5 June 2008-quant

5 June 2008-quant - 5June2008 MATH1303...

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Unformatted text preview: 5June2008 MATH1303 Dr.MarcoMorazan,morazanm@shu.edu OH:MW,4:306pSC121 SyllabusNotes Secondexamisnotcumulative Onlylettergradesarerecorded(adv.a0Fvs.a59F) Eachsection(exam)willbecurvedindividually;finalgradeswillnot. CourseNotes Willbetimeintensive,require12hrspernightforproblemsets Willstressapplications Canalsobringnongraphingornonfinancialcalculatortoquizzesandexams ExamDates FirstQuizJune10 FirstExamJune12 SecondQuizJune19 SecondExamJune23 ThirdQuizJuly1 FinalExamJuly3 Examswillhavecomputeraided(maplebased)andwrittensections 2Functions ingeneralarulethatassignsoneinputnumberanoutput Thesetofvalidinputsisthedomain Thesetofoutputsistherange Xisaninput(domain);Yisoutput(range) Whatisdomainoff(x)=x^3+x^2? Allrealnumbers;fisalwaysvalid Whatisthedomainoff(x)=x/x^2x2)? Can'tdivideby0,thuswefactortofindthat F(x)=x/((x2)(x+1)) X=/=1,x=/=2 Whatisthedomainofg(t)g(t)=sqrt(2t1)? Canttakesqrt 2t1>=0 2t>=1 t>=1/2 Domain=[1/2,+inf) Example F(x)=x^3+x^2 F(2)=8+4 =12 Application:thedemandfunction Wecanmodeldemandbasedonnumbersystemfunctions Eg.P=100/Q Homeworkfor2.1:516,1824,2938,4446 2.2Taxonomyoffunctions Constantfunctions H(x)=c wherecisaconstant Polynomialfunctions H(x)=cx^n+cx^n1+...cx+c Exf(x)=20x^3+4x^2+300x+31 Wheretermsareorderedbydescendingexponent RationalFunctions G(x)=q(x)/q(x) Wherenumeratoranddenominatorarepolynomials CompoundFunctions Ruleisspecifiedbymorethanoneexpression Abs(x)=xifx>=0,else=x Homeworkfor2.2:14,1316,1922,29,31 2.3CombinationsofFunctions Functionsrepresentnumbers Numberscanbeadded,thusfunctionscanbeadded (f+g)(x)=>f(x)+g(x) (fg)(x)=>f(x)g(x) (f*g)(x)=>f(x)*g(x) (f/g)(x)>f(x)/g(x) exf(x)=x+1g(x) Functioncomposition (fog)(x)=f(g(x)) for2.3:1,3,4,7,10,1215 2.4InverseFunctions I(x)=xistheidentityfunction Iffog=I=gof,thengistheinverseoff Tofindaninverse Solvey=f(x)forx Swapxsforys Application:Givenademandfunctionandaquantity,onecanthenuseaninverse functiontofindaprice. For2.4:16 2.5Graphsinregularcoordinateplanes Itseasyandunsophisticated.Downsidesareaccuracy. Key:Plotinterestingpoints,likethexandyintercept.Tofindxintercept,sety=0 andsolve.Inverseforyintercept VerticalLineTest Ifyoucandrawaverticallinethroughthegraphofsomethingandit intersectsmorethanonepoint,itisnotafunctions 2.5:2130,3538 2.7TranslationsandReflections Y=f(x)+cmoveupbyc Y=f(x)cmovedownbyc etc. 2.7:110 3Lines,Parabolas,andSystems LinearFunctions Linearfunctionsarelines.Lineshaveaslope.Slopeisdenotedasm.m= (delta)y/(delta)x.Ifm=0,horizontalline. PointSlopeFormula yy(1)=m(xx(1)) Slopeintercept Y=mx+b Sameslope,thenlinesareparallel.Perpendicularifm(1)=1/m(2). Ifm=2 andF(4)=8 theny8=2(x4) 3.1:14,912,2530,4143 3.2:1520 3.3QuadraticFunctions Graphisalwaysaparabola:F(x)=ax^2+bx+c Ifa<0,opensupward Vertex:b/2a,f(b/2a) yintercept=0,c ex:f(x)=x^24x+12 vertex(2,16) yintercept(0,12) usequadraticformulaifitdoesn'tfactor Application:Maximumrevenue Givenp=10002q AndR=p*q R=(10002q)q R=1000q2q^2 Vertex(highestpoint)=250 Thus,Maximumrevenue(totalrevenueatvertex)is125,000 3.3:18,1320,2331,40 SystemsofLinearEquations Afactorygets335wigets,850klunkerseveryday. ModelAuses4widgets4widgetsand9klunkers ModelBneeds5w,14k HowmanyAandBuseupalltheday'sresources? X=#A Y=#B 4x+5y=335(widgetsupply) 9x+14y=850(klunkersupply) Canuseeithersimultaneoussolutionorsolveforonevariableandthenpluginto other ForMonday:willcontinuewith"chemicals"application.Completeassignments. ...
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This note was uploaded on 06/07/2008 for the course MATH 1303 taught by Professor Morazan during the Spring '08 term at Seton Hall.

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