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valuebeciiuse thcy arc not vcly precise are Craphicaltechniques ilf limited practical ol'rootsTheseestiHowevcr,graphical methods can be utilizedto obtainroughcstimatcs gucsscs numcrical in lor mcthods discussed this chapter mates can be ernployed starting as firr roughestimatcs ol'tlreroot,graphicul interpretations usefirl are Asidefiorn providing ol'the lirnctions and anticipating pitlallsof the nurnerical the understanding ploperties the rrethods For cxample,Fig -51 showsa numberof'ways in which rootscan occur (or be prescribcd a lowcr bound,r1 lb by andan uppcrboundr,,Figurc-5 dcabsent) an interval in (r) Howpictsthecase by and values o1'/ wherea singlcroot is brackctcd ncgative positive he r f e v e r , F i g 5 l r l , w h e r ( - r r ) a n d / ' ( - r , , ) a r e a l s o o n o p p o s i t e s itd c soa x i s , s h o w s t h r c c /c In if havcoppositc signs, thcrc rootsoccurring within the interval general, / (rr)and / (-r,,) As la r', of by arean odd number rootsin the interval indicatcd Fig-5 ancl il' l (rr ) andf (r,, ) ol'rootsbctwecn values thc havethe sarnc sign,thereareeitherno rootsor an evennunrbcr gcncralizalions usually arc lrue,lherearecases wherethcy do not holcl Althoughthcse l u ) F o r c x a r n p l e , r n c t i o n t h a ta r ct a n g c n t i a l t h c , r a x i s( F i g - 5 2 aa n dd i s c o n t i n u o u's n c ti s to p A o n tl t i o n s( F i g 5 2 b )c a nv i o l a t e h e s c r i n c i p l c s n c x a r n p l c l ' a I ' u n c t i o t h a ti s t a n g e n t i a t l t : ' t t h ca x i si s t h ec u b i ce q u a t i o n/ ( - r ' ) ( r - 2 ) ( r- 2 ) ( x - 4 ) N o t i c ct h a t , r: 2 t n a k c sw t r l n t e r m si n t h i s p o l y n o m i ac q u a lt o z e r o M a t h e r n a t i c a l l y , r : 2 i s c a l l e d' tt r r u l t i l t l c r t t that Although they are bcyond the scopeof this book, thereare specialtcchniqr"rcs arc 2002) and Canale expressly designed locaternultipleroots(Chapra to in nrakes difiicult to dcveloptirolit The cxistencc cases thc typedepictcd Fig-52 of of guaranteed locate the rootsin an interval Howevcr,whcn proof computer algorithms to all in with graphical approaches, rnethods the described thc lirlkrwingsccusedin conjunction routinelyby cnginccrs, confl'onted tions are extrerrelyusefulfor solvingrnanyproblerns scientists, appliedrnathematicians and.



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you'd oftenbe told to use"trial and If you hada rootsproblemin thedaysbefbrccomputing, makeguesses until the function error" to come up with the rootThiit is, you'd repcatcdly wasgrea(ly lacilitated the advent sofiware by of was sufTiciently closeto zeroThe process

Part II:

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lllustrotion someexceptions lhe generolcoses lo of when depicted in Fig 5 1 (o) Multiplerootsfhot,occur the function tongentic to the -r oxis For thiscose, is





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4 Tab to move to the Password box The system administrator determines the minimum length and case sensitivity of passwords (The Administrator user name initially contains no password) 5 Select the Authentication source for your user name 6 Click OK If you have entered the preceding information correctly, you will be presented with a Designer screen or wizard If you entered an invalid user name, password, or authentication source, you will receive an error As shown next, the error message does not clearly indicate if the error is related to an incorrect user name or password or if you chose the incorrect authentication source Within BusinessObjects Enterprise, user names can be authenticated against one or more security databases The default authentication source is Enterprise However, if your company uses Windows NT, for example, then your NT user name and password can be used to log you in to Designer Authentication options are discussed more fully in 13

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FIGURE I 5 I lustrolion crnumber generol of woysthoio roolmoy of prescribed o lowerbound ond by r, occurrnon intervol (oJ thct on upperbound Poris ond (c)indicoie if both x,, there wili sign,either ,/ (rr) ond /(r,,) hovethesome be no roots there be on evennumber rools will of or h w i t h i n h ei n t e r v oP o r t ( b )o n d ( d )i n d i c o tte o tl f l h e t l s ih w f u n c l i oh o sd i f f e r e n t g n s i t h ee n d p o i n t s , e r e i l l n si o be on odd number roolsin theintervol of

for on even numberof oxis inlercepiions the inlervol (b) Discontinuous funciions where end pointsof opposiie ic s i g ^ o ' o c [ e t o n e v e nn u r r b e r , or[o o ' s , S p e o l s t r o ' e g i e s

Once you have logged in to the CMS repository, you can open a universe that you have saved locally or you can import a universe from the repository To open a universe from the repository, follow these steps: 1 From the pull-down menu, select File | Import 2 From the Import Universe dialog, select the repository folder that contains the desired universe If you do not see the universe listed, click the down arrow to navigate to a different universe folder 3 From the list provided, select the name of the universe you wish to open In the preceding example, eFashion is selected 4 Select OK Designer imports the universe definitions from the repository and displays classes, objects, and the universe structure During the import process, Designer also

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