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Learning Guide Unit 3 -MATH 1211
Calculus (University of the People)
Studocu is not sponsored or endorsed by any college or university
Learning Guide Unit 3 -MATH 1211
Calculus (University of the People)
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MATH 1211-01 Calculus - AY2023-T3
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MATH 1211-01 - AY2023-T3
9 February - 15 February
Learning Guide Unit 3
Learning Guide Unit 3
Learning Guide Unit 3
Overview
Unit 3: Derivative of a function, Derivative rules of Algebraic, and Trigonometric Functions including Power, Sum, Difference, Product, and Quotient rules
Topics:
Limit Definition of Derivative
Derivative as a Function
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Derivative Rules
Derivatives as a Rates of Charge
Derivatives of Trigonometric Functions
Derivatives of Exponential and Logarithm Functions
Learning Objectives:
By the end of this Unit, you will be able to:
Recognize the limit definition of a derivative.
Apply the derivative rules to the functions.
Explain derivatives as a rate of change
Determine the derivatives of trigonometric, exponential, and logarithmic functions
Tasks:
Read the Learning Guide and Reading Assignments
Complete and submit the Learning Journal
Take the Self-Quiz
Take the Graded Quiz
Introduction
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Further critical concepts in calculus are addressed here. The Hennessey Venom GT is one of the fastest cars in the world. In 2014, it reached a record-setting speed of 270.49 mph. It can go from
0 to 200 mph in 14.51 seconds. The techniques in this chapter can be used to calculate how the acceleration of the Venom achieves in this feat.
Calculating velocity and changes in velocity are important uses of calculus, but it is far more widespread than that. Calculus is important in all branches of mathematics, science, and engineering, and it is critical to analysis in business and health as well. In this unit, we explore one of the main tools of calculus, the derivative, and show convenient ways to calculate derivatives. We apply these rules to a variety of functions in this unit so that we can then explore applications of these techniques. Downloaded by Whitney turner (ct8682126@gmail.com)
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You will find it very helpful to memorize the derivatives of all the basic functions including the trigonometric functions (especially sine and cosine). We will also introduce the limit definition of the derivative here. You should familiarize yourself with all the definitions and the derivative rules.
The information in this introduction was obtained from Openstax and the LibreText Project. LibreTexts content is licensed by CC BY-NC-SA 3.0
. Legal
Reading Assignment
1. Herman, E. & Strang, G. (2020).
Calculus volume 1
. OpenStacks. Rice University.
Read Chapter 3, pages 215-289 o
sections 3.1, 3.2, 3.3, 3.4, and 3.5
Review the completed examples to understand the concepts and then complete some problems on your own. Review and practice will contribute to your success in this course.
You should attempt the problems in the book as indicated, and you are allowed to use the book and other resources to understand how to answer the problems You are welcome to ask about these in the discussion forum.
o
3.1 #’s 3, 13, 23, 27, 31, 45
o
3.2 #’s 54–63, 64, 75, 79, 85, 99
o
3.3 #’s 109, 117, 119, 127, 133, 141
o
3.4 #’s 153, 161, 163
o
3.5 #’s 175, 177, 181, 187, 197, 203
2. The derivative as a function.
(n.d.). Geogebra. https://www.geogebra.org/m/MeMdCUEm
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Explore derivative of functions with this Java applet
3. Changing a coefficient in polynomials of low degree. (n.d.). WOLFRAM Demonstrations Project. https://demonstrations.wolfram.com/ChangingACoefficientInPolynomialsOfLowD
egree/
Explore different graphs to see if they have a tangent line
Unit: Derivatives: Definition and basic rules
[Video]. (n.d.). Khan Academy. https://www.khanacademy.org/math/calculus-1/cs1-derivatives-definition-and-
basic-rules
Watch the videos located under the heading Derivative definition to learn more on definitions and derivative rules
Learning Journal
Instructions:
Read Chapter 3, pages 215-289, sections 3.1, 3.2, 3.3, 3.4, and 3.5 reading the definition of derivative, slope of tangent line, rate of change, differentiation rules and to draw a graph of a derivative function from the given function. Herman, E. & Strang, G. (2020). Calculus volume 1
.
OpenStacks. Rice University. Downloaded by Whitney turner (ct8682126@gmail.com)
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Provide your answers to the following problems. Write each step clearly when you answer each question. 1. Using the limit definition of derivative, find for the function 2. Find the slope of the secant line between the values 3 and 4 for the function 3. Applying limit definition of derivative, find the slope of the tangent line at x=3
4. What do you understand from question numbers 2 and 3 about secant lines and tangent lines? Explain any difference or any similarity.
5. The total cost of producing x winter jackets in dollars is given by using the limit definition of the derivative, find average cost per jacket in [10,12]. Then find the average cost of making 1500 jackets. 6. Apply the derivative rules, find for Downloaded by Whitney turner (ct8682126@gmail.com)
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7. Apply the derivatives rules, find for 8. Find the equation of the tangent line to the graph of at x=1.
9. Use Desmos graphing calculator to graph the function 10. The concentration of antibiotic in the bloodstream t hours after being injected is given by the function C(t) is measured in milligrams per litre of blood. Find the rate of change of .Determine the rate of change for t
=2 hours. Read the rubric on how you are going to be assessed for grading. Self-Quiz
The Self-Quiz gives you an opportunity to self-assess your knowledge of what you have learned so far.
The results of the Self-Quiz do not count towards your final grade, but the quiz is an important part of the University’s learning process and it is expected that you will take it to ensure Downloaded by Whitney turner (ct8682126@gmail.com)
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understanding of the materials presented. Reviewing and analyzing your results will help you perform better on future Graded Quizzes and the Final Exam.
Please access the Self-Quiz on the main course homepage; it will be listed inside the Unit
.
Graded Quiz
T
he Graded Quiz will test your knowledge of all the materials learned thus far. The results of the quiz will count towards your final grade.
Please access the Graded Quiz on the main course homepage; it will be listed inside the Unit. After you click on it, the quiz’s introduction will inform you of any time or attempt limits in place.
Good luck!
Graded Quiz
T
he Graded Quiz will test your knowledge of all the materials learned thus far. The results of the quiz will count towards your final grade.
Please access the Graded Quiz on the main course homepage; it will be listed inside the Unit. After you click on it, the quiz’s introduction will inform you of any time or attempt limits in place.
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Good luck!
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