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School: Kennesaw
Course: College Algebra
Stop by the Lifelong Learning Center Today 2 College Can be Overwhelming. Check out our newly Adult Learner Programs works toward improving the retention, progression, and graduation of adult learner, nontraditional, and commuter students at KSU by creati
School: Kennesaw
School: Kennesaw
MATH 1106: ELEMENTARY APPLIED CALCULUS Fall 2014 Instructor - Bruce Thomas CRN Days Time Course Num/Sec Location 83273 MW 12:30PM-1:45PM MATH 1106/06 Burruss Bldg Room 109 A Course in the General Education Program Program Description: The General Educatio
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide whether the limit exists. If it exists, find its value. 1) 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #2 (Please let me know if you spot any typographic or other errors!) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = (9x + 8
School: Kennesaw
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day5-Chapter5-P.l cfw_am distributionfo,b . Bring coins sampling for t 3t3 Dav 5 5 Chapter -Binomial hobabilities of the Tossa coin5 times. Record number heads.fompute the proportion of headsby dividingby 5. of headsfor the sampleand symbolizedby p . The
School: Kennesaw
Course: ELEMENTARY STATISTICS
1 1.4- P.1 Day8- Sections .1, frame. Cueup ebookto To me: Bring candy lesson.Numberclassroll startingat 0 not I to createsampling for Bring TI-83 showwheretofind homework. ' To you: Bring TI-83. Day 8 on l.l,1.4 (Note:I .2 was covered Day I ) ChapterI Sec
School: Kennesaw
Course: ELEMENTARY STATISTICS
3-p.l Day9-Sections2.2 and2.3andChapter and Chapter3 Day 9-sections 2.2 and,2.3 Data Displaysfor Quantitative Data is the 3 2.2,2.3andall of Chapter in thetext. Remember ebook in readoverSections will A wisestudent MathConnect at the top of the page. Days
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day2-SECTION2.4AND 2.1-p.1 Day 2 Bad Data Displays Data Displaysfor CategoricalData Note to me: Bring protractor, compass, ruler. Cue up virtual TI and Lost in Space video. for Excelbarchartdirections project Handout: Additional Typesof Displaysthat you c
School: Kennesaw
Course: ELEMENTARY STATISTICS
Da y 1 3 -S e c t i o n6 . 3 - p . l Day 13 and Probabilities .r Section 6.3-Sampling Distribution of AVERAGES - For QuantitativeData 9, we madea histogramof the heartratesof the peoplein the 8 am class. Using a sampling From Day bowl, take a sampleof siz
School: Kennesaw
Course: CALCULUS
Author:_ Peer Reviewer:_ Peer Conference Questions Directions: As you listen to the writers piece or read the writers piece, ask yourself the following questions. 1. What things do you like about this piece? (Use this for your compliment) 2. What do you w
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #3 ASSIGNMENT Film Critique-Evaluation Essay You will be writing a critique of a film viewed as a class. To write a review of this film, refer to chapter 10 on Evaluations in the textbook Everythings an Argument wit
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #4 ASSIGNMENT Rhetorical Analysis Essay You will be writing an analysis of either Excerpt from Bottlemania: How Water Went on Sale and Why We Bought It on p. 717 OR Its Not about You on p. 108, both in the textbook
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #2 ASSIGNMENT Causal Argument Research Paper You will be writing a formal research essay using MLA documentation. Your writing textbook A Writers Reference will be a good resource for this. The following guidelines
School: Kennesaw
Course: CALCULUS
Chelsea Spear MATH 1190 Castle 24 January 2008 Many mathematical concepts are intertwined throughout our everyday lives. Whether calculating the tip for a waiter at a fancy restaurant, managing the checkbook, or just meeting the challenge of learning
School: Kennesaw
Course: CALCULUS
Demonstration Proofs of the Two Fundamental Theorems of Calculus We start by refreshing ourselves with the Definition of a Definite Integral based on Riemann Sums: If is defined on the closed interval and the Riemann Sum limit exists (note that is the n
School: Kennesaw
Course: CALCULUS
Generalizing the Upper/Lower Limits of the First Fundamental Theorem of Calculus The First Fundamental Theorem of Calculus (some textbooks call it the Second) states the following amazing result: ( ) ( ) This theorem establishes that integration (as in fi
School: Kennesaw
Course: Calculus 1
Lecture 8, September 14, 2011 1. 2. 3. Answer questions Quiz 3 Sections 2.5 and 2.6 2.5 Derivatives of Trigonometric Functions Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a The proof is on page 103. s o n E d u c a C o p y i g h 2 0
School: Kennesaw
Course: Calculus 1
Lecture 24 , November 28, 2011 Task 1: questions Task 2: Sections 4.6 and 4.7 C o p y i g h 2 0 0 7 P e a 4.6 Indefinite Integrals and the Substitution Rule s o n E d u c a Let us first work on a simple problem Example 1 on page 287. C o p y i g h 2 0 0
School: Kennesaw
Course: Calculus 1
Lecture 23, November 21 2011 Task 1: questions Task 2: A quiz Task 3: Sections 4.5 and 4.6 4.5 The Fundamental Theorem of Calculus Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u
School: Kennesaw
Course: Calculus 1
Lecture 22, November 16, 2011 Task 1: questions Task 2: A quiz Task 3: Sections 4.4 and 4.5 4.4 The Definite Integral Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a This int
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide whether the limit exists. If it exists, find its value. 1) 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #2 (Please let me know if you spot any typographic or other errors!) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = (9x + 8
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Final Examination If you spot a mistake or typo, please let your instructor know ASAP! MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Final Examination MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if it exists. 1) lim x5 x2 + 25 x+5 1) A) 0 C) Does not exist B) 5 D) 10
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = (9x + 8)5 1) A) f'(x) = 5(9x + 8)4 B) f'(x) = 45(9x + 8)4 D) f'(x) = 9(9x
School: Kennesaw
Course: CALCULUS
Limits of Rational and Rational Form Functions (26 January 2014) Limit of a Rational Function The topic Limit of a Function includes a brief theorem on finding the limit of a Rational Function, restated here slightly differently: Limit of a Rational Funct
School: Kennesaw
Course: CALCULUS
Rewrite as: Since Then multiplying all parts of the inequality by As (note that then by the Squeeze (or Sandwich) Theorem, is positive!) we get: , or that We also have Therefore, (A comment for students after studying differentiation and L'Hpital's Rule.)
School: Kennesaw
Course: CALCULUS
Calculus 1 (Math 1190) Preparedness Diagnostic Test The following unofficial self-diagnostic test will help you determine whether or not you are adequately prepared and ready to take Math 1190, Calculus 1. If any significant part of this diagnostic test i
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day 10Sections 2.2 and 2.3 and Chapter 3p.12 Day 10 Homework Testing on numbers: I want you to be able to get these numbers from the calculator and be able to interpret them. I will also ask you to calculate the numbers by hand on a small set of numbers s
School: Kennesaw
Course: ELEMENTARY STATISTICS
ll 3.3 Day 11-12-Sections and6.1to 6.2- p'10 for Homework DaYIl-12 deviationof 8 bpm for your class,find the zheartrate was 70 bpm with a standard I . If the average Is this scoreunusual scorefor a personwith a heartrate of 82 beatsper minute. lnterpretth
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day 9Homework p.8 Day 9 Homework 1. The histogram shows the lengths of hospital stays (in days) for all the female patients admitted to hospitals in New York in 1993 with a primary diagnosis of acute myocardial infarction (heart attack). Answer Who was me
School: Kennesaw
Course: ELEMENTARY STATISTICS
DataLabI HannahLeighCrawford Categorical Data: Choose 2 categorical variables a. Construct a contingency table b. Create a bar chart or a pie chart c. Discuss any unusual features revealed by the display of the variable. Describe patterns found. Hint:youm
School: Kennesaw
Course: CALCULUS
Limit of a Function (revised 26 January 2014) We are interested in finding the (two-sided) limit, if it exists, of a function () as , where is Real (and thus finite.) Stating this in a more informal way, we would like to know whether () approaches the s
School: Kennesaw
MATH 1106: ELEMENTARY APPLIED CALCULUS Fall 2014 Instructor - Bruce Thomas CRN Days Time Course Num/Sec Location 83273 MW 12:30PM-1:45PM MATH 1106/06 Burruss Bldg Room 109 A Course in the General Education Program Program Description: The General Educatio
School: Kennesaw
Course: LINEAR ALGEBRA I
MATH 3260/01 Linear Algebra Summer 2014 Instructor: Dr. Liancheng Wang Office: MS 223A E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 12:00-2:00 pm, MW, or by appointment Text: Elementary Linear Algebra, 7th edition, by Ron Larson, BROOKS/C
School: Kennesaw
MATH1112CollegeTrigonometry CourseSyllabusSpring2014 Instructor: MonicaDoriney Time/location:M5:00 6:15 PM and 6:30 7:45 PM Mathematics and Statistics - Room108 Email: mdoriney@kennesaw.edu Office/hours:Varioustimesavailable,byappointment CourseDescriptio
School: Kennesaw
Course: College Algebra
MATH 1111: College Algebra Fall Semester 2013 Instructor Lori Joseph CRN 83606 Days MWF Time 11:00 am 11:50 am Course Num/Sec MATH 1111/32 Location Science 213 A Course in the General Education Program Program Description: The General Education Program at
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
MATH 3310 Differential Equations, Spring 2010 Instructor: Dr. Liancheng Wang Office: Sci. & Math. 511 E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 2:00-3:15 pm, 5:00-6:00 pm, T TH, or by appointment Text: A First Course of Differential Eq
School: Kennesaw
Course: College Algebra
Stop by the Lifelong Learning Center Today 2 College Can be Overwhelming. Check out our newly Adult Learner Programs works toward improving the retention, progression, and graduation of adult learner, nontraditional, and commuter students at KSU by creati
School: Kennesaw
School: Kennesaw
MATH 1106: ELEMENTARY APPLIED CALCULUS Fall 2014 Instructor - Bruce Thomas CRN Days Time Course Num/Sec Location 83273 MW 12:30PM-1:45PM MATH 1106/06 Burruss Bldg Room 109 A Course in the General Education Program Program Description: The General Educatio
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide whether the limit exists. If it exists, find its value. 1) 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #2 (Please let me know if you spot any typographic or other errors!) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = (9x + 8
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Final Examination If you spot a mistake or typo, please let your instructor know ASAP! MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Final Examination MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if it exists. 1) lim x5 x2 + 25 x+5 1) A) 0 C) Does not exist B) 5 D) 10
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = (9x + 8)5 1) A) f'(x) = 5(9x + 8)4 B) f'(x) = 45(9x + 8)4 D) f'(x) = 9(9x
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #1 Please email me ASAP if you find a typographical error or any other kind of error in this version of the practice test. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
School: Kennesaw
MATH 1106 Review for Final Examination Topics to Review Limit of a Function Numerical Graphical Algebraic Continuity Derivative as Limit of Difference Quotient Tangent Line at a Point Horizontal Tangent Line Derivative is Rate of Change Rules of
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #3 Be sure to email me if you spot any errors in the following annotated solution! MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1)
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = e3x A) 1 e3x 3 2) f(x) = 4e-7x A) 28e-7x 1) B) 3ex C) e3x D) 3e3x 2) B) -
School: Kennesaw
Course: CALCULUS
Author:_ Peer Reviewer:_ Peer Conference Questions Directions: As you listen to the writers piece or read the writers piece, ask yourself the following questions. 1. What things do you like about this piece? (Use this for your compliment) 2. What do you w
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #3 ASSIGNMENT Film Critique-Evaluation Essay You will be writing a critique of a film viewed as a class. To write a review of this film, refer to chapter 10 on Evaluations in the textbook Everythings an Argument wit
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #4 ASSIGNMENT Rhetorical Analysis Essay You will be writing an analysis of either Excerpt from Bottlemania: How Water Went on Sale and Why We Bought It on p. 717 OR Its Not about You on p. 108, both in the textbook
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #2 ASSIGNMENT Causal Argument Research Paper You will be writing a formal research essay using MLA documentation. Your writing textbook A Writers Reference will be a good resource for this. The following guidelines
School: Kennesaw
Course: CALCULUS
Demonstration Proofs of the Two Fundamental Theorems of Calculus We start by refreshing ourselves with the Definition of a Definite Integral based on Riemann Sums: If is defined on the closed interval and the Riemann Sum limit exists (note that is the n
School: Kennesaw
Course: CALCULUS
Limits of Rational and Rational Form Functions (26 January 2014) Limit of a Rational Function The topic Limit of a Function includes a brief theorem on finding the limit of a Rational Function, restated here slightly differently: Limit of a Rational Funct
School: Kennesaw
Course: CALCULUS
Limit of a Function (revised 26 January 2014) We are interested in finding the (two-sided) limit, if it exists, of a function () as , where is Real (and thus finite.) Stating this in a more informal way, we would like to know whether () approaches the s
School: Kennesaw
Course: CALCULUS
Rewrite as: Since Then multiplying all parts of the inequality by As (note that then by the Squeeze (or Sandwich) Theorem, is positive!) we get: , or that We also have Therefore, (A comment for students after studying differentiation and L'Hpital's Rule.)
School: Kennesaw
Course: CALCULUS
Generalizing the Upper/Lower Limits of the First Fundamental Theorem of Calculus The First Fundamental Theorem of Calculus (some textbooks call it the Second) states the following amazing result: ( ) ( ) This theorem establishes that integration (as in fi
School: Kennesaw
Course: CALCULUS
Table of Fundamental Indefinite Integrals The following table lists the fundamental indefinite integrals. This table is essentially the inversion of the Table of Fundamental Differentials with only minor generalizations. These fundamental indefinite integ
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #2 Covering Lessons 2.12.3 SOLUTIONS 17 February 2014; Sections 07 and 08; 5 points per numbered problem, 15 points total 1) Find the derivative, , for the function ( ) ( ) 2) Use the Product Rule (show work!) to find ( ) for the function
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #1 Covering Lessons 1.3 and 1.4 SOLUTIONS 15 January 2014, For Sections 07 and 08 1) What is the average rate of change of the function over the interval [ ] ? (Notes: this interval is the -interval; the average rate of change is the slope
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #6 Covering Lesson 4.1 SOLUTIONS 16 April 2014; Sections 07 and 08; 15 points total (Note: Where required use as the constant of integration) ( ) ( ) | | ( ) ( ) ( ) The Beatles ( )
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #4 Covering Lesson 2.8 SOLUTIONS 03 March 2014; Sections 07 and 08; 5 points per numbered problem, 15 points total 1) Using implicit differentiation, find (or ) for the implicit relation Differentiating both sides with respect to ( ) ( ) 2
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #7 Covering Lessons 4.24.4 SOLUTIONS 28 April 2014; Sections 07 and 08; 15 points total in the interval [ 1. Estimate the area under the graph of the function the Midpoint Rule with three equal-width intervals. ] using [ ], each with a The
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #5 Covering Lessons 3.13.3 SOLUTIONS ( ) (Note: ( ) ( and a. Find all critical points in the interval [ ) ( ) ) ] (2 points) A critical point of a function ( ) is defined to be the value of in the domain of the function where the derivativ
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #3 Covering Lessons 2.52.7 SOLUTIONS 24 February 2014; Sections 07 and 08; 5 points per numbered problem, 15 points total 1) Find the derivative, , for the function The derivative of this function is simply the sum of the derivatives of ea
School: Kennesaw
Course: CALCULUS
Math 1111 (College Algebra): Fall Semester 2013, Sections 10 and 11 Final for Chapters R to 5, Version A Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your workprint your name on the separate
School: Kennesaw
Course: CALCULUS
Math 1111 (College Algebra): Fall Semester 2013, Sections 10, 11, and 46 ANSWERS to the FINAL for Chapters R to 5, Version A 5 points per numbered problem except for Problem 1 (45 points) and Problem 43 (10 points). For certain problems, partial credit wi
School: Kennesaw
Course: CALCULUS
Calculus 1 (Math 1190) Preparedness Diagnostic Test The following unofficial self-diagnostic test will help you determine whether or not you are adequately prepared and ready to take Math 1190, Calculus 1. If any significant part of this diagnostic test i
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Chapter 4 (rev. 27 Apr 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each s
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Final (rev. 04 May 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each separ
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Chapter 2 (rev. 08 Mar 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each s
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Chapter 1 Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each separate sheet! 5 po
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Chapter 3 (rev. 06 Apr 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each s
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 (ANSWERS) Practice Test for Chapter 2 (rev. 08 Mar 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Practice Test for Chapter 3 Rev. 08 April 2014 Problems 118 are theorems/definitions. Refer to the Answers document. Problems 1921 use the function ( ) which is continuous for
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Practice Test for Chapter 2 Rev. 09 March 2014 1. Table of Fundamental Differential Rules ( ) ( ) ( ) | | | | | | | | 2. Give the fundamental definition of the Derivative of a
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Answers/Solutions to the Practice Test for the Final Rev. 05 May 2014 1. Complete the following table of Fundamental Differential Rules. Note that are differentiable functions in logarithm bas
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Answers/Solutions to the Practice Test for Chapter 4 Rev. 27 April 2014 1. Complete the following table of Fundamental Indefinite Integrals (the antiderivatives of the integrands). Include the
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 (ANSWERS) Practice Test for Chapter 3 (rev. 06 Apr 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Practice Test for Chapter 1 Rev. 08 February 2014 For problems 1 and 2, find the Average Rate of Change of the function over the given -interval. [ [ [ ] ] ] 3. Find the equat
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 More Detailed Solution to Problem 12 in the Practice Test for Chapter 2 Rev. 09 March 2014 ( ) Find the derivative of ( ) and simplify. Differentiate using the Product Rule: ( ) ( ) ( ) ( ( (
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Chapter 3 Test Version A Rev. 12 April 2014 1. Extreme Value Theorem: This theorem states that a function attains both an absolute ] if what? maximum and an absolute minimum v
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Chapter 4 Test Version A Rev. 30 April 2014 1. Complete the following table of Fundamental Indefinite Integrals (the antiderivatives of the integrands). Include the Real const
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Chapter 2 Test Version A Rev. 16 March 2014 1. Table of Fundamental Differential Rules ( ) ( ) ( ) | | | | | | | | 2. Give the fundamental definition of the Derivative of a fu
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Chapter 1 Test Version A Rev. 08 February 2014 For problems 1 and 2, find the Average Rate of Change of the function over the given -interval. [ [ ] [ ] ] 3. Find the equation
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day5-Chapter5-P.l cfw_am distributionfo,b . Bring coins sampling for t 3t3 Dav 5 5 Chapter -Binomial hobabilities of the Tossa coin5 times. Record number heads.fompute the proportion of headsby dividingby 5. of headsfor the sampleand symbolizedby p . The
School: Kennesaw
Course: ELEMENTARY STATISTICS
1 1.4- P.1 Day8- Sections .1, frame. Cueup ebookto To me: Bring candy lesson.Numberclassroll startingat 0 not I to createsampling for Bring TI-83 showwheretofind homework. ' To you: Bring TI-83. Day 8 on l.l,1.4 (Note:I .2 was covered Day I ) ChapterI Sec
School: Kennesaw
Course: ELEMENTARY STATISTICS
3-p.l Day9-Sections2.2 and2.3andChapter and Chapter3 Day 9-sections 2.2 and,2.3 Data Displaysfor Quantitative Data is the 3 2.2,2.3andall of Chapter in thetext. Remember ebook in readoverSections will A wisestudent MathConnect at the top of the page. Days
School: Kennesaw
Course: ELEMENTARY STATISTICS
TYPES OF DATA AND WHAT YOU CAN DO WITH IT Whom are we studying? What did you record on each _? Is this answer a category or a number quantity? What are the units for the quantitative data? (Categories do not have units.) Categorical Data color, male/femal
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day 10Sections 2.2 and 2.3 and Chapter 3p.12 Day 10 Homework Testing on numbers: I want you to be able to get these numbers from the calculator and be able to interpret them. I will also ask you to calculate the numbers by hand on a small set of numbers s
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day2-SECTION2.4AND 2.1-p.1 Day 2 Bad Data Displays Data Displaysfor CategoricalData Note to me: Bring protractor, compass, ruler. Cue up virtual TI and Lost in Space video. for Excelbarchartdirections project Handout: Additional Typesof Displaysthat you c
School: Kennesaw
Course: ELEMENTARY STATISTICS
TJ % I e., 5 *orrur^lof[ ="1-3 hnW- P Yteu)-s =. cfw_,8 -1I n = IOO ?r (6 = ri ,r3 (r-,73]) Y \i ' i l/ t o o ='c4\3abq+sg -v \ qoq \^tCIfrrir cd-f ( -L Eqt- , bg ,J 3 , ,OLL+3 +58 ) ;' _ ) ) ) ? i vd i: "l?oo3*S-s-gg-r* rs'Q- *N11rc+eod ctr eserr+g -l=-.
School: Kennesaw
Course: ELEMENTARY STATISTICS
= ?,(A4B) ?G)?(B) Day3-4-Chapter 4-p.ll Day 4 Homework Set Testing StatisticalIndependence ho\ydb are u,)l^!n ilB) -PrA) , which will allows samplingvariabilityand thereis a Chi Square Test of Independence In furthercourses, table at once. The Chi-Square
School: Kennesaw
Course: ELEMENTARY STATISTICS
4-p.9 Day3-4-Chapter Day 3 Homework Set Probabilities Calculating Conditional BO, doesnot like l. If you know someone what is the probability skateboardsn that the personlikes snowmobiles? Skptsbsnrds I Shetefi'a*rds 11,_-i A I ._-_,1 ,t-"*;"*,-tr- for Wr
School: Kennesaw
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day5-Chapter5-P.l cfw_am distributionfo,b . Bring coins sampling for t 3t3 Dav 5 5 Chapter -Binomial hobabilities of the Tossa coin5 times. Record number heads.fompute the proportion of headsby dividingby 5. of headsfor the sampleand symbolizedby p . The
School: Kennesaw
Course: ELEMENTARY STATISTICS
1 1.4- P.1 Day8- Sections .1, frame. Cueup ebookto To me: Bring candy lesson.Numberclassroll startingat 0 not I to createsampling for Bring TI-83 showwheretofind homework. ' To you: Bring TI-83. Day 8 on l.l,1.4 (Note:I .2 was covered Day I ) ChapterI Sec
School: Kennesaw
Course: ELEMENTARY STATISTICS
3-p.l Day9-Sections2.2 and2.3andChapter and Chapter3 Day 9-sections 2.2 and,2.3 Data Displaysfor Quantitative Data is the 3 2.2,2.3andall of Chapter in thetext. Remember ebook in readoverSections will A wisestudent MathConnect at the top of the page. Days
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day2-SECTION2.4AND 2.1-p.1 Day 2 Bad Data Displays Data Displaysfor CategoricalData Note to me: Bring protractor, compass, ruler. Cue up virtual TI and Lost in Space video. for Excelbarchartdirections project Handout: Additional Typesof Displaysthat you c
School: Kennesaw
Course: ELEMENTARY STATISTICS
Da y 1 3 -S e c t i o n6 . 3 - p . l Day 13 and Probabilities .r Section 6.3-Sampling Distribution of AVERAGES - For QuantitativeData 9, we madea histogramof the heartratesof the peoplein the 8 am class. Using a sampling From Day bowl, take a sampleof siz
School: Kennesaw
Course: ELEMENTARY STATISTICS
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School: Kennesaw
Course: ELEMENTARY STATISTICS
ll.2-p.I Day24- Section DaY24 Line Regression SectionSection11.2LeastSquares 66who" on Still dealingwith two quantitative measures the same o'Does linearrelationship two these variables?" existbetween a the Correlationanswers question, | relationshio?" "w
School: Kennesaw
Course: ELEMENTARY STATISTICS
ll Day23-section 11.1-P.1 Day 23 Section11.1 Correlation "Who" on Measurements the Same Two Quantitative Wherethis informationfits into the "big picture" T nnk ar vorrrrestinJooklet. Everythingwe havedone on quantitativedatais cal Look at your testingbook
School: Kennesaw
Course: ELEMENTARY STATISTICS
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School: Kennesaw
Course: ELEMENTARY STATISTICS
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School: Kennesaw
Course: ELEMENTARY STATISTICS
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School: Kennesaw
Course: ELEMENTARY STATISTICS
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School: Kennesaw
Course: ELEMENTARY STATISTICS
w,ft \,ilr, lcfw_W n W ilrI I use vocab Correctly in interps Identify appropriate methodsfor collecting data Qualitative/ quantitative Describe graphsfor histogram measures or LO l l interpret and make conclusions basic probabilities and use computations
School: Kennesaw
Course: ELEMENTARY STATISTICS
IT Day 14-section 6.3 and 6.4-P.l DaY 14 Section6.3-Sampling Distribution and Probabilitiesof f p Section6.4-Sampling Distribution and Probabilitiesof problem on the next Review the CentralLimit Theoremby graphingthe x and I distributionsfor the following
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day3-Chapter 4-p.1 Toyou: Bring 3 x 3 inchstickies'and colored markers tomorrow. Day 3 Chapter 4-Probability Rules Mutually ExclusiveEvents exclusive it is impossible bothevents occur. if for Two events mutually are to Mutuolly lxclusive Nof l$utuslly lxc
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day 18-Section8.1and8.2-p.1 DaY18 Testing 8.1. Section BasicPrincipleof Hypothesis Testfor a PopulationMean, StandardDeviationKnown 8.2 Section Hypothesis The paclqigryblne to chipsis stated be 10ounces. The weightof potato is supposed be to is 'Fe+underf
School: Kennesaw
Course: ELEMENTARY STATISTICS
zan@vr lfr;,* Section 8.2 Hypothesis Test for a Population Mean, Standard Deviation Known Section 7.1 Confidence Intervals for a Population Mean, Standard Deviation Known REVIEW OF HYPOTHESISTESTING . We begina hypothesis by assuming null hypothesis be tr
School: Kennesaw
Course: ELEMENTARY STATISTICS
ll Circleone:B am 9: Name: TEST3 G TO TO PROIECT EARN5 POINTS ADD TO IN-CLASS SODIUM QUestroNseilour FATSUGARAND am 11 am DE. relationshipbe 1. Do you expecta positiveor negative Fat and sugar? Fatand sodium? and sugar? Sodium . the r-squared the 2. Write
School: Kennesaw
Course: ELEMENTARY STATISTICS
Name Phone Circle (circle):8am/ 9:30amI 11 am TEST I FormA Math 1107-Fall2014 LearningObjectives 1. Students will be able to use statistical vocabulary and notation appropriately. SGircn thic i'- 3. Students will be able distinguish the differencebetween
School: Kennesaw
Course: CALCULUS
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School: Kennesaw
Course: CALCULUS
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School: Kennesaw
Course: CALCULUS
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School: Kennesaw
James Garfields Proof of the Pythagorean Theorem College Trigonometry (MATH 1112) Kennesaw State University The Pythagorean Theorem states that for any right triangle with sides of length a and b and hypotenuse of length c, it is true that . There are man
School: Kennesaw
Course: Elemenary Statistics
B&W CONFIRMINGS 58 Chapter 2 Frequency Distributions and Graphs Exercises 23 1. Do Students Need Summer Development? For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct a hist
School: Kennesaw
Course: College Algebra
Math 1111 Fall 2013 Sample Practice Problems This is not an all inclusive list of problems that might be on the test. In addition to these problems, please review your notes, the homework and the pretest problems in MML. Given the line 9x-3y = 12, write i
School: Kennesaw
Course: College Algebra
Math 1111 Fully answer all questions on this sheet or on your own paper, using graph paper when necessary. Make sure your name is on all pages and that problem numbers are clearly marked. There are extra graphs at the end of the test. For questions 1-4, s
School: Kennesaw
Course: College Algebra
Rational Expressions Section R.6 (p. 35-43) MATH 1111 A rational expression is the quotient of two polynomials. Skills Determine the domain of a rational expression. Simplify rational expressions. The Domain of Rational Expressions Multiply, divide, add,
School: Kennesaw
Course: College Algebra
The Basics of Equation Solving Section R.5 (p. 30-34) MATH 1111 An equation is a statement that two expressions are equal. Skills Solve linear equations. Solve quadratic equations. Solve a formula for a given variable. To solve an equation in one variable
School: Kennesaw
Chapter R: Functions, Graphs, and Models_ Section Objectives: Defining a function and its domain/range Linear functions Quadratic functions The graph of an equation is a drawing that represents all ordered pairs that are solutions of the equation. Exam
School: Kennesaw
Section 5.2: Applications of Models Section Objectives: Perform computations involving interest compounded continuously and continuous money flow. Calculate the total consumption of a natural resource. Find the present value of an investment. Growth Fo
School: Kennesaw
Sec 5.1: An Econ Application: Consumer & Producer Surplus Section Objectives: Given demand and supply functions, find the consumer surplus and the producer surplus at the equilibrium point. DEFINITION Suppose that consumer surplus describes the demand fu
School: Kennesaw
Section 4.4: Properties of Definite Integrals Section Objectives: Use the properties of definite integrals to find the area between curves. Solve applied problems involving definite integrals. Determine the average value of a function. THEOREM 5 For Fo
School: Kennesaw
Section 4.3: Area and Definite Integrals Section Objectives: Find the area under a curve over a given closed interval. Evaluate a definite integral. Interpret an area below the horizontal axis. Solve applied problems involving definite integrals. DEFI
School: Kennesaw
Section 4.2: Antiderivatives as Areas Section Objectives: Find the area under a graph to solve real-world problems Use rectangles to approximate the area under a graph. Example 1: A vehicle travels at 50 mi/hr for 2 hours. How far has the vehicle travel
School: Kennesaw
Section 4.1: Antidifferentiation Section Objectives: Find an antiderivative of a function. Evaluate indefinite integrals using the basic integration formulas. Use initial conditions, or boundary conditions, to determine an antiderivative. THEOREM 1 The
School: Kennesaw
Section 3.6: An Economics Application: Elasticity of Demand Section Objectives: Find the elasticity of a demand function. Find the maximum of a total-revenue function. Characterize demand in terms of elasticity. DEFINITION The elasticity of demand () i
School: Kennesaw
Section 3.4: Applications: Decay Section Objectives: Find a function that satisfies Convert between decay rate and half-life. Solve applied problems involving exponential decay. The equation , where , shows to be decreasing as a function of time, and t
School: Kennesaw
Section 3.3: Uninhibited and Limited Growth Models Section Objectives: Find functions that satisfy Convert between growth rate and doubling time. Solve application problems using exponential growth and limited growth models. RECALL Example: Differentia
School: Kennesaw
Section 3.2: Logarithmic Functions Section Objectives: Convert between logarithmic and exponential equations. Solve exponential equations. Solve problems involving exponential and logarithmic functions. Differentiate functions involving natural logari
School: Kennesaw
Section 3.1: Exponential Functions Section Objectives: Graph exponential functions. Differentiate exponential functions. DEFINITION An exponential function Where is given by is any real number, () and . The number Example 1: Graph ( ) DEFINITION: ( We c
School: Kennesaw
Section 2.6: Marginals and Differentials Section Objectives: Find marginal cost, revenue, and profit. Find and Use differentials for approximations. DEFINITION Let and represent, respectively, the total cost, revenue, and profit from the production and
School: Kennesaw
Section 2.5: Max-Min Problems; Business & Econ Applications Section Objectives: Solve maximum and minimum problems using calculus. A Strategy for Solving Maximum-Minimum Problems: 1. Read the problem carefully. If relevant, make a drawing. 2. Make a list
School: Kennesaw
Section 2.4: Using Derivatives to Find Absolute Max & Min Section Objectives: Find absolute extrema using Maximum-Minimum Principle 1. Find absolute extrema using Maximum-Minimum Principle 2. DEFINITION: Suppose that is an is an is a function with domai
School: Kennesaw
Sec. 2.3: Graph Sketching: Asymptotes & Rational Functions Section Objectives: Find limits involving infinity. Determine the asymptotes of a functions graph. Graph rational functions. DEFINITION: A rational function is a function that can be described
School: Kennesaw
Section 2.2: Using Second Derivatives to Find Max & Min Values and Sketch Graphs Section Objectives: Find the relative extrema of a function using the Second-Derivative Test. Sketch the graph of a continuous function. Suppose that is a function whose de
School: Kennesaw
Course: CALCULUS
Author:_ Peer Reviewer:_ Peer Conference Questions Directions: As you listen to the writers piece or read the writers piece, ask yourself the following questions. 1. What things do you like about this piece? (Use this for your compliment) 2. What do you w
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #3 ASSIGNMENT Film Critique-Evaluation Essay You will be writing a critique of a film viewed as a class. To write a review of this film, refer to chapter 10 on Evaluations in the textbook Everythings an Argument wit
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #4 ASSIGNMENT Rhetorical Analysis Essay You will be writing an analysis of either Excerpt from Bottlemania: How Water Went on Sale and Why We Bought It on p. 717 OR Its Not about You on p. 108, both in the textbook
School: Kennesaw
Course: CALCULUS
English Composition Prof. Schofer ESSAY #2 ASSIGNMENT Causal Argument Research Paper You will be writing a formal research essay using MLA documentation. Your writing textbook A Writers Reference will be a good resource for this. The following guidelines
School: Kennesaw
Course: CALCULUS
Chelsea Spear MATH 1190 Castle 24 January 2008 Many mathematical concepts are intertwined throughout our everyday lives. Whether calculating the tip for a waiter at a fancy restaurant, managing the checkbook, or just meeting the challenge of learning
School: Kennesaw
Course: CALCULUS
Demonstration Proofs of the Two Fundamental Theorems of Calculus We start by refreshing ourselves with the Definition of a Definite Integral based on Riemann Sums: If is defined on the closed interval and the Riemann Sum limit exists (note that is the n
School: Kennesaw
Course: CALCULUS
Generalizing the Upper/Lower Limits of the First Fundamental Theorem of Calculus The First Fundamental Theorem of Calculus (some textbooks call it the Second) states the following amazing result: ( ) ( ) This theorem establishes that integration (as in fi
School: Kennesaw
Course: Calculus 1
Lecture 8, September 14, 2011 1. 2. 3. Answer questions Quiz 3 Sections 2.5 and 2.6 2.5 Derivatives of Trigonometric Functions Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a The proof is on page 103. s o n E d u c a C o p y i g h 2 0
School: Kennesaw
Course: Calculus 1
Lecture 24 , November 28, 2011 Task 1: questions Task 2: Sections 4.6 and 4.7 C o p y i g h 2 0 0 7 P e a 4.6 Indefinite Integrals and the Substitution Rule s o n E d u c a Let us first work on a simple problem Example 1 on page 287. C o p y i g h 2 0 0
School: Kennesaw
Course: Calculus 1
Lecture 23, November 21 2011 Task 1: questions Task 2: A quiz Task 3: Sections 4.5 and 4.6 4.5 The Fundamental Theorem of Calculus Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u
School: Kennesaw
Course: Calculus 1
Lecture 22, November 16, 2011 Task 1: questions Task 2: A quiz Task 3: Sections 4.4 and 4.5 4.4 The Definite Integral Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a This int
School: Kennesaw
Course: Calculus 1
Lecture 21, November 14, 2011 Task 1: Sections 4.3 and 4.4 4.3 Sigma Notation and Limits of Finite Sums Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7
School: Kennesaw
Course: Calculus 1
Lecture 20, November 9, 2011 Task 1: Questions? Task 2: A Quiz Task 3: Sections 4.1 and 4.2 Chapter 4 Integration Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a 4.1 Antiderivatives s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E
School: Kennesaw
Course: Calculus 1
Lecture 19, November 7, 2011 3.6 Applied Optimization 3.7 Indeterminate Forms and L' Hopital's Rule Copyright 2007 Pearson Education, Inc. 3.6 Copyright 2007 Pearson Education, Inc. C o p y i g h Work on Example 1on page 209 2 0 0 7 P e a s o n E d u c a
School: Kennesaw
Course: Calculus 1
Lecture 18, November 2, 2011 Task 1: Section 3.5 Task 2: Section 3.6 Copyright 2007 Pearson Education, Inc. C o p y i g h Section 3.5 Parametrizations of plane curves 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g
School: Kennesaw
Course: Calculus 1
Lecture 17, October 24, 2011 Task 1: Section 3.4 Task 2: Section 3.5 Copyright 2007 Pearson Education, Inc. 3.4 Concavity and Curve Sketching Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a
School: Kennesaw
Course: Calculus 1
Lecture 16, October 19, 2011 Task 1: Section 3.3 Monotonic Functions and the First Derivative Test Task 2: Section 3.4 Concavity and Curve Sketching Inc. Copyright 2007 Pearson Education, 3.3 Monotonic Functions and the First Derivative Test Copyright 200
School: Kennesaw
Course: Calculus 1
Lecture 15, October 17, 2011 Section 3.2 The Mean Value Theorem Copyright 2007 Pearson Education, Inc. C o p y i g h Review 2 0 0 7 P e a This is a very important result. Its proof is on page 178-179. s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E
School: Kennesaw
Course: Calculus 1
Lecture 14, October 12, 2011 Task 1: any questions on HW Task 2: a quiz Task 3: Section 3.1 3.1 Extreme Values of Functions Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C
School: Kennesaw
Course: Calculus 1
Lecture 13, October 10, 2011 Task 1: any questions on HW Task 2: Finish up Section 1.12 2.12 Related Rates Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0
School: Kennesaw
Course: Calculus 1
Lecture 12, October 5, 2011 Task 1: questions Task 2: Quiz Task 3: Section 2.11 Section 2.11 Inverse Trigonometric Functions Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C
School: Kennesaw
Course: Calculus 1
Lecture 11, October 3, 2011 Task 1: Sections 2.9-2.10 2.9 - 2.10 Derivatives of Inverse Functions and Logarithms Copyright 2007 Pearson Education, Inc. C o p y i g h Inverses When we go from an output of a function back to its input or inputs, we get an i
School: Kennesaw
Course: Calculus 1
Lecture 10, September 28, 2011 Task 1: Discuss Test 1 Task 2: Section 2.8 2.8 Implicit Differentiation Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a Work on Example 1 on page 121 C o p y i g h Work on Example 2 on pag
School: Kennesaw
Course: Calculus 1
Lecture 9, September 19, 2011 Task 1: Any questions? Task 2: Section 2.7 2.7 The Chain Rule Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n
School: Kennesaw
Course: Calculus 1
Lecture 7, September 12, 2011 1. 2. Answer questions Section 2.3 and 2.4 2.3 Differentiation Rules for Polynomials, Exponentials, Products, and Quotients Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2
School: Kennesaw
Course: Calculus 1
Lecture 6, September 7, 2011 2.1 Tangents and Derivatives at a Point Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h Work on Example 1 on page 72 2 0 0 7 P e a
School: Kennesaw
Course: Calculus 1
Lecture 5, August 31, 2011 C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a Wor
School: Kennesaw
Course: Calculus 1
Lecture 4, Fall 2011 (Sections 1.6 and 1.7) Task 1: a quiz Task 2: Finish up Section 1.6 Task 3: Section 1.7 An important limit (Section 1.6) Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h An important li
School: Kennesaw
Course: Calculus 1
Lecture 3, Fall 2011 (Sections 1.5, 1.6) 1.5 The Precise Definition of a Limit Copyright 2007 Pearson Education, Inc. C o p y i g h Work on Example 1 on page 34. Let f(x)=2x-1. We will work on |f(x)-7|<2 to get |x-4|<1. 2 0 0 7 P e a s o n E d u c a C o
School: Kennesaw
Course: Calculus 1
Lecture 2, August 22, 2011 Copyright 2007 Pearson Education, Inc. 1.4 Limit of a Function and Limits Laws Copyright 2007 Pearson Education, Inc. Limit of a function and limit laws Let f(x) be defined on an open interval about a, except possibly at a itsel
School: Kennesaw
Course: Calculus 1
Math 1190/01 Welcome to my class! Lecture 1, August 17, 2011 Copyright 2007 Pearson Education, Inc. 1.3 Rates of Change and Tangents to Curves Copyright 2007 Pearson Education, Inc. It assumes negligible air resistance to slow the object down, and that gr
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide whether the limit exists. If it exists, find its value. 1) 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #2 (Please let me know if you spot any typographic or other errors!) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = (9x + 8
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Final Examination If you spot a mistake or typo, please let your instructor know ASAP! MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Final Examination MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the limit, if it exists. 1) lim x5 x2 + 25 x+5 1) A) 0 C) Does not exist B) 5 D) 10
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = (9x + 8)5 1) A) f'(x) = 5(9x + 8)4 B) f'(x) = 45(9x + 8)4 D) f'(x) = 9(9x
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #1 Please email me ASAP if you find a typographical error or any other kind of error in this version of the practice test. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
School: Kennesaw
MATH 1106 Review for Final Examination Topics to Review Limit of a Function Numerical Graphical Algebraic Continuity Derivative as Limit of Difference Quotient Tangent Line at a Point Horizontal Tangent Line Derivative is Rate of Change Rules of
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #3 Be sure to email me if you spot any errors in the following annotated solution! MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1)
School: Kennesaw
Math 1106 - Instructor: Bruce Thomas Practice Test #3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Differentiate. 1) f(x) = e3x A) 1 e3x 3 2) f(x) = 4e-7x A) 28e-7x 1) B) 3ex C) e3x D) 3e3x 2) B) -
School: Kennesaw
Course: CALCULUS
Table of Fundamental Indefinite Integrals The following table lists the fundamental indefinite integrals. This table is essentially the inversion of the Table of Fundamental Differentials with only minor generalizations. These fundamental indefinite integ
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #2 Covering Lessons 2.12.3 SOLUTIONS 17 February 2014; Sections 07 and 08; 5 points per numbered problem, 15 points total 1) Find the derivative, , for the function ( ) ( ) 2) Use the Product Rule (show work!) to find ( ) for the function
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #1 Covering Lessons 1.3 and 1.4 SOLUTIONS 15 January 2014, For Sections 07 and 08 1) What is the average rate of change of the function over the interval [ ] ? (Notes: this interval is the -interval; the average rate of change is the slope
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #6 Covering Lesson 4.1 SOLUTIONS 16 April 2014; Sections 07 and 08; 15 points total (Note: Where required use as the constant of integration) ( ) ( ) | | ( ) ( ) ( ) The Beatles ( )
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #4 Covering Lesson 2.8 SOLUTIONS 03 March 2014; Sections 07 and 08; 5 points per numbered problem, 15 points total 1) Using implicit differentiation, find (or ) for the implicit relation Differentiating both sides with respect to ( ) ( ) 2
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #7 Covering Lessons 4.24.4 SOLUTIONS 28 April 2014; Sections 07 and 08; 15 points total in the interval [ 1. Estimate the area under the graph of the function the Midpoint Rule with three equal-width intervals. ] using [ ], each with a The
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #5 Covering Lessons 3.13.3 SOLUTIONS ( ) (Note: ( ) ( and a. Find all critical points in the interval [ ) ( ) ) ] (2 points) A critical point of a function ( ) is defined to be the value of in the domain of the function where the derivativ
School: Kennesaw
Course: CALCULUS
Math 1190: Quiz #3 Covering Lessons 2.52.7 SOLUTIONS 24 February 2014; Sections 07 and 08; 5 points per numbered problem, 15 points total 1) Find the derivative, , for the function The derivative of this function is simply the sum of the derivatives of ea
School: Kennesaw
Course: CALCULUS
Math 1111 (College Algebra): Fall Semester 2013, Sections 10 and 11 Final for Chapters R to 5, Version A Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your workprint your name on the separate
School: Kennesaw
Course: CALCULUS
Math 1111 (College Algebra): Fall Semester 2013, Sections 10, 11, and 46 ANSWERS to the FINAL for Chapters R to 5, Version A 5 points per numbered problem except for Problem 1 (45 points) and Problem 43 (10 points). For certain problems, partial credit wi
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Chapter 4 (rev. 27 Apr 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each s
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Final (rev. 04 May 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each separ
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Chapter 2 (rev. 08 Mar 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each s
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Chapter 1 Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each separate sheet! 5 po
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Practice Test for Chapter 3 (rev. 06 Apr 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name on each s
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 (ANSWERS) Practice Test for Chapter 2 (rev. 08 Mar 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Practice Test for Chapter 3 Rev. 08 April 2014 Problems 118 are theorems/definitions. Refer to the Answers document. Problems 1921 use the function ( ) which is continuous for
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Practice Test for Chapter 2 Rev. 09 March 2014 1. Table of Fundamental Differential Rules ( ) ( ) ( ) | | | | | | | | 2. Give the fundamental definition of the Derivative of a
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Answers/Solutions to the Practice Test for the Final Rev. 05 May 2014 1. Complete the following table of Fundamental Differential Rules. Note that are differentiable functions in logarithm bas
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Answers/Solutions to the Practice Test for Chapter 4 Rev. 27 April 2014 1. Complete the following table of Fundamental Indefinite Integrals (the antiderivatives of the integrands). Include the
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 (ANSWERS) Practice Test for Chapter 3 (rev. 06 Apr 2014) Print Name_ Score _ Signature_ Record your answers in the space provided. You may use separate sheets to show your work print your name
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Practice Test for Chapter 1 Rev. 08 February 2014 For problems 1 and 2, find the Average Rate of Change of the function over the given -interval. [ [ [ ] ] ] 3. Find the equat
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 More Detailed Solution to Problem 12 in the Practice Test for Chapter 2 Rev. 09 March 2014 ( ) Find the derivative of ( ) and simplify. Differentiate using the Product Rule: ( ) ( ) ( ) ( ( (
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Chapter 3 Test Version A Rev. 12 April 2014 1. Extreme Value Theorem: This theorem states that a function attains both an absolute ] if what? maximum and an absolute minimum v
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Chapter 4 Test Version A Rev. 30 April 2014 1. Complete the following table of Fundamental Indefinite Integrals (the antiderivatives of the integrands). Include the Real const
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Chapter 2 Test Version A Rev. 16 March 2014 1. Table of Fundamental Differential Rules ( ) ( ) ( ) | | | | | | | | 2. Give the fundamental definition of the Derivative of a fu
School: Kennesaw
Course: CALCULUS
Math 1190 (Calculus 1): Spring Semester 2014, Sections 7 and 8 Solutions to the Chapter 1 Test Version A Rev. 08 February 2014 For problems 1 and 2, find the Average Rate of Change of the function over the given -interval. [ [ ] [ ] ] 3. Find the equation
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 6 (Version 1) Solutions October 21, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 8 (Version 1) Solutions November 18, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 7 (Version 1) Solutions November 4, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 7 (Version 2) Solutions November 4, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 1) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 2) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 2 (Version 2) Solutions June 23, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 3 (Version 2) Solutions July 7, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use co
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 4 (Version 1) Solutions July 16, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 2 (Version 1) Solutions June 23, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 3 (Version 1) Solutions July 7, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use co
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 4 (Version 2) Solutions July 16, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 3 (Version 1) Solutions July 9, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Write in complete sentences where
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 2 (Version 1) Solutions June 25, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Write in complete sentences wher
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 1 (Version 2) Solutions June 11, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Also, write in complete sentence
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 2 (Version 1) Solutions February 27, 2014 S. F. Ellermeyer Name Instructions for Problems 14: In each of Problems 14, a definite integral (with answer) is given. For each integral, show how to evaluate the integral (using the integration st
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 2 (Version 2) Solutions February 27, 2014 S. F. Ellermeyer Name Instructions for Problems 14: In each of Problems 14, a definite integral (with answer) is given. For each integral, show how to evaluate the integral (using the integration st
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Version 2) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Version 1) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 4 (Version 2) Solutions April 24, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 4 (Version 1) Solutions April 24, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Practice Version) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 1 (Version 1) Solutions January 23, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: CALCULUS
Limits of Rational and Rational Form Functions (26 January 2014) Limit of a Rational Function The topic Limit of a Function includes a brief theorem on finding the limit of a Rational Function, restated here slightly differently: Limit of a Rational Funct
School: Kennesaw
Course: CALCULUS
Rewrite as: Since Then multiplying all parts of the inequality by As (note that then by the Squeeze (or Sandwich) Theorem, is positive!) we get: , or that We also have Therefore, (A comment for students after studying differentiation and L'Hpital's Rule.)
School: Kennesaw
Course: CALCULUS
Calculus 1 (Math 1190) Preparedness Diagnostic Test The following unofficial self-diagnostic test will help you determine whether or not you are adequately prepared and ready to take Math 1190, Calculus 1. If any significant part of this diagnostic test i
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day 10Sections 2.2 and 2.3 and Chapter 3p.12 Day 10 Homework Testing on numbers: I want you to be able to get these numbers from the calculator and be able to interpret them. I will also ask you to calculate the numbers by hand on a small set of numbers s
School: Kennesaw
Course: ELEMENTARY STATISTICS
ll 3.3 Day 11-12-Sections and6.1to 6.2- p'10 for Homework DaYIl-12 deviationof 8 bpm for your class,find the zheartrate was 70 bpm with a standard I . If the average Is this scoreunusual scorefor a personwith a heartrate of 82 beatsper minute. lnterpretth
School: Kennesaw
Course: ELEMENTARY STATISTICS
Day 9Homework p.8 Day 9 Homework 1. The histogram shows the lengths of hospital stays (in days) for all the female patients admitted to hospitals in New York in 1993 with a primary diagnosis of acute myocardial infarction (heart attack). Answer Who was me
School: Kennesaw
Course: LINEAR ALGEBRA I
1.2 Gaussian and Gauss-Jordan Elimination 1. Denition: A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix. A general m n matrix can be written as A= a11 a12 a1n a21 a22 a2n . . . . . . . . . am1 am2 a
School: Kennesaw
Course: LINEAR ALGEBRA I
Chapter 1. Systems of Linear Equations 1.1 Introduction to Systems of Linear Equations 1. Linear Equations. Def: A linear equation in n variables x1 , x2 , ., xn is an equation that can be written in the form a1 x1 + a2 x2 + + an xn = b where b and the co
School: Kennesaw
Course: LINEAR ALGEBRA I
Chapter 2. Matrices 2.1 Operations with Matrices 1. Operations: Let A = [aij ]mn and B = [bij ]mn , and c is a number, then 1. A = B if and only if aij = bij for all i, j. 2. Let C = [cij ]mn = A B, then cij = aij bij . 3. Let C = [cij ]mn = cA, then cij
School: Kennesaw
Course: LINEAR ALGEBRA I
2.2 Properties of Matrix Operations 1. Properties of Matrix Operations: Assuming that the sizes of the matrices are such that the indicated operations can be performed, then the following rules of matrix arithmetic are valid. A+B =B+A (Commutative law)
School: Kennesaw
Course: LINEAR ALGEBRA I
2.3 The Inverse of a Matrix 1. Inverses: If A is a square matrix, and if a matrix B of the same size can be found such that AB = BA = I, then A is said to be invertible and B is called an inverse of A, denoted by A1 . If no such matrix B exists, then A is
School: Kennesaw
Course: LINEAR ALGEBRA I
2.4 Elenmentary Matrices 1. Denition: An n n matrix is called an elenmentary matrix if it can be obtained from the n n identity matrix In by performing a single elementary row operation. 2. Row operation by matrix multiplication: Let E be the elementary m
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 3 Determinants 3.1 The Determinant of a Matrix 1. The determinant of a 2 2 matrix. The determinant of a 2 2 matrix a b A= c d is given det(A) = |A| = ad bc. Def: Minors and Cofactors. Let A = (aij )nn be an matrix, then the minor of entry aij is denot
School: Kennesaw
Course: LINEAR ALGEBRA I
3.2 Determinants and Elementary Operations Theorem: Let A = (aij )nn be an matrix. If a multiple of one row (column) of A is added to another row (column) to produce a matrix B, then det(A)=det(B). If two rows (columns) of A are interchanged to produce
School: Kennesaw
Course: LINEAR ALGEBRA I
3.3 Properties of the Determinants Theorem: If A and B are nn matrices, then det(AB) = (det(A)(det(B) Theorem: If A is an n n matrix and c is a scalar, then det(cA) = cn det(A). Theorem: A square matrix A is invertible if and only if detA = 0. Theorem: If
School: Kennesaw
Course: LINEAR ALGEBRA I
3.4 Applications the Determinants 1. The Adjoint of a Matrix: cofactor of aij , then the matrix C11 C 21 A= . . . Cn1 If A is an n n matrix and Cij is the C12 C1n C22 C2n . . . . . . Cn2 Cnn is called the matrix of cofactors from A. The transpose of thi
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 Vector Spaces 4.1 Vectors in Rn 1. Vectors in the plane. A vector in the plane is represented geometrically by a directed line segment whose initial point is the origin and whose terminal point is the point (x1 , x2 ). This vector is represented by
School: Kennesaw
Course: LINEAR ALGEBRA I
4.2 Vector Spaces 1. Real Vector Spaces. Def: Let V be a set on which two operations (vector addition and scalar multiplication) are dened. If the following axioms are satised by all objects u, v and w in V and all scalars k and m, then we call V a vector
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 General Vector Spaces 4.7 Coordinates and Change of Basis 1. Coordinates Relative to a Basis: If B = cfw_u1 , u2 , , un is an ordered basis for a vector space V , and x = c1 u1 + c2 u2 + + cn un is the expression for a vector x in terms of the basi
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 General Vector Spaces 4.6 Rank of a Matrix and systems of Linear Equations Def: For an m n matrix A= a11 a12 a1n a21 a22 a2n . . . . . . . . . am1 am2 amn the vectors r1 = [a11 a12 a1n ] r2 = [a21 a22 a2n ] . . . rm = [am1 am2 amn ] in Rn that ar
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 6 Linear Transformations 6.1 Introduction to Linear Transformations 1. Def: If V and W are vector spaces, and if T is a function with domain V and codomain W , then we say f is a transformation from V to W or that f maps V to W , which we denote by wr
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 6 Linear Transformations 6.3 Matrices for Linear Transformations 1. Standard Matrix for a Linear Transformation: Let T be a linear transformation from Rn to Rm and let e1 , e2 , ., en be the standard basis for Rn . If the images of these vectors are T
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 7 Eigenvalues and Eigenvectors 7.1 Eigenvalues and Eigenvectors 1. Eigenvalues and Eigenvectors: If A is an n n matrix, then a nonzero vector x in Rn is called an eigenvector of A if Ax is a scalar multiple of x; that is, if Ax = x for some scalar . T
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 Vector Spaces 4.5 Basis and Dimension 1. Basis. If V is a vector space and S = cfw_u1 , u2 , , ur is a set of vectors in V , then S is called a basis for V if the following two conditions hold: (a) S is linearly independent. (b) S spans V . Ex: 1.
School: Kennesaw
Course: CALCULUS
! " 3 2.5 2 1.5 1 0.5 0 1.2 1.8 1x 1.4 1.6 0.2 0.4 0.6 0.8 2 # $ $ ! " % 2.5 2 1.5 1 0.5 -0.8 -0.6 -0.4 -0.2 0
School: Kennesaw
Course: CALCULUS
! ! " ! ! # $ ! #$ % ! ! ! ! ! ! & ! '! ! ! ! ! ! ! ! ( ) ! ! ! ! ! ! ! ! !
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Math 3310 Section 4.6 Solutions Ryan Livingston Section 4.6 Page 193: 1-11 odd For Problems 1-8, Find the General Solution 1. y + y = sec t SOLUTION: We nd the homogeneous solution by rst dening y = et so that the auxiliary equation becomes 2 + 1 = 0 so =
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
MATH 3310 Exercises on Higher Order ODEs Exercises On Higher Order ODEs For exercises 1-6, (a) nd the characteristic equation (b) the eigenvalues and (c) the corresponding eigenvectors for the matrix Exercise 1 6 3 A= 2 1 SOLUTION: (a) To nd the eigenvalu
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Ryan Livingston Section 1.3 Pg. 22 Exercises 1-7 odd 1. (a) If we wanted to sketch a line that runs through the initial point (0, 2) that is in the direction of the eld, we would get If we recall that the ODE was dy = 2x + y dx with the initial condition
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Ryan Livingston Section 1.1 Pg. 5 Exercises 1-17 1. d2 y dx2 2x dy + 2y = 0 dx From the equation above, we can deduce that it is a second order ordinary dierential equation. We can also deduce that the equation must be linear. Lastly, we can see that the
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Ryan Livingston Section 1.4 Eulers Method pg. 28 1-11 odd 1. Use Eulers method to approximate the solution to the intital vlaue problem dy x = dx y y (0) = 4 at the points x = 0.1, 0.2, 0.3, 0.4 and 0.5 using steps of size 0.1 (h = 0.1) Given the inital c
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Ryan Livingston Section 2.1 pg 46 1-25 odd Determine wether or not the following equations are seperable 1. dy dx sin (x + y ) = 0 SOLUTION: The equation dy sin (x + y ) = 0 dx is not seperable becasue we cannot break up the x and y variables in the term
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Math 3310 Section 4.3 Solutions Ryan Livingston Section 4.3 Page 173: 1-29 For Problems 1-19, Find the General Solution 1. y + y = 0 SOLUTION: We dene y = ex so the auxiliary equation is then 2 + 1 = 0 we solve for and get = i so the general solution is g
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Math 3310 Section 4.4 Solutions Ryan Livingston Section 4.4 Page 182: 9-31 odd For Problems 9-25, Find the Particular Solution 9. y + 2y y = 10 SOLUTION: We begin by nding the homogeneous solution, so we dene y = ex so that the auxiliary equation is then
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Math 3310 Section 4.7 Solutions Ryan Livingston Section 4.7 Page 200 For Problems 9-14, Find the General Solution to the Cauchy Euler Equation 9. t2 y + 2ty 6y = 0 SOLUTION: We suppose that y = tr and y = rtr1 and y = r (r 1) tr2 . If we make these substi
School: Kennesaw
Course: ELEMENTARY STATISTICS
1.13 The answer is part c. A bar graph can be drawn using A,B,C,D and F as lables for the bars and the frequency for the vertical height. A pie chart would require slices labeled with A,B,C,D and F and we would have to figure out the percent.
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
ODE Homework Assignment (A First Course of Differential Equations with Modeling Applications) By Dennis G. Zill 2.2 2.3 2.4 2.5 2.6 4.1 4.2 4.3 4.4 1-25 (odd) 1-29 (odd) 1-19 (odd), 21, 23, 27, 29, 31, 33 1-21 (odd), 23, 25 1, 2, 3 1, 3, 15, 17, 19, 21, 2
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
ODE Homework Assignment (A First Course of Differential Equations with Modeling Applications) By Dennis G. Zill 2.2 2.3 2.4 2.5 2.6 4.1 4.2 4.3 4.4 4.6 7.1 7.2 7.3 7.4 1-25 (odd) 1-29 (odd) 1-19 (odd), 21, 23, 27, 29, 31, 33 1-21 (odd), 23, 25 1, 2, 3 1,
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
4.1 Homework Homework 1, 3, 15, 17, 19, 21, 23, 25, 31, 33 - 56 -
School: Kennesaw
Solutions to Homework Problems from Section 7.3 of Stewart 1. Given that sin x 5/13 and that x is in quadrant I, we have 2 144 cos 2 x 1 sin 2 x 1 5 169 13 so 144 12 . 13 169 Since x is in quadrant I we know that cos x 0 so cos x 12/13. Fro
School: Kennesaw
Answer and Solutions to Section 4.5 Homework Problems S. F. Ellermeyer November 19, 2006 1. It has been shown in class that H = fR0 ; R1 ; R2 g is a subgroup of D3 . Since H is a group of order 3 and Z3 (under addition) is also a group of order 3, an
School: Kennesaw
Answers and Solutions to Selected Section 4.5 Homework Problems Problems 1, 5, 9, 10, 11, 14, 15, 17, 19, 20, 21, 23, 29, 30, 31, 32, 33, and 34. S. F. Ellermeyer 1. s 2t st 3t 1 1 0 9. 1 : s, t s 1 0 2 , 1 3 . t 2 1 3 : s, t . This is a su
School: Kennesaw
Course: ELEMENTARY STATISTICS
DataLabI HannahLeighCrawford Categorical Data: Choose 2 categorical variables a. Construct a contingency table b. Create a bar chart or a pie chart c. Discuss any unusual features revealed by the display of the variable. Describe patterns found. Hint:youm
School: Kennesaw
Course: CALCULUS
Limit of a Function (revised 26 January 2014) We are interested in finding the (two-sided) limit, if it exists, of a function () as , where is Real (and thus finite.) Stating this in a more informal way, we would like to know whether () approaches the s
School: Kennesaw
MATH 1106: ELEMENTARY APPLIED CALCULUS Fall 2014 Instructor - Bruce Thomas CRN Days Time Course Num/Sec Location 83273 MW 12:30PM-1:45PM MATH 1106/06 Burruss Bldg Room 109 A Course in the General Education Program Program Description: The General Educatio
School: Kennesaw
Course: LINEAR ALGEBRA I
MATH 3260/01 Linear Algebra Summer 2014 Instructor: Dr. Liancheng Wang Office: MS 223A E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 12:00-2:00 pm, MW, or by appointment Text: Elementary Linear Algebra, 7th edition, by Ron Larson, BROOKS/C
School: Kennesaw
MATH1112CollegeTrigonometry CourseSyllabusSpring2014 Instructor: MonicaDoriney Time/location:M5:00 6:15 PM and 6:30 7:45 PM Mathematics and Statistics - Room108 Email: mdoriney@kennesaw.edu Office/hours:Varioustimesavailable,byappointment CourseDescriptio
School: Kennesaw
Course: College Algebra
MATH 1111: College Algebra Fall Semester 2013 Instructor Lori Joseph CRN 83606 Days MWF Time 11:00 am 11:50 am Course Num/Sec MATH 1111/32 Location Science 213 A Course in the General Education Program Program Description: The General Education Program at
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
MATH 3310 Differential Equations, Spring 2010 Instructor: Dr. Liancheng Wang Office: Sci. & Math. 511 E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 2:00-3:15 pm, 5:00-6:00 pm, T TH, or by appointment Text: A First Course of Differential Eq