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1、CHALLENGEPROBLEMSCHAPTER3CHAPTER3AClickhereforanswers.SClickhereforsolutions.1.(a)Findthedomainofthefunctionfxs1s2s3x.(b)Find.fx;(c)Checkyourworkinparts(a)and(b)bygraphingandffonthesamescreen.CHAPTER4CHAPTER4AClickhereforanswers.SClickhereforsolutions.1.Findtheabsolutemaximumval
2、ueofthefunction11fx1x1x2C2.(a)LetABCbeatrianglewithrightangleandhypotenuseAaBC.(Seethefigure.)Iftheinscribedcircletouchesthehypotenuseat,showthatD1DCD2(BCACAB)1(b)If2C,expresstheradiusoftheinscribedcircleintermsofand.ra(c)Ifisfixedandvaries,findthemaximumvalueof.
3、ar3.Atrianglewithsidesa,b,andvarieswithtime,butitsareaneverchanges.LetbethectABangleoppositethesideoflengthandsupposealwaysremainsacute.aFIGUREFORPROBLEM2(a)Expressddtintermsof,,,bcdbdt,anddcdt.(b)Expressdadtintermsofthequantitiesinpart(a).4.Letandbepositivenumbers.Showthatnotbot
4、hofthenumbersaba1bandb1a1canbegreaterthan.45.LetABCbeatrianglewithBAC120andABAC1.(a)ExpressthelengthoftheanglebisectorADintermsofxAB.(b)FindthelargestpossiblevalueofAD.CHAPTER5CHAPTER5AClickhereforanswers.SClickhereforsolutions.12171.Showthatydx.41711x242.Supposethe
5、curveyfxpassesthroughtheoriginandthepoint1,1.Findthevalueof1theintegralxfxdx.03.InSections5.1and5.2weusedtheformulasforthesumsofthethpowersofthefirstknintegerswhenk1,2,and3.(TheseformulasareprovedinAppendixE.)Inthisproblemwederiveformulasforany.Theseformulaswerefirstpublishedin1713
6、bytheSwissmathe-kmaticianJamesBernoulliinhisbookArsConjectandi.(a)TheBernoullipolynomialsBnaredefinedbyB0x1,BnxBn1x,and1xBnxdx0for.n1,2,3,...FindBnxforn1,2,3,and4.0SixthEdition.ISBN:0495011606.©2008Brooks/Cole.Allrightsreserved.(b)UsetheFundamentalTheoremofCalculustoshowth
7、atBn0Bn1forn2.Calculus,Stewart:12■CHALLENGEPROBLEMS(c)IfweintroducetheBernoullinumbersbnn!Bn0,thenwecanwritexb1B0xb0B1x1!1!232xb1xb2xb1xb2xb3B2xB3x2!1!1!2!3!1!2!2!1!3!and,ingeneral,n1nnn!nkBnxbkxwheren!k0kkk!nk!n[Thenumbers(k)aret
