# Calculus: Single and Multivariable

Title: Calculus: Single and Multivariable

Author: Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum, Daniel E. Flath, Patti Frazer Lock, Thomas W. Tucker, David O. Lomen, David Lovelock, David Mumford, Brad G. Osgood, Douglas Quinney, Karen Rhea, Jeff Tecosky-Feldman

Rating:

###### Document Preview

Week #10 - The Integral Section 5.3 From “Calculus, Single Variable” by Hughes-Hallett, Gleason, McCallum et. al. Copyright 2005 by John Wiley & Sons, Inc. This material is used by permission of John Wiley & Sons, Inc. SUGGESTED PROBLEMS 1. If f (t) is measured in dollars per year and t is measured in years, what are the units of b f (t)dt? a The units are the product of the the function, f (t), and dt...

##### Unformatted Document Excerpt
Coursehero

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Virginia Tech - ACIS - 1504
Chapter 1Information Pages 10 - 161Todays Objectives Define data and information. Know the characteristics of good information. Understand how to be information literate. Explore ethical issues concerning the use of misdirected information.
Virginia Tech - CHEM - 1015
Chemistry in Focus 3rd edition TroChapter 1 Molecular ReasonsFiresticks A chemical reaction is an extraordinary transformation. Microscopic vs. Macroscopic Worlds Interpretation of a situation depends manner in which it is framed And so, why
Virginia Tech - ACIS - 1504
ACIS 1504 File Management Homework Uploading Homework to Courseware ServerYou may begin this homework assignment during the second week of classes. Do not start before that date because the Courseware folders will not be setup until that time. The
Virginia Tech - CHEM - 1015
Chemistry in Focus 3rd edition TroChapter 2 The Chemists ToolboxCurious? To revisit Chapter 1, why should nonscience majors study science ? If you cannot think of a question you want answered, try to think of one for which a group of people mig
Virginia Tech - CHEM - 1015
Chemistry in Focus 3rd edition TroChapter 3 Atoms and ElementsThe connection between the atom and the element is the key to understanding the chemical world. An atom is the smallest identifiable unit of an element. Similarities and differences
Mary Washington - BUAD - 259
CHAPTER 10 Survey Research: Basic Methods of Communication with Respondents Brief Outline Zikmund Chapter Content Media types of media used to communicate with respondent Personal Interviews advantages and disadvantages, types of interviews
Mary Washington - BUAD - 259
Chapter 1 The Role of Business Research Brief Outline Zikmund Lecture Content Definition of Business Research all research techniques applicable to business Basic Research and Applied Research important to clarify the difference Value of
Mary Washington - BUAD - 259
Chapter 3 Theory Building Brief Outline ZikmundLecture Content Concept of Theory what it means to theory Ways of thinking approaches to knowledge acquisition Terminology basic terminology related to theory building Generating and Verify
Mary Washington - BUAD - 259
CHAPTER 13 Measurement and Scaling Concepts Brief Outline Zikmund Chapter Content Deciding What to measure scaling concepts, operational definitions, and rules of measurement Type of Scales properties of nominal, ordinal, interval, and ratio sc
Mary Washington - BUAD - 259
CHAPTER 9 Survey Research Overview Brief Outline Zikmund Chapter Content Nature of surveys objectives, advantages and disadvantages Errors in Survey Research two broad types random sampling error and systematic error Random Sampling Er
Mary Washington - BUAD - 259
CHAPTER 6 Problem Definition and the Research Proposal Zikmund Chapter Content Nature of the Problem first step is assessing the level of uncertainty The Process of Problem Definition a six step sequence of analyses The Research Proposal a wr
Mary Washington - BUAD - 259
Chapter 4 The Research Process: An Overview Brief Outline ZikmundChapter Content Three Research Decision Situations degree of uncertainty about the problem The Six Stages of the Research Process step-by-step sequence of research stages Res
Mary Washington - BUAD - 259
CHAPTER 14 Attitude Measurement Brief Outline ZikmundChapter Content Terminology and Concepts definitions and four common measurement approach Physiological Measures of Attitudes brief mention of these techniques Attitude Rating Scales
Mary Washington - BUAD - 259
Chapter 6It is extremely important to define the business problem carefully because the definition determines the purpose of the research and, ultimately, the research design The right answer to the wrong question may be absolutely worthless Do not
Mary Washington - BUAD - 259
Chapter 3Prediction and understanding are the two purposes of theory Theory is a coherent set of general propositions, used as principles of explanation of the apparent relationships of certain observed phenomena allow generalizations beyond indiv
Mary Washington - BUAD - 259
Chapter 4 Decision making the process of resolving a problem or choosing among alternative opportunities keys to decision making are recognizing the nature of the problem or opportunity, identifying how much info is available, and determining what i
Mary Washington - BUAD - 259
Business Research Chapter 1Primary task of management is effective decision making The task of business research is to generate accurate info for the use of decision making Business research the systematic and objective process of gathering record
Mary Washington - BUAD - 259
Chapter 13The definition of the problem, based on exploratory research or managerial judgment, indicates the concepts to be investigated True measurement of concepts requires a process of assigning precise scores or numbers to the attributes of peo
McGill - CHEM - 110
PERIODCITY TESTBANK MC SOLUTIONS1. D 3. B 4. D 6. B 7. C 11. B 12. C 15. B 16. B 17. B 18. A 19. C 20. B 24. C 25. B 29. B 30. D
McGill - CHEM - 110
ORGANIC TESTBANK SOLUTIONS SHORT ANSWER4.5.6.11.12.13. Missing14.18.19.20.21.22.28.29.30.31.35.36.37.38.45.46.47.51.52.53.54.59.60. Missing61.62.66.67.68.69.70.71.76.77.7
McGill - CHEM - 110
IB PERIODICITY TESTBANK SOLUTIONS SHORT ANSWER2.5.8.9.10.13.14.ligand: a molecule or ion that can bond to a (central) metal ion (to form a complex); 2+ NH3: Lewis base and Cu : Lewis acid (need both for mark); each NH3 / ligand donate
McGill - CHEM - 110
ORGANIC TEST BANK SOLUTIONS2. D 7. D 8. C 9. A 10. C 16. D 17 B 23. A 24. B 25. B 26. C 27. D 32. B 39. C 40. A 41. A 42. D 43. B 44. D 48. B 49. C 50. D 55. A 56. C57. D 58. C 63. B 64. C 65. D 72. B 73. D 74. B 75. A missing MC: 1, 3, 15, 33, 3
Uni. Akureyri - LITERATURE - 101
Icelandic translation From the book of evil g-me Hestur- horse Hs- House Ms- mouse Blindur- blind Sjr- sea Efnafri- chemistry Sofa- sleeping Skrsmli- monster Bjr- beer Brennivn Black death, an Icelandic liquid Mamma- mom Tussa- bitch
Uni. Akureyri - HISTORY - Literature
Matvla- og nringarfrideild Haust 2008Inngangur a nringarfri NR101GFING 3 MATSELAGERTveir og tveir vinna saman a ger matsela. Hver hpur velur tvo einstaklinga/ hp og vinnur eins dags matseil fyrir hvorn eirra. Stust er vi matarvefinn vi rvinnslu
Uni. Akureyri - HISTORY - Literature
Matvla- og nringarfrideild Haust 2008Inngangur a nringarfri NR101GFING 2 Nringarefnainnihald matvlaFramkvmd Skoaar vera msar matvrur m.t.t. innihalds eirra af orku og msum nringarefnum me hjlp nringarefnataflna. Nringarefnatflur eru vef Mats (h
Uni. Akureyri - HISTORY - Literature
Vinnu plan verklegt 2008: Vika 1 (08.-13.09) Kynning , ryggisreglur og afhending skpa. fing1. Introduction to laboratory techniques &amp; fing 2. Nomenaclature and reaction stoichiometry Framkvmir hver fyrir sig Pre-lab: allar slttttluspurningar einnig b
Uni. Akureyri - HISTORY - Literature
Matvla- og nringarfrideild Haust 2008Inngangur a nringarfri NR101GFING 3 MATSELAGERTveir og tveir vinna saman a ger matsela. Hver hpur velur tvo einstaklinga/ hp og vinnur eins dags matseil fyrir hvorn eirra. Stust er vi matarvefinn vi rvinnslu
Minnesota - BMEN - 3001
Lecture 4 BMEn 3001 Biomechanics 10 September 2008 Last Lecture Linear Algebraic Systems LU Decomposition PivotingTopics for Today LU (nish) Pivoting Matrix Inversion The Eigenproblem Condition NumberAn LU Decomposition Note tha
Minnesota - BMEN - 3001
Lecture 3 BMEn 3001 Biomechanics 8 September 2008 Last Lecture Dimensional vs. Dimensionless Numbers Start Math Review Scalars, Vectors, Matrices, and Tensors Notation Basic operationsTopics for Today Gauss Elimination LU Decompositi
Minnesota - BMEN - 3001
Lecture 5 BMEn 3001 Biomechanics 12 September 2008 Last Lecture Matrix Inverse The eigenproblem (in brief) Condition NumberTopics for Today Special Matrices Symmetric Banded Sparse Iterative Solution TechniquesSymmetric Matrices
Minnesota - BMEN - 3001
Lecture 6 BMEn 3001 Biomechanics 15 September 2008 Last Lecture Review of Linear EquationsTopics for Today Review of Linear Physics Newton's First and Second Laws Superposition and the additivity of forces Equilibrium Review of Angul
Minnesota - BMEN - 3001
Meeting 2 BMEn 3001 Biomechanics 5 September 2008 Last Lecture Course IntroductionTopics for Today Dimensional vs. Dimensionless Numbers Start Math Review Scalars, Vectors, Matrices, and Tensors Notation Basic operationsMATLAB Tutor
University of Florida - MCB - 3020
Lecture overview Size and shape of microbes used in classification Envelopes (cytoplasmic/plasma membranes, cell walls, outer membranes, S-layers) Prokaryotic appendages (flagella and pili) Cytoplasmic structures (nucleoid, ribosomes, cytoskeleto
University of Florida - MCB - 3020
Lecture overview Microbial nutritional requirements and classification Prokaryotic transport systems Measuring microbial growth1Microbial nutritional requirements Basic requirements are sources of carbon precursors (12-13); source of electron
University of Florida - MCB - 3020
Microbes Microbeseitherprokaryotic(lackatrue nucleus)oreukaryotic(haveatruenucleus) Somefreeliving,somenot Mostaresinglecelled,butsomemaycome togetheratdifferenttimesofthelifecycle Varyinsize(E.coliis1x2m),butmost aresmall(needamicroscopetosee)
University of Florida - MCB - 3020
MCB 3020MCB 3020 Instructor information INSTRUCTOR: Sharon Ogden, Ph.D. Office: Room 1047, MCSB E-mail: sdogden@ufl.edu Office phone: 352-392-7203 Thurs. (Appts. only 10 AM 2 PM) distance calls Office hrs: Tues. (10 11 AM); Wed. (1 2 PM);
University of Florida - MCB - 3020
Lectureoverview Unitsofmeasurementforsmallobjects Thelightmicroscope Cellstainsusedinmicrobiology Othermicroscopictechniques123Thecompoundlightmicroscope Partsofmicroscopeonleft,lightpathonright Bauman(2006)Fig.4.44Howmicroscopesen
LSU - ENGL - 3220
Day 111/08/2008 09:17:00Book List: Peter Broner, Night of the Broken Glass (Krystalnacht) Lucy Dawidovicz, The ware against the Jews 1933-1945 Thomas Keneally, Schindlers List Beonard Schlink, The Reader: a Novel Leon Uris,Mila 18 Elie Wiesel, Ni
LSU - ENGL - 3220
Holocaust Literature04/08/2008 09:25:00Book List: Peter Broner, Night of the Broken Glass (Krystalnacht) Lucy Dawidovicz, The ware against the Jews 1933-1945 Thomas Keneally, Schindlers List Beonard Schlink, The Reader: a Novel Leon Uris,Mila 18
LSU - ENGL - 3220
Mila 1809/08/2008 10:02:00Multiple narrative method Excerpts from the Alexander Brandels Diary The omniscient narrative voice (of author) The German military documents and printed orders The headline in old movie theater newsreels Andrei Androfsk
LSU - ENGL - 3220
06/08/2008 09:33:00Miguel de Unamuno St. Emmanuel, Chirstian Martyr Ashkenazi Jews Northwest European Sephardic Jews Southern Europe/Africa/Morrocco/ Yemenite Jews Yemen (some men were bigamists) All conflict (casually) with each otherwest Brai
LSU - ENGL - 3220
The Night of the Broken Glass 07/08/2008 09:50:00o Main Characters Emilia and Samuel Silver o Daughter Sophie (proudly Jewish), son Paul Leopold works in Sams jewelery shop Herbert walks with a limp Baron Otto von Hallenberg Olga, Ottos wife,
New Hampshire - HIST - 406
Alex MacPherson Venetia Guerrasio 2/22/2008 History 406 Section14 American Imperialism Up until the Spanish-American War in 1898, America had been, rightfully so, an isolationist country. Isolationism is a foreign policy that avoids international all
Valdosta - ENGL - 80257
Hiatt 1 Morgan Hiatt Karen Morris English 1102- X 6 March 2008 Cons of Same-Sex Marriage The argument over an approval for same-sex marriage has been long and drawn out. Yes, both sides have valid points to support their arguments; however, opponents
Valdosta - ENGL - 80257
2. Marriage as culture Marriage is, and has been for millennia, the institution that forms and upholds for society, the cultural and social values and symbols related to procreation. That is, it establishes the values that govern the transmission of
Valdosta - EDUC - 80454
Morgan Hiatt September 4, 2008 Education 2110 Teacher Dress Codes: Article Critique The concerns that are addressed in this article include the proper attire for educators. How far is too far when administrators and school boards set these standards?
Valdosta - ENGL - 80257
Think back to when you were the age of ten. The majority of children in this age group spend most of their days in a third grade classroom or watching cartoons on the weekend. Some have the opportunity at this age to travel to Disney World or go to a
Valdosta - ENGL - 80257
Hiatt 1 Morgan Hiatt Karen Morris English 1102- X 6 March 2008 Cons of Same-Sex Marriage The argument over an approval for same-sex marriage has been long and drawn out. Yes, both sides have valid points to support their arguments; however, opponents
Harvard - MATH - 21B
Chapter 6ISM: Linear AlgebraChapter 6 6.11. Fails to be invertible; since det 2. Invertible; since det 3. Invertible; since det 1 2 = 6 - 6 = 0. 3 62 3 = 10 - 12 = -2. 4 5 3 5 = 33 - 35 = -2. 7 11 1 4 = 8 - 8 = 0. 2 8 4. Fails to be invertib
Harvard - MATH - 21B
Chapter 7ISM: Linear AlgebraChapter 7 7.11. If v is an eigenvector of A, then Av = v. Hence A3 v = A2 (Av) = A2 (v) = A(Av) = A(Av) = A(2 v) = 2 Av = 3 v, so v is an eigenvector of A3 with eigenvalue 3 .1 2. We know Av = v so v = A-1 Av = A-1 v
Harvard - MATH - 21B
ISM: Linear AlgebraSection 8.1Chapter 8 8.11. e1 , e2 is an orthonormal eigenbasis. 2. 3.1 21 1 , 12 1 -1is an orthonormal eigenbasis.2 -1 , 15 is an orthonormal eigenbasis. 1 2 1 1 1 1 1 1 4. 3 1 , 2 -1 , 6 1 is an orthono
Harvard - MATH - 21B
Chapter 9ISM: Linear AlgebraChapter 9 9.11. x(t) = 7e5t , by Fact 9.1.1. 2. x(t) = -e e-0.71t = -e1-0.71t , by Fact 9.1.1. 3. P (t) = 7e0.03t , by Fact 9.1.1. 4. This is just an antiderivative problem: y(t) = 0.8 t2 + C = 0.4t2 + C, and C = -0.
Harvard - MATH - 21B
Chapter 5ISM: Linear AlgebraChapter 5 5.1 72 + 112 = 49 + 121 = 170 13.04 2. v = 22 + 32 + 42 = 4 + 9 + 16 = 29 5.39 3. v = 22 + 32 + 42 + 52 = 4 + 9 + 16 + 25 = 54 7.35 1. v = 4. = arccos 5. = arccos 6. = arccosuv u v uv u v uv u
Harvard - MATH - 21B
ISM: Linear AlgebraSection 4.1Chapter 4 4.11. Not a subspace since it does not contain the neutral element, that is, the function f (t) = 0, for all t. 2. This subset V is a subspace of P2 : The neutral element f (t) = 0 (for all t) is in V .
Harvard - MATH - 21B
ISM: Linear AlgebraSection 3.1Chapter 3 3.11. Find all x such that Ax = 0: . 1 2. 0 . . . 0 3 4. - . 1 0. 0 , so that x = x = 0. . 1 2 . . 0 0 1.ker(A) = {0}. 2. Find all x such that Ax = 0: . . 3. 2 3. 0 - 1 2 . 0 , so that . . . 6 9. 0 .
Harvard - MATH - 21B
Chapter 2ISM: Linear AlgebraChapter 2 2.11. Not a linear transformation, 0 2 2. Linear, with matrix 0 0 1 0 9 3 -3 1 2 -9 4. A = 4 -9 -2 5 1 5 5. By Fact 2.1.2, the three columns of the 2 3 matrix A are T (e1 ), T (e2 ), and T (e3 ), so
Harvard - MATH - 21B
ISM: Linear AlgebraSection 1.1Chapter 1 1.11. x + 2y x + 2y = 1 -y 2x + 3y = 1 -2 1st equation x + 2y = 1 -2 2nd equation x y=1 y 2. 4x + 3y 7x + 5y3 x + 4y 1 -4y 3 x + 4y = 2 4 =3 7x + 5y=1 = -1 (-1)= -1 , so that (x, y) = (-1, 1). =
UGA - ACCT - 7605
ACCT 7605 Exam I- Practice Questions Gleim's Exam Questions Test Prep Financial Accounting [1] Gleim #: 25.1.1 - Source: Publisher A business combination may be structured as a merger, a transfer of equity interests, a direct acquisition of net asset
UGA - LEGL - 4400
Chapter 14: Mistakes, Fraud, and Voluntary Consent 1) Mistakes of Fact: occur in two forms bilateral and unilateral a) Bilateral Mistake made by both of the contracting parties; occurs when both parties are mistaken as to an existing material fact
UGA - LEGL - 4400
Chapter 11: Agreement 1) Requirements of the Offer: a) Offer: is a promise or commitment to do or refrain from doing some specified thing in the future. b) 3 elements necessary for an offer to be effective: i) The Offeror must have a serious intentio
UGA - LEGL - 4400
Chapter 15: The Statute of Frauds Writing Requirement 1) The Origins of the Statute of Frauds a) In 1677, statute passed by the English Parliament known as the Act for the Prevention of Frauds and Perjuries i) Established that certain types of contr