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Feldman jean feldmansbrewtonLaura SalganikWestatWESTATJonathan Troper Susan Rifkin eoffrey Saxe????? mcasillasAmy Stuart Wells Eifannag LiKimberley M Crawford !"#$%&'(. O features 1. rhetorical text funtions speech act functions B. Structal features 1. length of response 2. other A. Response formatsuestions/D F B. Structural F. Response F 1. scoring by computer/human . response captured on computer/videotape B.Scoring 1. rubric a. vocabulary b. grammatical accuracy c. fluency . coherence e. cohesion f. length of reHSC/EDSg the tasks identified in the first stage, conducting two sorts, and an end user tryout to determine thfeasibility and validity of using the current descriptors to meaningfully differentiate among students r specific purposes. 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Talley Jeff DaulerBBN Laura Murdy Kim BicknellTricia Petrosillo Bruce RosenNancy Kay Sturm#Center for Educational Technologies Bruce HowardAdministration CenterElaine ColemanirlIRL Gayle Britt Wadi HaddadWadi D. Haddad Martha AgredaSaxe Jim SlottaL LadaoJoseph KrajcikCarolyn Staudt Shea McGovernDixonRussell G. ComgaltonSASPG Rebecca Boger Sherry Hsi John Kupiecjfeldman Kristin Barrbthomas Kate HarveyCynthia McIntyreGeorge Collison WestEd Staffjanice schafer FWL StaffFAR WEST LABORATORY.sKps Ann Abeille Jonathan Ruhe helen collinsTodd WallingfordKaren SchwartzDr. Perry Davis Sherry WalkerLiz PapeLarriveeDavid PerlmutterMass. 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BinghamDavid Moursund Dave Moursund Jim Parry Milton ChenSteveAnaisMicheleOlivia TaguinodUSER Mark SargentComputer ServicesComputer Services.Edward R. LongoTera Lungstrom Bill Calhoun Bob CondursoRonald B. SobelAlexis DobbinsBellcoreEd Longo Cary Toor Ramez GhattasCharles P. Kapp Thang Nguyen Alan Kramer Diane Jones Alan LewineAlan R. Lewine Kathi BowieJRUDD Karen Austin0  LRochelle DeJongDesktop Services Eric S. CohendveitkusROSALYN D. YOUNGAUTHORIZED GATEWAY CUSTOMER Diane LorencDiana BeckmannSridhar IyengarBartus H. Batson Pat TinsleyX-Analoginformation technologies pbsReplacement LaptopNina Marie RomontioRobert EdwardsMichael Schwarz Jo MillerMogollonMSchwarz Steve Bennett KIKIM MEDIAGilaSara ArmstrongIna Rae Levine MELC USERCathleen Fulton Gloria GibsonSandraStaffStephen C. 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Thompson Tenth PlanetGateway Authorized Customer Anna Sfard J.D.TinsleyThomas LingefjrdNicholas K. OppongDenise S. MewbornVILMA MARIA MESAHeide G. WiegelClariceDPI???Eunice*x0"_ #P _ys:Gr. 3-5 WRiting Assign.@Anni Waters MartinAmy and Chad CarrollZhonghong JiangJim Burnett Jr.dball Deborah Ballqqq Ira PapickNMREnrique GalindoLRDCStanley LombardoAlfred B. ManasterAlfred ManasterEducational Technology Unit Dan Koretz Brian StecherJoan L. HermanLynee Gilfillan Harry O'NeilUCSB Eva L. Baker Eva Bakeretu Katharine FryStevie D'AmicoCSE"Center for the Study of EvaluationRobert A. DennisSAIS Ron DietelVernaWallace Etterbeek.MDTP Cindy Johnson Michael KatzCarol E. Henry Renee Wilmeth Freelance Selim Tuvi"Carol E. Henry a book in itself -- Hank Resnik CDM STAFFvalued customer Jeff Olsen Donn RitchiePat HSan Diego State University Brock Allen Donna Forbes Bob HoffmanLisa M. Butler Geoffrey SaxeSteven R. Guberman Tine F. Sloan John Iwanagaeducational technology unitDr. John V. Richardson Jr.yasmincseDr. Anthony B. Maddox, P.E. Aimee DorrETUKarina B. Otoya Gene KrausJohn M. Carethers om serverHenryE. Henry l E. Henry. Henry E. Henry Donna AmesCarol Wickham MidgettMary M. LindquistDouglas H. ClementsIndiana UniversityLyneette EsparzacccNetwork Operations Groupbc Liz FischerMichael HumphrysCUNYDan DickKristina Garrett Joanne BradyOCRThe College FundEnd User Iman HobbsStephanie BryantDeborah Bryant KTO'Connell Jan Ellis Powerbook 520 Cindy OrrellLINDA TSUKAMOTOGreg HendersonMichael Fradellajose arredondoMichael Rufflo sespinosaRicardo DominguezComputer Curriculum Corporation Susanne Cohen Theodore WhamDaniela SalvadoriRobin C. Stevens Steve Haney Gail Bordi Robin Stevens Vicki Gundrum Dan Zalleszippy the software pinheadMary Sue Dillingsofski Kate WilsondogboyCCC QA EngineerMarilyn QuinsaatKathleen HolanCindy AhlquistLorraine RossiniComputer Curriculum Corp. Mark LunrdoniIvana AbruzzeseGregg LebovitzField Sales #10BBN-MISTerri Drew TuraKim M. 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Quinto Sted Chenmariename Alex KroogmanPerdigon, JoseLaura Lee Bennetta-khatch Mark OlsonRicky Tan, LorraineClaudine T DavidReyes, Eleonora (Nori)Ahmad Zan JunusAhmad Zahidi IsmailMOHD NOOR ABDULLAHreengZahari Abu MansorFauziah KamsariTMBSity Farizah AbidinRICHARD DENTON BORDEN Cowan, Keith Colby Harder Video_ConOrion Technologies Inc.Oscar ApacibleApacible, OscarDONALD J. O'MARAPre-loaded UserWhitey C. LopaJayme, Edgar J. DIVERSIFIED STEVE HESSBuenaventura, Arsenio A.Jun BuenaventuraGeomatics Engineering David BurkeyC&I Betsy McNeal Jeff McNealMartin A. Simon Sheila Flood Fred Crouse ReflectorBledsoe Neil PatemanNeil A. Patemanmwalker Tom GondaRichard D'Andrea Alan Bishop Larry SowderJudith T. Sowder Math SciencesJRMERachel MontgomeryCharlotte Higuchi Judy Miyoshi David Niemi Phil EnderQSP 9500RandyMaryl Gearhart"SB 1274 School Restructuring Study Saxe/Gearhart Larry Picus SonnenscheinGustavo E. FischmanJean I. Feldman jean feldmansbrewtonLaura SalganikWestatWESTATJonathan Troper Susan Rifkin eoffrey Saxe????? mcasillasAmy Stuart Wells Eifannag LiKimberley M Crawford !"#$%&'(. O features 1. rhetorical text funtions speech act functions B. Structal features 1. length of response 2. other A. Response formatsuestions/D F B. Structural F. Response F 1. scoring by computer/human . response captured on computer/videotape B.Scoring 1. rubric a. vocabulary b. grammatical accuracy c. fluency . coherence e. cohesion f. length of reHSC/EDSg the tasks identified in the first stage, conducting two sorts, and an end user tryout to determine thfeasibility and validity of using the current descriptors to meaningfully differentiate among students r specific purposes. During the third stage, the results of the sorts and the tryout will be analyzed to determinehe degree of match between expert and non-expert user judgments of proficiency and the current descriptor The outcome the work in the skill area of wr  ,nse g. comprehensibility Paula Hilgado valuation n L. HermanJ&er HermanK45J 7 va L. Baker . DennisEational Technology UnitK Phil EnderL HiguchiOTTine F. SloanUy SaxeX ffrey Saxed[^ Saxe _ e F. SloanSloan Sloanrey SaxeHh offrey Saxeqt"u~ ! k "!`""!e" les by adminng wilof EvaluationBaker. Herman an L. HermanJ&HermanK)K*aker. BakerK34etu6K manK> tB)DRobert A. DennisEISJEducational Technology UnitKBMharlotte HiguchiONiemiRGeoffrey SaxeSubermanTn F. SloanxDebbie StevensonArizona State University West Cheryl Burkey Deanna WasmanjeremyMichael CapetoTimpreferred customer Maria Blanton James KaputEric R. HamiltonLawrence E. Brandt - CISE/ASCDASCLawrence E. BrandtV.GREGGGDE Systems, IncPDC LabGDE SYSTEMS Inc.GDE SYSTEMS, INC.cpg....Keith ThurstonAlison RichardsMichelle Boyette Caryn ReadingJennifer KaganMeredith Ittner Rita Oates Production Heidi Gilman Pat ThompsonJamal Z Bernhard Elise Harmon Janet Utech Gina Funaro Joanne LobatoJuline AguilarBonnie SchappelleKingKevCollege of Art & Sciences Helen DoerrJoanna O. MasingilaSarah BerensonCollege of Ed & Psy 420 PMac 05 420 PMac 117500 11Michael J. JacobsonLUCIAJTOSEMANAAASJo Ellen RosemanKelvin E Bennett Peter Taylor Site License - Curtin UniversityF J & PA FORSTERFischer Uni Bremen Thomas PutneyGraduate School of EducationWilliam Prothero Jim GaskellDG IIIDDAF 69Pascal et EricadejongKarine RobinaultCOASTUMR GRIC CNRS LYON IIGECCRIBIM CLIPS/IMAGPierre-Yves Raccah medves nino Equipe IHMPTFranz Peter SeilerprennouMRASH rossi marioKohler Etienne KLEIN Grard COLLETKh LaiEMSECOLONNAAlbert Chr. 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Keith HolderNorbert Pachler Unknown UserPhilippa Chloe Pout Adrian WhealElizabeth Newmanadmin computing user supportADMIN COMPUTING SERVICES Roger Gair ADMIN COMPUTING SERVICES M51/007 David TaylorDepartment Of Educationadrian hollidayJane HuddlestonDidaktik der PhysikHorstptdeDemoCEPHYLEN/LABO DIDASCO Votre nomLaurent Veillard.Mits/ '/ _Garo Bisdikian_ Lorenza Grard COLLETKh LaiMarie Genevive Sruser prennouOphthalmology & OrthopticsBERNARD GARNIER MAClient PrferChristoph KodronH.KodronHK David YeomansSchool of PCET Allan Martin S S Jordan s s jordanDr. E.J.Foster Stephen Bax Mary Haggard Rob Nanstad iris randall nicky_lucasHolliday Gary HepburnfeldmantechctrHHScotty & Angie Scott & Angie Ray CalabreseScott Alan WestMikeSusan N. Boyer/ '/ H"0 1Paul GathercoalJohn A. ThorpeDept. Mathematical SciencesAngela Andrews Robin FrischITSKenneth Arnold Bratland, Jr.UCFAnnie and John Selden Debra CurisePeace Corps Fellows ProgramPatricia & MichaelDepartment of EconomicsISU - SociologyLarry A. AlferinkPaul YuWilliam Connelly Tom LouisDesk01 Lucinda Beierdxz5IK %9;H\^dxzp   P d f   6 J L ? S U m  * , } ::::::::::::::::::::::::::::::%lxy,B$%- Y):@x@l(  4 w C A@ ? S T U V X Y b d  - . 8 G j k } @ @@@1A1@A^@A1A1A@A1Ad2Av2AA5A5A8A8A5A 5A"5A$5A,5A.5A05Az2A25A2A$@A>5AB5A2A 8A8@2A.AJ5AL5AZ@F$@A8@8A.A8A8AZ@8@8A8A8AA8A8AZ@8A.A9A9AZ@9A9A@A<A>A>A2>Ax>A><A@Ab<Ad<A@Af<@$@ @J$@@L$@@$@@$@ GTimes New Roman5Symbol3 Arial3Times"qh)q#qF >4d1  Calculus II Roger Day Roger Day  ՜.+,0  hp  'Illinois State UniversityI1   Calculus II Title FMicrosoft Word DocumentNB6WWord.Document.8<0|4J 8 1-4x 2 dx   Oh+'0`   ( 4@HPX' Calculus IIalc Roger DayIogeNormala Roger DayI29eMicrosoft Word 9.0d@2j&@&s6@Urepresents angle measures (or, more generally, real numbers) 3 Jjbjb^^^^^^^@h<h< #lvvzbT4.$ G6 88883;3;3;;C=C=C=C=C=C=C,H JdiCd3;;"3;3;3;iC;88cf$#;;;3;F88;C;6,6663;;C;;@rkBhbBR{S Dy;vBBLGGB;K;;KB;Calculus II MAT 146 Derivatives and Integrals Involving Inverse Trig Functions As part of a first course in Calculus, you may or may not have learned about derivatives and integrals of inverse trigonometric functions. These notes are intended to review these concepts as we come to rely on this information in second-semester calculus. Derivatives of Inverse Trig Functions One way to translate into words the meaning of the function  EMBED Equation.3  is as follows, based on right-triangle trigonometry: y represents the sine ratio for an angle of measure x. We write the inverse of this function as  EMBED Equation.3  and translate this equation into words as y is the angle measure whose sine ratio is x. The right triangle shown here illustrates this, for the sine of angle y is opposite/hypotenuse=x/1=x. For use in the derivation that follows, we note that in the triangle above, ?2+x2=12. Solving for the unknown, we have  EMBED Equation.3 . From that we deduce that  EMBED Equation.3 . Our goal is to determine the derivative of  EMBED Equation.3 . We start that process by noting that an equivalent form for  EMBED Equation.3  is  EMBED Equation.3 . We now apply implicit differentiation to this equivalent form:  EMBED Equation.3  We now have the derivative of the inverse sine function and, because differentiation and integration are inverse operations, we have an integral as well:  EMBED Equation.3  Through a similar derivation as just presented, we can show that  EMBED Equation.3  and  EMBED Equation.3  as well as  EMBED Equation.3  and  EMBED Equation.3 . Likewise, we can generate derivatives for three other inverse trig functions:  EMBED Equation.3  We use these derivatives and integrals to solve additional problems involving inverse trig functions. Here are some examples, first involving derivatives and then involving integrals. Example #1: Determine the derivative of  EMBED Equation.3 . We use derivative rules we already knowin this case, the chain ruleas well as the new information about derivatives of inverse trig functions:  EMBED Equation.3  Example 2: Determine the derivative of  EMBED Equation.3 .  EMBED Equation.3  Example 3: Determine the derivative of  EMBED Equation.3 . Here we recognize that arcsin(u)=sin-1(u). We also use the trig identity sin2(x)+cos2(x)=1.  EMBED Equation.3  Depending on the value of x, this last expression will simplify to either 1 or 1. 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If we let , giving us dx, we are left with / =!"#$% T%- Y)h\(xc` 0 = r R f#\Cn'3{j^jY"3020201Uuv9!^ 0!f!hN lo\=^ :gBr632쀫a#=\@=(z4\_5 D+zxf5, so u2=4x2,we getdx. We L5N5P58888888899998;b<d<f<j<|> jtEHU#jS: CJOJPJQJUVmH jEEHU#j S: CJOJPJQJUVmH jEHU#ju S: CJOJPJQJUVmH>* jcEHU#j" S: CJOJPJQJUVmH j ~EHUb' $a$6d h i 6 J K L M > ? S T U V X Y b d  - ^ r s t u v w x @ @@@1A1@A^@A1A1A@A1Ad2Av2AA5A5A8A8A5A 5A"5<04CompObjRObjInfoEquation Native _978521808FXÓ\XÓ\ thatnow haveThis is similar to Example 4 and we proceed with a solution by inspection: . Example 6:  This is similar to previous problems with the added task of evaluating a definite integral.  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B#_TnH T#_TnH&8) px}U_oD;ݶt $tKⵝ}DB*kSml'MS| z$wkٻ3;ή c!RyjnC,>7>ZjtrOX0/ VyȦnLЁGp`plQx#3\w)oofYzFZC{0bڅ``Ԡ[%ļQ_xr*yxiXQ+. y/O("t- 1ӭeA,I_`*Y+@p{X,K/?ېUeW.̆e\%IIWs,EĩCRi:qQ?bi(*l*e`Y2ܷSh&Y[lOEgBTB8. )3.Z#mk~bI6NNiSv_n9;l9X$qjiEg9Tw{ʪȮBz?3qq89U1>3lwfّG5԰.dDSHr6NmAK mՑ+eQ,DSFEVDž(*ͮSL::?ZOG[ #̳([Re}pD*Saj'RXp%$,7WQ"[2i`C.<*/Z+wWFue'# ]vuIܳ:RM6S{T1vk%̵գCmU99hqZߜ CfdwƄIJ/w?;n1yhpH% 1̟Or1ɶ9K3_nf/Dd4H * c $A? Bduєo Tgduє ;) =p5xWoE.Mtƍբ2jUa+3MTBpTRrukU(@o @Brr !]oc#g޼7hk< ;Ї#ta` ;o f )yuI^_p>蝭0AF."FsNK7 , @ is defined for angle measures over the interval . 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