# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

10 Pages

### M202-L37

Course: FACULTY 202, Fall 2009
School: Salisbury
Rating:

Word Count: 537

#### Document Preview

Power 11.8a Series Series of Powers of x [1] A power series convergent for 0 only [3] A power series convergent on the line Radius of Convergence [4] A power series convergent on finite interval 11.8a Power Series 1 1+ x = n =0 ( -x) xn n! n for - 1 &lt; x &lt; 1 for all real x e = x n =0 ln ( 1 + x ) = cos x = ( -1) n-1 x n n =1 n for - 1 &lt; 1 x for all real x for all real x for all...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Maryland >> Salisbury >> FACULTY 202

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.
Power 11.8a Series Series of Powers of x [1] A power series convergent for 0 only [3] A power series convergent on the line Radius of Convergence [4] A power series convergent on finite interval 11.8a Power Series 1 1+ x = n =0 ( -x) xn n! n for - 1 < x < 1 for all real x e = x n =0 ln ( 1 + x ) = cos x = ( -1) n-1 x n n =1 n for - 1 < 1 x for all real x for all real x for all real x for all real x (-1) n =0 n x2 n (2 n )! sin x = n =0 (-1) n x2 n (2 n )! x 2 n+1 (2 n +1)! cosh x = n =0 sinh x = n =0 x 2 n+1 (2 n +1)! 11.8a Power Series c0 + c1 x + c2 x + c3 x + c4 x 2 3 4 x n =0 cn x n for - r < x < r 11.8a Questions About a Power Series For what x does the P.S. converge? Does the P.S. converge absolutely or conditionally? Does the P.S. represent a familiar function? 11.8a Radius of Convrgnc; Ratio Test Decide whether a n = n =0 x cn x n converges. n =0 x an +1 cn +1 x n +1 cn +1 1 cn +1 L = lim = lim = x lim = , where = lim . n n * 8 n n an cn x cn R R n cn Then because x = L R , the RATIO TEST concludes absolute convergence for x < R, meaning - R < x < R , concludes and is divergence for x > R, meaning x < - R or x > R inconclusive for x = R, meaning x = R . In the inconclusive case, the series may converge conditionally. 11.8a [1] Example of Ratio Test Decide whether a n =0 x n = c x n=0 n n = n !x n =0 n converges. cn +1 1 (n + 1)! = lim = lim = lim (n + 1) =* n n * R n cn n! R = 0 Then because x = L R , the RATIO TEST concludes divergence for x > 0. . Clearly the series converges for x = 0 and no other x. 11.8a [3] Example of Ratio Test Does a n =0 x n = c x n =0 n n = ( -1) n=0 n x2 n 22 n ( n!)2 converge ? an +1 x 2 (n !) = 2 n+2 an 2 [(n + 1)!]2 x 2 n 2n+2 2n 2 x = 2 2 2 n! n + 1)! ( 2 an +1 x2 1 L = lim = lim 2 = 0 . 2 n n an 2 ( n + 1) R = This series converges for all real x . 11.8a Radius of Convrgnc; Root Test Decide whether a n = n =0 x cn x n converges. n =0 L = lim * n 8 n an = lim cn x n n n 1 = x lim cn = , where = lim n cn . n R R n n x Then because x = L R , the ROOT TEST concludes absolute convergence for x < R, meaning - R < x < R , concludes and is divergence for x > R, meaning x < - R or x > R inconclusive for x = R, meaning x = R . In the inconclusive case, the series may converge conditionally. 11.8a [4] Power Series ( -3)n x n n =0 an+1 an n +1 = 3 n +1 x n +1 n n +1 n+2 3n x = 3 x 1+ 1 n 2 1+ n 3x The given series converges if 3 x < 1 OR x < 1 3 and diverges if 3 x > 1 OR x > 1 3 If x = 1 , the series becomes 3 11.8a [4] Power Series If x = 1 3 , the series becomes = n =0 x ( -3)n x n n +1 n =0 ( -3) n ( 1 )n 3 n +1 = n =0 (m n 1) n +1 which fails to converge absolutely. If x = + 1 , the series alternates and 3 converges by the alternating series theorem. If x = - 1 , the series diverges. 3
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:

Salisbury - FACULTY - 202
11.8a Power Series Series of Powers of x-a [2] A power series convergent on finite interval Radius of Convergence [5] A power series convergent on finite interval11.8a Power Series1 1+ x= ( x)n =0 nfor 1 &lt; x &lt; 1 for all real xe =
Salisbury - FACULTY - 202
11.9 Differentiation of PS Watch the endpoints of the interval of convergence [4] Differentiating a Bessel function [5] Differentiating one representation to get another 11.9 [4] Differentiating PSJ 0 ( x) = (-1)n =0 n x2 n 22 n ( n!)2for al
Salisbury - FACULTY - 202
11.10a Taylor &amp; McLaurin Series Formula for Coefficients [1] McLaurin series for exp(x) Formula for the remainder; inequality for the remainder [4] Show sin(x) is the sum of its McLaurin series [5] McLaurin series for cos(x) [6] McLaurin series
Salisbury - FACULTY - 202
11.10b Taylor &amp; McLaurin Series [2] Show exp(x) is the sum of its McLaurin series [3] Taylor series for exp(x) centered at 2 [7] Taylor series for sin(x) centered at pi/3 [8] Using series to integrate functions [9] Using series to evaluate limit
Salisbury - FACULTY - 202
DIRECTION FIELDS EXAMPLE 0: EXAMPLE 1: EXAMPLE 2: EXAMPLE 3: EXAMPLE 4: PRODUCE FIGURE 3 PRODUCE FIGURE 7 PRODUCE FIGURE 10 COMPUTE A SOLUTION COMPUTE A SOLUTIONEXAMPLE 0: PRODUCE FIGURE 3y = x + y HORIZONTAL TANGENTS y = 0 0 = x+ y y = xEX
Salisbury - FACULTY - 202
9.3 Separable Equations [1] y' = x2/y2 [2] [3] y' = x2ySEPARABLE EQUATIONS REDUCING TO ANTIDERIVATIVES CONSTANTS OF INTEGRATION LOGS OF CONSTANTS OF INTEGRATION AUTONOMOUS EQUATIONSREDUCING TO ANTIDERIVATIVESdy = p( x) q( y ) dx dy = p (
Allan Hancock College - COMM - 11003
FACULTY OF ARTS, HUMANITIES AND EDUCATION ASSIGNMENT COVER SHEET: ELECTRONIC OR PRINTStudent number: Student name:I certify that this assignment is my own work, based on my personal study and/or research, and that I have acknowledged all materials
Toledo - AST - 320
Mini-Problem Set XVII: BBN: Deuterium and Carbondue 6 Apr 2009We continue with looking at the expected abundance of Deuterium, for three cases of the baryonto-photon ratio, = 0.06, 6, and 600 10-10 . You need the reaction rates mentioned in the
Allan Hancock College - COMM - 11003
COMM11003 Professional &amp; Technical CommunicationLesson9 InformationGathering: ResearchandInformationLiteracyWhatisInformationLiteracy? InformationLiteracytheabilitytoknowwhenthereisaneedforinformation,tobe abletoidentify,locateandeffectivelyuset
Allan Hancock College - COMM - 11003
Lesson 4Planning, Logic and OrganisationObjectives: This section will examine planning the structure of communication, regardless of how you are communicating, to ensure that you give yourself every opportunity to be understood. By the end of this
Rutgers - BME - 402
Senior Design May 2, 2008 Conference ScheduleBreakfast Welcome, Dr. Noshir Langrana &amp; Dean (may be) Keynote speech Class Overview, Dr. Papathomas Coffee Break Chair Intro Friedlander, Ronn Onibokun, Oluwatosin Adimorah, Ogochikwu Patel, Hiren Patel,
Rutgers - BME - 402
Department of Biomedical Engineering, School of Engineering Busch Campus, 617 Bowser Road, Piscataway, New Jersey 08854-8014 Phone: (732) 445-8526 Fax: (732) 445-3753Class of 2008Senior Class SurveyName: __ Permanent Address: _ City: _ State: _ Z
Rutgers - BME - 401
JOB SEARCH STRATEGIES AND RESUME WRITINGJoe Scott, Assistant Director joscott@rci.rutgers.edu Career Services Career and Interview Center Busch Campus Center 732-445-6127, ext 0What we will cover. Basic Steps in a Job Search Job Search Strateg
Rutgers - BME - 402
1 3 5 Cover Images2 4 61. By applying pattern recognition techniques, one can identify pertinent characteristics of an image. This picture represents a computational effort to quantify neuron characteristics such as size, length, and branching po
Rutgers - BME - 402
Department of Biomedical Engineering, School of Engineering Busch Campus, 617 Bowser Road, Piscataway, New Jersey 08854-8014 Phone: (732) 445-8526 Fax: (732) 445-3753Class of 2006Senior Class SurveyName: __ Permanent Address: _ City: _ State: _ Z
Rutgers - BME - 402
Senior Design April 21, 2006 Conference ScheduleName Breakfast WelcomeSpeeches KeynoteSpeaker ClassOverview ChairIntro DAWSON, EILEEN R NIKITCZUK, JESSICA S SHIKHANOVICH, ROMAN WINTER, ASHLEY G GABALE, HEBAH PATEL, PAYAL G YOUSSEF, MERIAM C Coffee B
Rutgers - BME - 401
AGREEMENTONDELIVERABLESFORSENIORDESIGN Date:_ TOTHEMENTOR:Thisformisintendedtobefilledoutbythestudentwiththementor(s)inputand approval.Itissupposedtobealistofitemsthathavetobehandedin,bytheendoftheFall2006 semester,bytheSeniorDesignstudentbelowtothem
Rutgers - MAE - 350
Laboratory Schedule for Each Group (Spring 2007) Week of Group A Group B Group C Group D1/15 1/22 1/29 2/5 2/12 2/19 2/26 3/5 3/19 3/26 4/2 4/9 4/161 1 2 2 3 3 4 4 5 5 6 6 -2 2 1 1 4 4 3 3 6 6 5 5 -1 1 2 2 3 3 4 4 5 5 6 62 2 1 1 4 4 3 3 6 6
Rutgers - MAE - 350
650:349 MECHANICAL MEASUREMENTSGROUP 4BJANUARY 23, 2007Strain Gage Measurements of Constant Stress and Cantilever BeamsYour Name Here*, Norwood Fisher, Lisa Grant, Walter Kibby, Kendall Jones, Chris Dowd, Angelo Moore Department of Mechanical
Rutgers - MAE - 350
650:349 Mechanical Engineering Measurements Laboratory #3 Fall 2006 Strain Gage MeasurementsI. PURPOSE The purpose of this experiment is to demonstrate the use of strain gages and strain rosettes for measuring the strain in different beams. Axial
Rutgers - MAE - 350
650:349 Mechanical Engineering Measurements Laboratory #4 Fall 2006 Fluid Flow Measurements I. PURPOSE. The purpose of this laboratory exercise is to demonstrate the use of different fluid flow measuring devices, namely a Venturi meter, a rotameter,
Rutgers - MAE - 350
650:349 Mechanical Engineering Measurements Laboratory #6 Fall 2006 Temperature Measurements I. PURPOSE The purpose of this laboratory exercise is to demonstrate the use of four different temperature sensors: Mercury in Glass Thermometer, Resistance
Utah - ME - 0304
PROJECT DESCRIPTION: RESCUE ROBOTS ME EN 3200 MECHATRONICS 2003/2004 Assignment: Design and build a robot to compete in the 2004 Mechanical Engineering Rescue Robots Competition. During fall semester your assignment will be to design and build a work
Utah - ME - 0304
PROJECT DESCRIPTION: RESCUE ROBOTS ME EN 3200 MECHATRONICS 2003/2004 Assignment: Design and build a robot to compete in the 2004 Mechanical Engineering Rescue Robots Competition. During fall semester your assignment will be to design and build a work
Utah - ME - 0304
PROJECT DESCRIPTION: RESCUE ROBOTS ME EN 3200 MECHATRONICS 2003/2004 Assignment: Design and build a robot to compete in the 2004 Mechanical Engineering Rescue Robots Competition. During fall semester your assignment will be to design and build a work
Utah - ME - 0304
PROJECT DESCRIPTION: RESCUE ROBOTS ME EN 3200 MECHATRONICS 2003/2004 Assignment: Design and build a robot to compete in the 2004 Mechanical Engineering Rescue Robots Competition. During fall semester your assignment will be to design and build a work
Utah - ME - 0304
RadioShack Store AvailabilityPage 1 of 1IN STORE AVAILABILITYZip Code: 84106 Catalog #: 276-170 Matching Printed Circuit Board This information is current as of 2/19/04 (yesterday), please contact the store to verify availability. Try another zi
Utah - ME - 0304
Utah - ME - 0304
Utah - ME - 0304
ME EN 3200 MECHATRONICS I Fall 2003 Final Project Group Member Evaluation Sheet Evaluators Name: Group: ID:This evaluation is mandatory and must be completed by every student to receive full credit for the project. Be honest and upfront about you
Utah - ME - 0304
2004 Mechanical Engineering Rescue Robots Poster Guidelines ME EN 3210 MECHATRONICS Spring 2004 Robot Competition: Friday April 23, 2004 8-10am. Setup posters in the Saltaire Room on the tables along the perimeter of the room. Tabletop easels will
Utah - ME - 0304
ME 3200 Project/Presentation Evaluation SheetFall 2003 Evaluator Name: Evaluator Group #:Instructions: Do not evaluate your own team. Complete the following evaluation based upon the presentations given in class. The maximum number of points are s
Utah - ME - 0304
Higher Current Motor Driver Alternative (Single chip H-Bridge solution) ME EN 3210 MECHATRONICS II- SPRING 2004 Background: One problem of motor control with the HandyBoard (HB) is current output capability. Solutions to this dilemma include modifyin
North-West Uni. - CS - 340
Introduction to Networking Instructor: Prof. Aleksandar KuzmanovicAdvanced SocketsJohn Otto TA , Intro to Networking Jan 24, 2007 Recital 3Homework grader Geet Duggal, geet@geetduggal.com. Office hours on Tuesdays between 4 and 6The problem
North-West Uni. - CS - 340
Welcome to CS 340 Introduction to Computer NetworkingOve w rvieourseAdm inistrativeTrivia C rne cture I nte t Archite twork Protocols Ne twork Edge Ne y m tworks A taxonom of com unication neSome slides are in courtesy of J. Kurose and K. R
North-West Uni. - CS - 340
Re w of Pre vie vious Le ctureourseAdm inistrativeTrivia C rne cture I nte t Archite twork Protocols Ne twork Edge Ne y m tworks A taxonom of com unication neSome slides are in courtesy of J. Kurose and K. RossOve w rviee Hom work 1 out,
North-West Uni. - CS - 340
Announce e m nt Re citation m rials online ate All find partne rs? Re to TA and ge group I P port taddre ss1Re w of Pre vie vious Le cture Ne twork acce and physical m dia ss e I nte t structureand I S rne Ps De &amp; loss in packe lay t-switc
North-West Uni. - CS - 340
Application laye r Ele ctronic Mail r S MTP, POP3, I MAP DNS P2P filesharing1Ele ctronic MailThre m com nts: e ajor pone use age r nts m se rs ail rve sim m transfe protocol: S ple ail r MTPm ail se r rve use r age ntoutgoing m ssageque
North-West Uni. - CS - 340
TransportLayerOurgoals: understandprinciples behindtransportlayer services:r r r r learnabouttransportlayerprotocolsintheInternet:r r rmultiplexing/demultiplexing reliabledatatransfer flowcontrol congestioncontrolUDP:connectionlesstranspo
North-West Uni. - CS - 340
Outline Transport-laye se r rvice s Multiple xing andde ultiple m xing C onne ctionle transport: ss UDP Principle of re s liabledata transfe r1Principle of Re s liabledata transfe r im portant in app., transport, link laye rs top-10 list
North-West Uni. - CS - 340
Midterm ReviewIn class, 1:002:30 pm, Tu. 2/6 Closed Book One 8.5&quot; by 11&quot; sheet of paper permitted (single side)Lecture 1 Internet Architecture Network Protocols Network Edge A taxonomy of communication networksA Taxonomy of Communication Net
North-West Uni. - CS - 340
Chapter4:NetworkLayer 4.1Introduction 4.2Virtualcircuitand 4.5Routingalgorithms r Linkstate r DistanceVector r HierarchicalroutingdatagramnetworksNetworkLayer41Networklayer transportsegmentfromsending toreceivinghost onsendingsideenc
Carnegie Mellon - STAT - 754
1136-752: Lecture 1How is this course different from your earlier probability courses? There are some problems that simply can't be handled with finite-dimensional sample spaces and random variables that are either discrete or have densities. Exa
Carnegie Mellon - STAT - 754
36-754, Advanced Probability II or Almost None of the Theory of Stochastic ProcessesCosma Shalizi Spring 2007ContentsTable of Contents iComprehensive List of Definitions, Lemmas, Propositions, Theorems, Corollaries, Examples and Exercises xxiii
North-West Uni. - CS - 340
MACAddre s and ARP sse 32-bit IP addre ss:rne twork-laye addre r ss r use to ge datagramto de d t stination IP subne t MAC(or LAN or physical or Ethe t) addre rne ss:ruse to ge datagramfromoneinte d t rfaceto anothe physicallyr conne d inte
North-West Uni. - CS - 340
Chapte 6: Wire ss and MobileNe r le tworksBackground: # wire ss (m le obile phonesubscribe now e e # wire ) rs xce ds dphonesubscribe rs! com pute ne laptops, palm r ts: tops, PDAs, I nte t-e rne nable d phoneprom anytim unte re I nte t acce ise
North-West Uni. - CS - 340
NetworkSecurityWhatisnetworksecurity? Principlesofcryptography Authentication Accesscontrol:firewalls Attacksandcountermeasures1Whatisnetworksecurity?Confidentiality:onlysender,intendedreceivershouldunderstand messagecontents r senderencryptsme
North-West Uni. - CS - 340
Introduction to NetworkingTHE UNIX SYSTEMJan 12 2005 Recital 2Unix Tools Shells Useful Commands Pipes &amp; RedirectsShells sh, csh, ksh, tcsh, bash, zsh Recommend tcsh or bash for interactive use. Both have command completion, simple comman
North-West Uni. - CS - 340
Introduction to NetworkingJohn Otto TA March 5, 2007 Recital 6RoutingRoutingprotocolGoal:determinegoodpath (sequenceofrouters)thru networkfromsourcetodest. A5 2 1B23 3 1C15Graph abstraction for routing algorithms: graph nodes are
North-West Uni. - CS - 340
TCP DetailsIntroduction to NetworkingJohn Otto TA Jan 31, 2007 Recital 4Netprog: TCP Details1The TCP ProjectImportant Handouts: Minet The Minet Technical Report The Minet Socket Interface TCP Guides RFC 793 (in convenient HTML format),
Wyoming - NASC - 5120
Science Week 1- June 11-15 Monday 7:30 - 8am 8-10:30 10:45 - 12 12 - 1:30 1:30 -3 3:15 - 5:1511 Tuesday1213 Wednesday14 Thursday Friday15Welcome Breakfast Astronomy Earth Science Lunch Earth Science Assessment Earth Science Astronomy Lunc
Michigan State University - ME - 475
ME 475 - Optimization of a FrameAnalysis Problem Statement: The following problem will be analyzed using Abaqus.7 5,000 N 4 6 37 10,000 N 6 5,000 N 445543 2 1 13211Figure 1. Full frame geometry and loading (gravity load not s
Mich Tech - FW - 4140
FW4140 Vegetation ModellingSpring 2009Assignment 7 Adams and Ek (1974)IntroductionDr. Webster once asked me why more capstone students didnt use the Adams and Ek (1974) equations instead of FVS, when developing their management plan. In this
BYU - ECE - 464
Lab #4 Coupled Line FilterECEn 464 Week 5 Introduction: Coupled line filters are among the most practical filters used in real microwave circuits. This laboratory exercise demonstrates their flexibility in adapting to a range of frequecies. Be sure
BYU - ECE - 464
Lab #5 Amplifier and Noise AnalysisECEn 464 Week 5 Introduction: Amplifiers are found in nearly all microwave systems. In particular, low noise amplifiers are necessary for front-end receiver amplifiers. This lab introduces the student to means of a
University of Florida - CNT - 4007
CNT4007C Computer Network Fundamentals Spring 2009 April/29/2009 Programming Assignment 3 Grading Guidelines Project Implementation a. Submission b. Compil
University of Florida - CNT - 4007
CNT4007C Computer Network Fundamentals Spring 2009 April/29/2009 Programming Assignment 3 Grading Distribution Distribution 91~100 81~90 71~80 61~
Virginia Tech - MATH - 4124
Math 4124Wednesday, April 29April 29, Ungraded HomeworkLet k = Z/7Z, the field with 7 elements. Prove that k[x]/(x3 +2) is a field with 343 elements. We show that x3 + 2 is irreducible. Indeed suppose x3 + 2 can be factored nontrivially as f g,
Virginia Tech - MATH - 4124
Math 4124Friday, May 1May 1, Ungraded HomeworkLet k = Z/2Z, the field with 2 elements. Prove that k[x]/(x5 + x2 + 1) is a field with 32 elements. First we show that x2 + x + 1 is the only irreducible polynomial of degree 2 in k[x]. Indeed there
Cal Poly - CS - 2214
CS2214 COMPUTER ARCHITECTURE &amp; ORGANIZATION SPRING 2009REMAINING WORKWhat is left for students for the rest of the semester ?1) Homework VII : Homework VII will not be submitted. Only cache memory related material is on the final exam.2) Reci
UNL - PSYCH - 941
1. Having developed a new program to treat test anxiety among college students, the research practitioner was eager to try it out. During the first week of classes she recruited 40 students from an Introductory Psychology class who self-identified as