trig Functions
Practice Questions: Limits of Trig Identities
Practice Questions: Squeeze Theorem
§1.4: One-Sided Limits
YouTube: One-Sided Limits from Graphs
YouTube: One-Sided Limits from Graphs: Asymptotes
YouTube: One-Sided Limits from Tables
YouTube: Connecting Limits and Graphical Behavior
••••••
Practice Questions: One-Sided Limits from Graphs
Practice Questions: One-Sided Limits from Tables
§1.4A: Continuity
YouTube: Continuity at a Point
YouTube: Worked Example of Continuity at a Point
YouTube: Continuity over an Interval
YouTube: Functions Continuous on all Real Numbers
YouTube: Functions Continuous at Specific x-values
YouTube: Types of Discontinuities
YouTube: Analyzing Functions of Discontinuities (Continuous)
YouTube: Analyzing Functions of Discontinuities (Discontinuous)
YouTube: Removing Discontinuities (Factoring)
YouTube: Removing Discontinuities (Rationalization)
••••••
Practice Questions: Continuity at a Point
Practice Questions: Continuity at an Interval
Practice Questions: Continuity and Common Functions
Practice Questions: Classify Discontinuities
Practice Questions: Analyzing functions for discontinuities: algebraic
Practice Questions: Removable discontinuities
§1.4B: Intermediate Value Theorem
••••••
YouTube: IVT
YouTube: Conditions of IVT
YouTube: Conditions of IVT on a graph
YouTube: IVT Example
§1.5: Infinite Limits
YouTube: Infinite Limits
YouTube: Infinite Limit and Asymptotes
YouTube: Analyzing Unbounded Limits of Rational Functions
YouTube: Analyzing Unbounded Limits of Mixed Fractions
••••••
Practice Questions: Analyze Unbounded Limits
Practice Questions: Limits of Rational Functions
Practice Questions: Limits of Rational Functions: Radicals
Practice Questions: Limits of Rational Functions: Trig
§3.5: Limits at Infinity
YouTube: Functions with the Same Limit at Infinity
YouTube: Limits at Infinity of Rational Functions (Part 1)
YouTube: Limits at Infinity of Rational Functions (Part 2)
YouTube: Limits at Infinity of Rational Functions (Odd Powers)
YouTube: Limits at Infinity of Rational Functions (Even Powers)
YouTube: Limits at Infinity of Rational Functions (Trig)
YouTube: Limits at Infinity of Rational Functions (Trig: Limit DE)
••••••
Practice Questions: Infinite Limits and Graphs
CHAPTER 2:
DERIVATIVES
§2.1: Tangent Lines & Definition of a Derivative and §2.1A: Alternate Definition of a Derivative
Derivative as a concept
Derivative notation review
Derivative & the direction of a function
Secant lines & average rate of change
Estimating derivatives
Secant line with arbitrary difference
Secant line with arbitrary point
Secant line with arbitrary difference (with simplification)
Secant line with arbitrary point (with simplification)
Formal definition of the derivative as a limit
Formal and alternate form of the derivative
Worked example: Derivative as a limit
Worked example: Derivative from limit expression
The derivative of x² at x=3 using the formal definition
The derivative of x² at any point using the formal definition
Differentiability and continuity
Differentiability at a point: graphical
Differentiability at a point: algebraic (function is differentiable)
Differentiability at a point: algebraic (function isn't differentiable)
YouTube: Basic differentiation rules (Part 1)
YouTube: Basic differentiation rules (Part 2)
YouTube: Differentiating linear functions
YouTube: Basic differentiation rules example
••••••
Secant lines & average rate of change
Estimate derivatives
Derivative as a limit
Practice Questions: Differentiating linear functions
Practice Questions: Basic differentiation rules
Derivative as slope of curve
Derivative & the direction of a function
Secant lines & average rate of change with arbitrary points
Secant lines & average rate of change with arbitrary points (with simplification)
Differentiability at a point: graphical
Differentiability at a point: algebraic
§2.2: Power Rule
Finding tangent line equations using the formal definition of a limit
Local linearity
Local linearity and differentiability
YouTube: Power rule
Differentiating polynomials
Differentiating polynomials example
Tangents of polynomials
Negative powers differentiation
Fractional powers differentiation
Radical functions differentiation intro
Worked example: Tangent to the graph of 1/x
Derivatives of sin(x) and cos(x)
Worked example: Sine & cosine differentiation
••••••
The derivative & tangent line equations
Approximation with local linearity
Practice Questions: Power Rule
Polynomial functions differentiation
Tangents of polynomials
Negative powers differentiation
Fractional powers differentiation
Radical functions differentiation intro
Sine & cosine differentiation
§2.3: Product and Quotient Rule
Product rule
Worked example: Product rule with table
Worked example: Product rule with mixed implicit & explicit
Quotient rule
Worked example: Quotient rule with table
Rational functions differentiation
Linear approximation of a rational function
••••••
Differentiate products
Product rule with tables
Differentiate quotients
Quotient rule with tables
Rational functions differentiation
§2.4: Chain Rule
Chain rule
Identifying composite functions
Worked example: Differentiating cos³(x) using the chain rule
Worked example: Differentiating √(3x²-x) using the chain rule
Common chain rule misunderstandings
Worked example: Chain rule with table
Radical functions differentiation
Derivatives of tan(x) and cot(x)
Derivatives of sec(x) and csc(x)
Trig functions differentiation
••••••
Identify composite functions
Differentiate composite functions (chain rule)
Chain rule with tables
Radical functions differentiation
Trig functions differentiation intro
Trig functions differentiation
§2.5: Implicit Differentiation
Differentiating functions: Find the error
Manipulating functions before differentiation
Implicit differentiation
Worked example: Implicit differentiation
Worked example: Evaluating derivative with implicit differentiation
Differentiating related functions intro
Differentiating related functions
Showing explicit and implicit differentiation give same result
••••••
Differentiating functions: Find the error
Manipulating functions before differentiation
Implicit differentiation
Differentiate related functions
§2.6: Related Rates
Applied rate of change: forgetfulness
Marginal cost & differential calculus
Related rates intro
Analyzing related rates problems: expressions
Analyzing related rates problems: equations (Pythagoras)
Analyzing related rates problems: equations (trig)
Related rates: Approaching cars
Related rates: Falling ladder
Related rates: water pouring into a cone
Related rates: shadow
Related rates: balloon
••••••
Applied rates of change
Analyzing related rates problems: expressions
Analyzing related rates problems: equations
Related rates intro
Related rates (multiple rates)
Related rates (Pythagorean theorem)
Related rates (advanced)
Derivative as a concept
Derivative notation review
Derivative & the direction of a function
Secant lines & average rate of change
Estimating derivatives
Secant line with arbitrary difference
Secant line with arbitrary point
Secant line with arbitrary difference (with simplification)
Secant line with arbitrary point (with simplification)
Formal definition of the derivative as a limit
Formal and alternate form of the derivative
Worked example: Derivative as a limit
Worked example: Derivative from limit expression
The derivative of x² at x=3 using the formal definition
The derivative of x² at any point using the formal definition
Differentiability and continuity
Differentiability at a point: graphical
Differentiability at a point: algebraic (function is differentiable)
Differentiability at a point: algebraic (function isn't differentiable)
YouTube: Basic differentiation rules (Part 1)
YouTube: Basic differentiation rules (Part 2)
YouTube: Differentiating linear functions
YouTube: Basic differentiation rules example
••••••
Secant lines & average rate of change
Estimate derivatives
Derivative as a limit
Practice Questions: Differentiating linear functions
Practice Questions: Basic differentiation rules
Derivative as slope of curve
Derivative & the direction of a function
Secant lines & average rate of change with arbitrary points
Secant lines & average rate of change with arbitrary points (with simplification)
Differentiability at a point: graphical
Differentiability at a point: algebraic
§2.2: Power Rule
Finding tangent line equations using the formal definition of a limit
Local linearity
Local linearity and differentiability
YouTube: Power rule
Differentiating polynomials
Differentiating polynomials example
Tangents of polynomials
Negative powers differentiation
Fractional powers differentiation
Radical functions differentiation intro
Worked example: Tangent to the graph of 1/x
Derivatives of sin(x) and cos(x)
Worked example: Sine & cosine differentiation
••••••
The derivative & tangent line equations
Approximation with local linearity
Practice Questions: Power Rule
Polynomial functions differentiation
Tangents of polynomials
Negative powers differentiation
Fractional powers differentiation
Radical functions differentiation intro
Sine & cosine differentiation
§2.3: Product and Quotient Rule
Product rule
Worked example: Product rule with table
Worked example: Product rule with mixed implicit & explicit
Quotient rule
Worked example: Quotient rule with table
Rational functions differentiation
Linear approximation of a rational function
••••••
Differentiate products
Product rule with tables
Differentiate quotients
Quotient rule with tables
Rational functions differentiation
§2.4: Chain Rule
Chain rule
Identifying composite functions
Worked example: Differentiating cos³(x) using the chain rule
Worked example: Differentiating √(3x²-x) using the chain rule
Common chain rule misunderstandings
Worked example: Chain rule with table
Radical functions differentiation
Derivatives of tan(x) and cot(x)
Derivatives of sec(x) and csc(x)
Trig functions differentiation
••••••
Identify composite functions
Differentiate composite functions (chain rule)
Chain rule with tables
Radical functions differentiation
Trig functions differentiation intro
Trig functions differentiation
§2.5: Implicit Differentiation
Differentiating functions: Find the error
Manipulating functions before differentiation
Implicit differentiation
Worked example: Implicit differentiation
Worked example: Evaluating derivative with implicit differentiation
Differentiating related functions intro
Differentiating related functions
Showing explicit and implicit differentiation give same result
••••••
Differentiating functions: Find the error
Manipulating functions before differentiation
Implicit differentiation
Differentiate related functions
§2.6: Related Rates
Applied rate of change: forgetfulness
Marginal cost & differential calculus
Related rates intro
Analyzing related rates problems: expressions
Analyzing related rates problems: equations (Pythagoras)
Analyzing related rates problems: equations (trig)
Related rates: Approaching cars
Related rates: Falling ladder
Related rates: water pouring into a cone
Related rates: shadow
Related rates: balloon
••••••
Applied rates of change
Analyzing related rates problems: expressions
Analyzing related rates problems: equations
Related rates intro
Related rates (multiple rates)
Related rates (Pythagorean theorem)
Related rates (advanced)
CHAPTER 5:
DERIVATIVES OF TRANS. FUNCTIONS
§5.1: Derivatives of Natural Bases
𝑒 and compound interest
𝑒 as a limit
Derivative of 𝑒ˣ
Exponential functions differentiation intro
Exponential functions differentiation
Derivative of eᶜᵒˢˣ⋅cos(eˣ)
••••••
Exponential functions differentiation intro
Exponential functions differentiation
§5.4: Derivatives of Natural Logs and §5.5: Log Derivatives
Derivative of ln(x)
Logarithmic functions differentiation intro
Logarithmic functions differentiation
Derivative of ln(√x)
Derivative of sin(ln(x²))
Differentiating logarithmic functions using log properties
••••••
Logarithmic functions differentiation intro
Logarithmic functions differentiation
𝑒 and compound interest
𝑒 as a limit
Derivative of 𝑒ˣ
Exponential functions differentiation intro
Exponential functions differentiation
Derivative of eᶜᵒˢˣ⋅cos(eˣ)
••••••
Exponential functions differentiation intro
Exponential functions differentiation
§5.4: Derivatives of Natural Logs and §5.5: Log Derivatives
Derivative of ln(x)
Logarithmic functions differentiation intro
Logarithmic functions differentiation
Derivative of ln(√x)
Derivative of sin(ln(x²))
Differentiating logarithmic functions using log properties
••••••
Logarithmic functions differentiation intro
Logarithmic functions differentiation
