Calculus I with Apex Calculus

Kevin Hopkins, Jan 25, 2017

A workbook created in Spring 2017 to use for Calculus I using Apex Calculus textbook. 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-Review of Algebra and Limits
    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 with Trig Added
    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. Logarithm to Exponential-Section 1.8
    31. Exponential to Logarithm-Section 1.8
    32. Solving Exponential Equations-Section 1.8
    33. Trig Review
    34. Section 1.1-Piecewise Defined Functions
    35. Section 1.1-Limits using numerical method
    36. Section 1.1-Functions with no limit at a point
    37. Section 1.1-Estimating Limits from Given Functions
    38. Section 1.1 and 1.3-Work with difference quotient
    39. Section 1.4-One-sided limits
    40. Section 1.5-The Intermediate Value Theorem
  2. Exam 2 Material-Section 1.6, 1.2, Chapter 2
    1. Section 1.6-Limit as x approaches infinity
    2. Section 1.6-Horizontal asymptotes
    3. Section 1.2-Precise definition of the limit
    4. Section 1.6-Precise definition of the limit as x approaches infinity
    5. Section 1.6-Precise definition of infinite limit
    6. Section 1.1, 4, and 2.1-Secant lines compared to tangent lines
    7. Section 2.1-Limits with Difference Quotients
    8. Section 2.1 in Apex-Sketching Graph of Derivative
    9. Section 2.3-2.5 from Apex-Derivative Practice
    10. Section 2.5-Chain Rule
    11. Section 2.6-Implicit Differentiation
    12. Section 2.6-Implicit Differentiation
  3. Exam 3 Material-Section 2.7-Section 4.4
    1. Section 2.7 in Apex-Inverse Functions
    2. Section 3.1 Apex-Absolute Extreme Values
    3. Section 3.2-Mean Value Theorem
    4. Section 3.3 Apex-Increasing versus Decreasing
    5. Section 3.4 Apex-Concavity
    6. Section 3.5-Curve Sketching
    7. Section 4.1 Apex-Newton's Method
    8. Section 4.2: Apex-Related Rates-Ladder Falling
    9. Section 4.2 Apex-Related Rates-Man Walking
    10. Section 4.2 Apex-Related Rates-Rotating Spotlight
    11. Section 4.2 Apex-Related Rates-Boat Pulling
    12. Section 4.3 Apex-Applied Max Min
    13. Section 4.4 Apex-Differential
  4. Exam 4 Material-Section 5.1-5.5, 6.1, 7.1-7.3
    1. Apex Section 5.1-Antiderivatives-Multiple Choice Problems
    2. Apex Section 5.1-Indefinite Integral
    3. Apex Section 5.2-Areas
    4. Apex Section 5.3-Riemann Sums
    5. Apex Section 5.3-Riemann Sums-Random Width Intervals
    6. Apex Section 5.4-Part 2 of Fundamental Theorem of Calculus
    7. Apex Section 5.4: Part 1 of Fundamental Theorem of Calculus
    8. Apex Section 5.5-Numerical integration
    9. Apex Section 6.1-Integration using substitution
    10. Apex Section 7.1-Areas
    11. Apex Section 7.2-Method of Disks
    12. Apex Section 7.2-Method of Washers
    13. Apex Section 5.3-Method of Shells

1.

Exam 1 Material-Review of Algebra and Limits

  • 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 with Trig Added
  • 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. Logarithm to Exponential-Section 1.8
  • 31. Exponential to Logarithm-Section 1.8
  • 32. Solving Exponential Equations-Section 1.8
  • 33. Trig Review
  • 34. Section 1.1-Piecewise Defined Functions
  • 35. Section 1.1-Limits using numerical method
  • 36. Section 1.1-Functions with no limit at a point
  • 37. Section 1.1-Estimating Limits from Given Functions
  • 38. Section 1.1 and 1.3-Work with difference quotient
  • 39. Section 1.4-One-sided limits
  • 40. Section 1.5-The Intermediate Value Theorem

1.1.

Representing a Function in Four Ways-Section 1.1

Four Ways to Represent a Function
– Kevin Hopkins

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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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1.34.

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1.35.

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1.36.

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1.37.

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1.38.

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1.39.

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1.40.

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2.

Exam 2 Material-Section 1.6, 1.2, Chapter 2

  • 1. Section 1.6-Limit as x approaches infinity
  • 2. Section 1.6-Horizontal asymptotes
  • 3. Section 1.2-Precise definition of the limit
  • 4. Section 1.6-Precise definition of the limit as x approaches infinity
  • 5. Section 1.6-Precise definition of infinite limit
  • 6. Section 1.1, 4, and 2.1-Secant lines compared to tangent lines
  • 7. Section 2.1-Limits with Difference Quotients
  • 8. Section 2.1 in Apex-Sketching Graph of Derivative
  • 9. Section 2.3-2.5 from Apex-Derivative Practice
  • 10. Section 2.5-Chain Rule
  • 11. Section 2.6-Implicit Differentiation
  • 12. Section 2.6-Implicit Differentiation

2.1.

Section 1.6-Limit as x approaches infinity

This interactive figure allows you to explore the concept of the limit of [math]f\left(x\right)[/math] as [math]x\to\infty[/math]. Drag the [color=#ff0000]red point[/color] on the [math]x[/math]-axis to the right to simulate [math]x\to\infty[/math]. You can use the slider to select different example functions or enter your own. You can change the maximum value on the [math]x[/math]-axis with the[color=#0000ff] blue button[/color]. You can see the [color=#38761d]green point[/color] on the function and determine what value the function seems to be approaching or you can use the [color=#38761d]function value[/color] given in the right side of the figure. Not every function has a limit as [math]x\to\infty[/math].
[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]
– Kevin Hopkins

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2.3.

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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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2.10.

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2.11.

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2.12.

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3.

Exam 3 Material-Section 2.7-Section 4.4

  • 1. Section 2.7 in Apex-Inverse Functions
  • 2. Section 3.1 Apex-Absolute Extreme Values
  • 3. Section 3.2-Mean Value Theorem
  • 4. Section 3.3 Apex-Increasing versus Decreasing
  • 5. Section 3.4 Apex-Concavity
  • 6. Section 3.5-Curve Sketching
  • 7. Section 4.1 Apex-Newton's Method
  • 8. Section 4.2: Apex-Related Rates-Ladder Falling
  • 9. Section 4.2 Apex-Related Rates-Man Walking
  • 10. Section 4.2 Apex-Related Rates-Rotating Spotlight
  • 11. Section 4.2 Apex-Related Rates-Boat Pulling
  • 12. Section 4.3 Apex-Applied Max Min
  • 13. Section 4.4 Apex-Differential

3.1.

Section 2.7 in Apex-Inverse Functions

See the relation between points, graphs, and derivatives on f and its inverse.
– Kevin Hopkins

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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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3.12.

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3.13.

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4.

Exam 4 Material-Section 5.1-5.5, 6.1, 7.1-7.3

  • 1. Apex Section 5.1-Antiderivatives-Multiple Choice Problems
  • 2. Apex Section 5.1-Indefinite Integral
  • 3. Apex Section 5.2-Areas
  • 4. Apex Section 5.3-Riemann Sums
  • 5. Apex Section 5.3-Riemann Sums-Random Width Intervals
  • 6. Apex Section 5.4-Part 2 of Fundamental Theorem of Calculus
  • 7. Apex Section 5.4: Part 1 of Fundamental Theorem of Calculus
  • 8. Apex Section 5.5-Numerical integration
  • 9. Apex Section 6.1-Integration using substitution
  • 10. Apex Section 7.1-Areas
  • 11. Apex Section 7.2-Method of Disks
  • 12. Apex Section 7.2-Method of Washers
  • 13. Apex Section 5.3-Method of Shells

4.1.

Apex Section 5.1-Antiderivatives-Multiple Choice Problems

– Kevin Hopkins

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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4.13.

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Information