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Lecture Videos 1     Krista King  Real Life lore     Calculus Rhapsody

 

Parts

Lecture Notes             YouTube Links

Practices

Part 1

 

 

 

 

 

 

Review

Basic Prealgebra Review  (6 pages)

 

Algebra Review(8 pages)             Equations (2 pages)

 

Linear Equations (6 pages)        Exponents(3 pages)

 

Factorization(4 pages)                 Quadratic Equations  (4 pages)

 

Radicals  (5 pages)                        Log  (4 pages)

 

Domain of a Function   Domain of a Function

 

Piecewise Functions

 

Difference Quotient

 

 

 

 

Practice 1

    

(4 Pagess)

 

Answer 1

 

(1 Page)

Part 2

 

Limits

 

 

Limits and Continuity

 

Finding Limits From a Graph

 

One Sided Limits

 

Finding a Limit of a Piecewise Function by Graphing

 

Squeeze Theorem

 

Limits at Infinity - Basic Idea

 

Average Rate of Change

 

Limits

 

Limits Practice Problems

 

Average Rate of Change

 

 

Practice 2

(4 pages)

 

 

 

Answer 2

 

(1 Page)

Part 3

 

Derivatives

 

 

 

 

Derivatives

 

 

 

 

Derivatives

 

 

 

 

Derivatives

 

 

 

 

Derivatives

 

 

 

 

Derivatives

 

 

 

 

Derivatives

 

 

 

 

Derivatives

 

 

 

 

Derivatives

 

 

 

 

Derivatives

 

 

 

Definition of the Derivative

 

Limit Definition of Derivative Square Root, Fractions

 

Derivative Formulas                    Derivative Rules

 

Power Rule Radical         

 

Derivatives of Radical Functions     Radical

 

How to find The Derivative of a Fraction

 

 

Chain Rule                           Chain Rule

 

Product Rule                       Quotient Rule

 

Derivatives of Exponential  

 

Derivatives of Log 

 

Derivatives of Exponential and Log  

 

Differentiation logarithmic function

 

Derivatives of Trig. function

 

Derivatives of Inverse Trig. function

 

Proof of Derivatives of Inverse Trig. function

 

Implicit Derivative           Implicit Derivative

 

Implicit Derivative            Implicit Derivative

 

Implicit Derivative of Trig

 

Derivatives of hyperbolic. function

 

Derivatives of hyperbolic function

 

Derivatives of inverse hyperbolic function

 

All Types (YouTube)

 

Mean Value Theorem

 

Rolle's Theorem Explained and Mean Value Theorem

 

Intermediate Value Theorem Explained

 

Find the derivative using the chain rule

 

 

 

Practice 3A    

(5 pages)

 

Chain Rule    

(4 pages)

 

 

Product & Quotient Rule    

(4 pages)

 

More Practices      

(7 pages)

 

Practice 3B    

(5 pages)

 

Answer 3B

(1 Page)

 

Part 4

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

 

 

 

Application of derivatives

 

 

 

 

 

 

Application of derivatives

 

Equation of tangent lines

 

Equation of tangent lines

 

Equation of tangent lines to trig functions

 

Curve Sketching

 

1.     What are critical points?

 

2.     Critical Points

 

3.     Finding Critical Numbers

 

4.     Increasing or Decreasing

 

5.     Increasing Decreasing by first derivative

 

6.     Increase or Decrease rational function

 

7.     Finding Absolute Maximum and Minimum Values - Absolute Extrema

 

8.     Finding Inflection Points & Concavity on a Graph

 

9.     First Derivative Test

 

10.  Second Derivative Test

 

11.  Concavity, Inflection Points, and Second Derivative

 

12.  Relative Extrema, Local Maximum and Minimum

 

13.  Local Maximum and Minimum Values

 

14.  Finding Absolute Maximum and Minimum Values

 

15.  Applications Graphs

 

16.  Curve Sketching - First & Second Derivatives -

 

17.  Curve Sketching Using The First And Second Derivatives

 

18.  Graphing       

 

19.  Graphing a Derivative Function

 

Optimization

 

Maximize Profit         Marginal Profit  

 

Marginal Analysis                  Optimization: Fence

 

Fence               Max Volume        Max can Volume   

 

  More Optimizations               Largest area

 

 

Optimization Fence Problems, Cylinder, Volume of Box, Minimum Distance & Norman Window

 

Optimization: cost of materials

 

 

Related Rules

1.     Many examples of Related Rates

 

2.     Related Rates(Ladder)

 

3.     Related Rates(Ladder)

 

4.     Related Rate(Circle) 

 

5.     Relates Rates - Gravel Being Dumped & Conical Tank Problem

 

6.     Related Rates - The Shadow Problem

 

7.     Related Rates - Inflated Balloon & Melting Snowball

 

8.     Related Rates - The Baseball Diamond

 

9.     Related Rates - Airplane Problems

 

10.  Related Rates - Angle of Elevation

 

L’Hopital’s Rule

 

1.     What is L'Hospital's rule?

 

2.     Tricks for Dealing with Indeterminate Forms of Limits

 

3.     Understanding Limits and L'Hospital's Rule

 

4.     L'hospital's Rule Indeterminate Forms

 

5.     L'hopital's rule

 

6.     L'Hospital's Rule Exercises Part 1

 

7.     Tricky L'Hopital's Rule problem

 

8.     Failure of L'Hospital's Rule

 

What is linear approximation

 

1.     What is linear approximation?

 

2.     Linear Approximation

 

3.     Finding The Linearization of a Function

 

4.     Differentials and Derivatives - Local Linearization

 

5.     Linear Approximation, Differentials

 

6.     delta y vs. dy (differential)

 

 

 

Tanget line    

(7 pages)

 

 

 

 

 

 

Increase/Decrease   

(3 pages)

 

Graphing Local MAX/MIN   

(5 pages)

 

 

MIN/MAX Ist Deriv. Test    

(4 pages)

 

 

MIN/MAX 2nd Deriv. Test    

(5 pages)

 

Absolute MIN/MAX    

(4 pages)

 

Concavity    

(7 pages)

 

 

 

 

 

 

 

 

 

 

 

 

Business App    

(14 pages)

 

 

Geomtery     (7 pages)

 

All types of Optimization problems     (17 pages)

 

 

 

 

 

 

 

 

 

 

Related rates

   (8 pages)

 

 

Related rates problems

 

 

 

Related rates problems

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L'Hospital Rule

   (8 pages)

 

 

L’Hospital interactive practice problems

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Practice Oon Linear Approximation    

(21 pages)

 

 

 

 

 

 

 

 

 

 

 

Practice 4     (21 pages)

 

Part 5

Integral

 

 

 

 

Part 5

Integral

 

 

 

 

Part 5

Integral

 

 

 

 

 

Part 5

Integral

 

 

 

 

Part 5

Integral

 

 

 

 

 

Part 5

Integral

 

 

 

 

Part 5

Integral

 

 

 

 

 

Part 5

Integral

 

 

 

 

 

Part 5

Integral

 

 

 

 

 

 

Part 5

Integral

1.     Antiderivatives

 

2.     Antiderivatives

 

3.     Basic integration rules

 

4.     Trigonometric integrals basic examples

 

5.      Basic Integration Rules, Problems, Formulas, Trig Functions

 

6.     Basic Antiderivatives of Trigonometric Functions

 

7.     Integrals Involving Exponential and Logarithmic Functions

 

8.     integrals of sin(x), cos(x), and eˣ

 

9.     Integration of Exponential Functions

 

10.  Lots of Basic Antiderivative

 

11.  Antiderivatives - Trig & Exponential Functions, Fractions, Square Roots, Substitution

 

12.  What Is an Integral?

 

13.  Why do integrals always have a dx?

 

14.  Summation Formulas and Sigma Notation - Calculus

 

15. Area Under A Curve Using Limits Of Sums     Related Practice

 

16.  Riemann Sums - Left Endpoints and Right Endpoints

 

17.   Riemann Sums Midpoint Rule

 

18.  Riemann Sums - Midpoint, Left & Right Endpoints, Area, Definite Integral, Sigma Notation

 

19.  Trapezoidal Rule

 

20.  Trapezoidal Rule & Simpson's Rule

 

21.  Fundamental Theorem of Calculus Part 1

 

22.  Fundamental Theorem of Calculus Part 2

 

23.  Definite Integrals

 

24.  Definite Integral Calculus Examples, Integration

 

25.  Finding the area using the limit definition & sigma notation

 

26.  U-Substitution, how to integrate

 

27.  U-substitution With Definite Integrals

 

28.  U-Substitution Integration,

 

29.  Integrating Exponential Functions By Substitution

 

30.  Integration of Logarithmic Functions By Substitution

 

31.  Improper Integrals

 

32.  Area Between Two Curves

 

33.  Area Between Two Curves & Under Curve - Respect to Y & X

 

34.  A Breathtaking Journey of Integration

 

 

 

 

Antideri. problems with answers

 

Practice on antiderivatives (6 pages)

 

Trig, Expo, logs (4 pages)

 

Interactive antiderivative practices

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Practice on Integral by Sub Part 1 (5 pages)

 

Practice on Integral by Sub Part 2 (16 pages)

 

 

Area between 2 curves  

(9 pages)

 

 

 

 

 

 

 

 

 

 

 

Part 6

Integral  Formulas(1 pages)

 

Integral Practices(5 pages)

 

What is an Integral(YouTube)

 

Basic Integral(YouTube)

Practice 6

(9 pages)

 

Answer 6

(1 Page)

 

 

HW1

 

HW2 (7 pages)

 

Answers

 

HW3

 

HW4

 

 HW5

  

 

 

Real Life lore

 

How deep is your earth?