Business Calculus

Kevin Hopkins, Aug 9, 2016

A workbook created in Fall 2016 to use for Business Calculus. Most of the worksheets in this book also appear in other places. Feel free to email me at khopkins@sbuniv.edu if you think there is an error in any worksheet (please be as specific as possible-a screenshot of the error would be most helpful). I tested them quite a bit, but there could be things that come up that I didn’t encounter in my testing. I would also like to know if you used these and found them useful. If so, can you think of ways I could expand them? Some are "self check" and others have you enter the answer and GeoGebra does the checking. I would encourage you to watch an introductory video ([url]http://youtu.be/zzz42Y_qZJw[/url]) to get a feel for how the worksheets operate.

Table of Contents

  1. Exam 1 Material
    1. Representing a Function in Four Ways-Section 1.1
    2. Tables as Functions: Solving and Evaluating-Section 1.1
    3. Graphs as Functions: Solving and Evaluating-Section 1.1
    4. Formulas as Functions: Solving and Evaluating-Section 1.1
    5. Basic Toolkit Functions-Section 1.1
    6. Graphing Functions-Section 1.1
    7. Finding Domain and Range of Functions: Section 1.1
    8. Algebra of Function
    9. Shifts or Translations-Section 1.2
    10. Reflections-Section 1.2
    11. Stretch/Compression-Section 1.2
    12. Simpler Determining the Transformation-Section 1.2
    13. More Difficulty Determine Transformation-Section 1.2
    14. Slope of a Line Given Two points-Section 1.3
    15. Slope Intercept form from Table-Section 1.3
    16. What do m and b do to graph of a line-Section 1.3
    17. Line Equation-Section 1.3
    18. Equation of Line from points-Section 1.3
    19. Matching graph with line equation-Section 1.3
    20. Simplify Expressions with Exponents-Section 1.4
    21. Simplify Expressions with Exponents, More Difficult-Section 1.4
    22. Simplify Expressions, More Complicated-Section 1.4
    23. Shifted Form of Quadratic-Section 1.5
    24. Demonstration-Quadratics-Section 1.5
    25. Quadratics and Parabolas-Section 1.5
    26. Polynomial Inequalities-Section 1.6
    27. Graphs of the Exponential-Section 1.7
    28. Matching Exponential Equations-Section 1.7
    29. Compounding Periods-Section 1.7
    30. Compound Interest-Section 1.7
    31. Logarithm to Exponential-Section 1.8
    32. Exponential to Logarithm-Section 1.8
    33. Solving Exponential Equations-Section 1.8
  2. Exam 2 Material
    1. Tangent Lines as Limits of Secant Lines with slider-Intro to Chapter 2
    2. Tangent Lines as Limits of Secant Lines/Input-Intro to Chapter 2
    3. Limits of Piecewise Functions-Section 2.1
    4. Estimating Limits-User enter the Function-Section 2.1
    5. Estimating Limits from Given Functions-Section 2.1
    6. Section 2.2-Sketching Graph of Derivative
    7. Section 2.2-Work with difference quotient
    8. Derivative Practice-Sections 2.3-2.5
    9. Section 2.7 & 2.8 Busn Calc-Increasing versus Decreasing
  3. Exam 3 Material
    1. Section 2.6-Concavity
    2. Section 2.6-Interpretations of Concavity
    3. Section 2.9-Applied Optimization
    4. Section 3.1-Areas
    5. Section 3.1-Riemann Sums
    6. Section 3.2-Graphing f from graph of f'(x).
    7. Section 3.2-Graphing f from graph of "random" f'(x).
    8. Section 3.2-Checking antiderivatives and using Fundamental Theorem
    9. Section 3.3-Antiderivatives-Multiple Choice Problems
    10. Section 3.3-Indefinite Integral
    11. Section 3.3 Antiderivative of Formulas
  4. Exam Review
    1. Worksheet for Exam Review
    2. Worksheet for three types of shared activities

1.

Exam 1 Material

Sections 1.1 to 1.8. Functions.

  • 1. Representing a Function in Four Ways-Section 1.1
  • 2. Tables as Functions: Solving and Evaluating-Section 1.1
  • 3. Graphs as Functions: Solving and Evaluating-Section 1.1
  • 4. Formulas as Functions: Solving and Evaluating-Section 1.1
  • 5. Basic Toolkit Functions-Section 1.1
  • 6. Graphing Functions-Section 1.1
  • 7. Finding Domain and Range of Functions: Section 1.1
  • 8. Algebra of Function
  • 9. Shifts or Translations-Section 1.2
  • 10. Reflections-Section 1.2
  • 11. Stretch/Compression-Section 1.2
  • 12. Simpler Determining the Transformation-Section 1.2
  • 13. More Difficulty Determine Transformation-Section 1.2
  • 14. Slope of a Line Given Two points-Section 1.3
  • 15. Slope Intercept form from Table-Section 1.3
  • 16. What do m and b do to graph of a line-Section 1.3
  • 17. Line Equation-Section 1.3
  • 18. Equation of Line from points-Section 1.3
  • 19. Matching graph with line equation-Section 1.3
  • 20. Simplify Expressions with Exponents-Section 1.4
  • 21. Simplify Expressions with Exponents, More Difficult-Section 1.4
  • 22. Simplify Expressions, More Complicated-Section 1.4
  • 23. Shifted Form of Quadratic-Section 1.5
  • 24. Demonstration-Quadratics-Section 1.5
  • 25. Quadratics and Parabolas-Section 1.5
  • 26. Polynomial Inequalities-Section 1.6
  • 27. Graphs of the Exponential-Section 1.7
  • 28. Matching Exponential Equations-Section 1.7
  • 29. Compounding Periods-Section 1.7
  • 30. Compound Interest-Section 1.7
  • 31. Logarithm to Exponential-Section 1.8
  • 32. Exponential to Logarithm-Section 1.8
  • 33. Solving Exponential Equations-Section 1.8

1.1.

Representing a Function in Four Ways-Section 1.1

Four Ways to Represent a Function
– Kevin Hopkins

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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1.17.

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1.18.

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1.19.

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1.20.

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1.21.

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1.22.

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1.23.

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1.24.

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1.25.

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1.26.

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1.27.

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1.28.

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1.29.

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1.30.

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1.31.

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1.32.

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1.33.

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2.

Exam 2 Material

Sections 2.1-2.11 Limits and Derivatives

  • 1. Tangent Lines as Limits of Secant Lines with slider-Intro to Chapter 2
  • 2. Tangent Lines as Limits of Secant Lines/Input-Intro to Chapter 2
  • 3. Limits of Piecewise Functions-Section 2.1
  • 4. Estimating Limits-User enter the Function-Section 2.1
  • 5. Estimating Limits from Given Functions-Section 2.1
  • 6. Section 2.2-Sketching Graph of Derivative
  • 7. Section 2.2-Work with difference quotient
  • 8. Derivative Practice-Sections 2.3-2.5
  • 9. Section 2.7 & 2.8 Busn Calc-Increasing versus Decreasing

2.1.

Tangent Lines as Limits of Secant Lines with slider-Intro to Chapter 2

Secant lines as an approximation for tangent lines.
– Kevin Hopkins

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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3.

Exam 3 Material

Section 2.6-4.2: Concavity, Applied Optimization, Integral and Functions of 2 variables (may not get to section 4.2)

  • 1. Section 2.6-Concavity
  • 2. Section 2.6-Interpretations of Concavity
  • 3. Section 2.9-Applied Optimization
  • 4. Section 3.1-Areas
  • 5. Section 3.1-Riemann Sums
  • 6. Section 3.2-Graphing f from graph of f'(x).
  • 7. Section 3.2-Graphing f from graph of "random" f'(x).
  • 8. Section 3.2-Checking antiderivatives and using Fundamental Theorem
  • 9. Section 3.3-Antiderivatives-Multiple Choice Problems
  • 10. Section 3.3-Indefinite Integral
  • 11. Section 3.3 Antiderivative of Formulas

3.1.

Section 2.6-Concavity

– Kevin Hopkins

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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4.

Exam Review

  • 1. Worksheet for Exam Review
  • 2. Worksheet for three types of shared activities

4.1.

Worksheet for Exam Review

Unit Exam Review
[color=#ff0000][b][size=150]You have a review sheet for the unit exam. I want you to work on this for 30-40 minutes in class, either separately or in a group of 2-3 if you are comfortable forming a group. Answer at least 2 of the questions below. About 8:50, we will look as a class at the results to see solutions to some problems or problems that people feel they need to see.[/size][/b][/color]
Solution for one Question--Identify which Question by number and give the solution to the question you are most confident on.
Please write a short answer to one of the review sheet questions. Indicate which question.
Solution for a second Question-Identify Question and give the solution to the Question you are second most confident on.
Please write a short answer to second one of the review sheet questions. Indicate which question.
Solution for another Question-Identify Question and give the solution to the Question another question.
Please write a short answer to second one of the review sheet questions. Indicate which question.
[size=150]Id[/size][size=150]entify a question you are struggling with. Specifically, what seems to be the difficulty for you?[/size]
– Kevin Hopkins

4.2.

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Information