**KHAN ACADEMY VIDEOS**

CHAPTER 1, 2, & 5

CHAPTER 1, 2, & 5

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**Khan Academy****CHAPTER 1:**

LIMITS

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 TablesPractice 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 SubstitutionYouTube: Limits of Direct Substitution

**YouTube: Undefined Limits by Direct Substitution**

YouTube: Limits by FactoringYouTube: 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 ConjugatesPractice 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 IdentityYouTube: 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 TheoremPractice 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 TablesYouTube: One-Sided Limits from Tables

**YouTube: Connecting Limits and Graphical Behavior**••••••

**Practice Questions: One-Sided Limits from Graphs**

Practice Questions: One-Sided Limits from TablesPractice 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-valuesYouTube: 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 IntervalPractice 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 ExampleYouTube: 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 FractionsYouTube: 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: TrigPractice 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)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**

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**2.1: Tangent Lines & Definition of a Derivative and**

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**2.1A: Alternate Definition of a Derivative**

**Derivative as a concept**

Derivative notation review

Derivative & the direction of a functionDerivative notation review

Derivative & the direction of a function

**Secant lines & average rate of change**

Estimating derivativesEstimating 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)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 definitionFormal 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)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 exampleYouTube: 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 functionDerivative & 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)Secant lines & average rate of change with arbitrary points (with simplification)

**Differentiability at a point: graphical**

Differentiability at a point: algebraicDifferentiability at a point: algebraic

**§**

**2.2: Power Rule**

**Finding tangent line equations using the formal definition of a limit**

Local linearity

Local linearity and differentiabilityLocal linearity

Local linearity and differentiability

**YouTube: Power rule**

__Differentiating polynomials__

Differentiating polynomials example

Tangents of polynomialsDifferentiating polynomials example

Tangents of polynomials

**Negative powers differentiation**

Fractional powers differentiation

Radical functions differentiation introFractional 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 linearityApproximation with local linearity

**Practice Questions: Power Rule**

**Polynomial functions differentiation**

Tangents of polynomialsTangents of polynomials

**Negative powers differentiation**

Fractional powers differentiationFractional 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 & explicitWorked example: Product rule with table

Worked example: Product rule with mixed implicit & explicit

**Quotient rule**

Worked example: Quotient rule with tableWorked example: Quotient rule with table

**Rational functions differentiation**

Linear approximation of a rational functionLinear approximation of a rational function

**••••••**

**Differentiate products**

Product rule with tablesProduct rule with tables

**Differentiate quotients**

Quotient rule with tablesQuotient 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 differentiationIdentifying 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)Derivatives of sec(x) and csc(x)

**Trig functions differentiation**

**••••••**

**Identify composite functions**

Differentiate composite functions (chain rule)

Chain rule with tables

Radical functions differentiationDifferentiate 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 differentiationManipulating 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 resultWorked 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 differentiationManipulating functions before differentiation

**Implicit differentiation**

Differentiate related functionsDifferentiate related functions

**§2.6: Related Rates**

**Applied rate of change: forgetfulness**

Marginal cost & differential calculusMarginal cost & differential calculus

**Related rates intro**

Analyzing related rates problems: expressions

Analyzing related rates problems: equations (Pythagoras)

Analyzing related rates problems: equations (trig)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: balloonRelated 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: equationsAnalyzing related rates problems: equations

**Related rates intro**

Related rates (multiple rates)

Related rates (Pythagorean theorem)

Related rates (advanced)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 differentiation𝑒 as a limit

Derivative of 𝑒ˣ

Exponential functions differentiation intro

Exponential functions differentiation

**Derivative of eᶜᵒˢˣ⋅cos(eˣ)**

**••••••**

**Exponential functions differentiation intro**

Exponential functions differentiationExponential 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 propertiesLogarithmic 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 differentiationLogarithmic functions differentiation