learning-guide-unit-7-math-1211
pdf
keyboard_arrow_up
School
University of the People *
*We aren’t endorsed by this school
Course
1211
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
11
Uploaded by ChancellorCapybaraPerson871
Studocu is not sponsored or endorsed by any college or university
Learning Guide Unit 7 -MATH 1211
Calculus (University of the People)
Studocu is not sponsored or endorsed by any college or university
Learning Guide Unit 7 -MATH 1211
Calculus (University of the People)
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
MATH 1211-01 Calculus - AY2023-T3
Dashboard
My courses
MATH 1211-01 - AY2023-T3
9 March - 15 March
Learning Guide Unit 7
Learning Guide Unit 7
Learning Guide Unit 7
Overview
Unit 7: Newton’s Method, Antiderivative and L’Hopital’s Rule
Topics:
L'Hopital's Rule
Newton’s Method
The Integral
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
Learning Objectives:
By the end of this Unit, you will be able to:
1.
Identify indeterminate forms with various operations and apply L’Hopital’s Rule 2.
Apply Newton’s Method to find the roots of a polynomial.
3.
Calculate the general antiderivative of a function.
4.
Identify the iterative process and when Newton’s method does and does not work.
Tasks:
Peer assess Unit 6 Written Assignment
Read the Learning Guide and Reading Assignments
Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
Complete and submit the Written Assignment
Make entries to the Learning Journal
Take the Self-Quiz
Introduction
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Image acquired from Calculus Volume 1,
https://openstax.org/books/calculus-volume-
1@14.1/pages/4-9-newtons-method
L’Hopital’s rule
is powerful for evaluating limit problems that show indeterminate forms like or . Using this rule, we can find the limits of many functions that we couldn’t do before. You
will see how the derivative makes it work. Newton’s method
is also an application of the derivative. It allows us to approximate the roots of functions to a desired accuracy. Newton’s method is an iterative process, and by every step, we get closer to the actual root. This method uses the x-intercepts of the tangents.
Although calculus's key concept is the derivative, which we learned so far in detail, now it’s time
to learn about the antiderivative. The antiderivative is the reverse of the derivative (like “subtraction” is the reverse of “addition”). Like the derivative, the antiderivative also has many Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
practical applications you will see here and more in advanced calculus. It will help if you become as comfortable with integration as you are with differentiation.
Reading Assignment
1. Herman, E. & Strang, G. (2020). Calculus volume 1
. OpenStacks. Rice University.
Read Chapter 4:
o
Sections 4.8, 4.9, and 4.10. pages 459-474, 477-485, and pages 490-50
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
Chapter 4: 4.8, 4.9, 4.10
o
4.8 #’s 356, 362, 370, 382, 401
o
4.9 #’s 407, 420, 428 o
4.10 #’s 466, 471, 476, 481, 492, 500, 513
2. L’Hopital’s rule
[Video].(n.d.). Khan Academy. https://www.khanacademy.org/math/ap-
calculus-ab/ab-diff-contextual-applications-new/ab-4-7/v/introduction-to-l-hopital-s-
rule
https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-contextual-applications-
new/ab-4-7/v/introduction-to-l-hopital-s-rule
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
3. Andrew Liang. (2015, June 20). Newton's method [Video}. YouTube. https://youtu.be/WuaI5G04Rcw
4. Antiderivatives
[Video]. (n.d.). Khan Academy. https://www.khanacademy.org/math/ap-
calculus-ab/ab-integration-new/ab-6-7/v/antiderivatives-and-indefinite-integrals
Discussion Assignment
How might Newton’s Method be used to find the square roots of numbers that are otherwise hard
to find. (eg, “the square root of 2”)? Provide examples.In the discussion forum, you are expected
to participate often and engage in deep levels of discourse. Please post your initial response by Sunday evening and continue to participate throughout the unit. You are required to post an initial response to the question/issue presented in the Forum and then respond to at least 3 of your classmates’ initial posts. You should also respond to anyone who has responded to you.
Discussion prompt:
How might Newton’s Method be used to find the square roots of numbers that are otherwise hard to find. (eg, “th
Provide examples.
Your Discussion should be a minimum of 200 words in length and not more than 300 words. Please include a word count. Following the APA standard, use references and in-text citations for
the textbook and any other sources.
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Written Assignment
1. Calculate the indicated limit.
. If a limit does not exist then answer +
, –
, or DNE (whichever is correct). Make sure to check that L’Hopital’s rule applies before using it. Also, whenever you apply L’Hopitals rule, indicate that you are using it.
2. Calculate the indicated limit. . If a limit does not exist then answer +
, –
, or DNE (whichever is correct). Make sure to check that L’Hopital’s rule applies before using it. Also, whenever you apply L’Hopitals rule, indicate that you are using it.
3. Calculate the indicated limit. . If a limit does not exist then answer +
, –
, or DNE (whichever is correct). Make sure to check that L’Hopital’s rule applies before using it. Also, whenever you apply L’Hopitals rule, indicate that you are using it.
4. Calculate the indicated limit. . If a limit does not exist then answer +
, –
, or DNE (whichever is correct). Make sure to check that L’Hopital’s rule applies before Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
using it. Also, whenever you apply L’Hopitals rule, indicate that you are using it.
5. Which of the following are indeterminate forms? , , , 6. Use Newton’s Method to determine and for the function and the value of .
7. Use Newton’s Method to determine and for the function and the value of .
8. Find the antiderivative of the following functions:
a) b) c) 9. Find the antiderivative of the following functions:
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
a) b) c) 10. Find the antiderivative of the following functions:
a) b) c) Learning Journal
The Learning Journal is a tool for self-reflection on the learning process. In addition to completing directed tasks, you should use the Learning Journal to document your activities, record problems you may have encountered, and to draft answers for Discussion Forums and Assignments. The Learning Journal should be updated regularly (weekly), as your instructor will
assess the learning journals as part of your Final Grade.
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Learning Journal: Choose one interesting problem from the text of medium difficulty that was not assigned.
Describe why you find it interesting.
either solve it or find a solution online
work through it using your own understanding to critique that solution and improve it. The Learning Journal entry should be a minimum of 500 words and not more than 750 words. Use APA citations and references if you use ideas from the readings or other sources. 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 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
.
Checklist
Peer assess Unit 6 Written Assignment
Read the Learning Guide and Reading Assignments
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649
Participate in the Discussion Assignment (post, comment, and rate in the Discussion Forum)
Complete and submit the Written Assignment
Make entries to the Learning Journal
Take the Self-Quiz
Downloaded by Whitney turner (ct8682126@gmail.com)
lOMoARcPSD|24613649