Instruction/ maintenance manual of the product 50g HP
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HP 5 0g gr aphing calc ulat or user ’s manual H Ed it io n 1 HP part number F2 2 2 9AA-90 001.
Notice REG I STER Y OUR PROD UC T A T: www .register .hp .com THI S MANUAL AND ANY EX AMPLES CONT AI NED HEREI N ARE PRO VIDED “ AS I S” AND ARE SUBJECT T O CHANGE WITHOUT NO TICE.
Pr ef ace Y ou hav e in y our hands a compact s y mbolic and n umer ical comput er that w ill f acilit ate calc ulation and mathe matical analy sis of pr oblems in a var iety of disc iplines, f r om elementary mathematics to ad vanced engineer ing and sc ie nce subjec ts .
Page TOC-1 T able of Contents Chapter 1 - Getting started Basic Operat ions , 1-1 Batteries, 1-1 Turning the calculator on and off, 1-2 Adjusting the display contrast, 1-2 Contents of the calculator.
Page TOC-2 Editing expressions i n the stack , 2-1 Creating arithmetic expressions, 2-1 Creating algebraic expressions, 2-4 Using the Equation Write r (EQW) to create expres sions , 2- 5 Creating arit.
Page TOC-3 Available units, 3-9 Attaching units to numbers, 3-9 Unit prefixes, 3-10 Operations with uni ts, 3-11 Unit conversions, 3- 12 Physical constants in the calculator , 3-13 Defining and using .
Page TOC-4 The PROOT fu nction, 5-9 The QUOT and R EMAINDER functions, 5-9 The PEVAL function , 5-9 Fractions , 5-9 The SIMP2 function, 5-10 The PROPFRAC function, 5-10 The PARTFRAC function, 5-10 The.
Page TOC-5 Addition, subtraction, multiplication, di vision, 7-2 Functions applied to lists, 7-4 Lists of complex number s , 7-4 Lists of algebraic objects , 7-5 The MTH/LIST menu , 7-5 The SEQ functi.
Page TOC-6 Matrix multiplication, 9-5 Term-by-term multiplication , 9-6 Raising a matrix to a real power, 9-6 The identity matrix, 9-7 The inverse matrix, 9-7 Characterizing a matrix (The matrix NO RM.
Page TOC-7 Chapter 12 - Multi-variate Calculus Applications Partial deriv atives , 12-1 Multiple integrals , 12-2 Reference , 12-2 Chapter 13 - Vector Analysis Applications The del operator , 13-1 Gra.
Page TOC-8 Reference , 15-4 Chapter 16 - Statistical Applications Entering data , 16-1 Calculating single-variable statistics , 16-2 Sample vs. population , 16-2 Obtaining frequency distributions , 16.
Page 1-1 Chapter 1 Ge tti ng s ta rte d T his chapt er pr ov ides basi c inf ormatio n about the oper ation of y our calc ulator . It is designed to f amili ar i z e y ou w ith the basic oper ations and settings be fo r e y ou perf orm a calc ulation .
Page 1-2 b . Insert a new CR203 2 lithium bat tery . Mak e sur e its positi v e (+) side is facing up. c. Replace the plate and push it to the or iginal place .
Page 1-3 Contents of the calculator ’s displa y T ur n y ou r c alc ul at or on on ce mor e . A t the to p o f the di spl ay y ou w il l h a v e two lines of inf ormati on that des cr ibe the settings of the calc ulator .
Page 1-4 The se si x functi ons for m the fir st page of the T OOL menu . This menu has actuall y ei ght entr ies arr anged in t wo pages . The second page is av ailable b y pr essing the L (N eXT menu) k e y . T his k e y is the thir d ke y fr om the lef t in the thir d r o w of k ey s in the k e yboar d.
Page 1-5 F or e x ample , the P key , key (4,4 ) , has the f ollo w ing six f unctio ns associ ated with it: P Main func tio n , to acti vate the S YMBolic menu „´ L eft -shift functi on, to ac ti .
Page 1-6 Of the si x functi ons assoc iated w ith a k ey onl y the fir st f our ar e show n in the k e y boar d itself . The f igur e in next page sho ws these f our labels for the P k e y .
Page 1-7 Operating Mode T he calc ulator off ers tw o operating modes: the Alge b raic mode, and the Revers e P ol i s h N ot a t io n ( RPN ) mode . T he def ault mode is the Algebr aic m o d e ( a s.
Page 1-8 Y ou could also type the e xpr essi on direc tly into the dis pla y w ithout using the equation w riter , as follo ws: R!Ü3.*!Ü5.- 1/3.*3.™ /23.Q3+!¸2.5` to obta in th e same r esult . Change the oper ating mode to RPN b y fir st pr es sing the H butt on .
Page 1-9 Le t's try some other simple oper ations bef or e trying the mor e compli cated e xpr essi on used earlie r for the algebr aic oper ating mo de: Note the po sition o f the y and x in the las t two oper atio ns.
Page 1-10 T o se lect between the AL G vs . RPN operating mode , y ou can also set/ c lear s y stem f lag 9 5 thr ough the follo w ing k e ys tr oke s equence: H @FLAGS! 9˜˜˜˜ ` Number F o rmat and decimal dot or comma Changing the n umber f ormat allo ws y ou to c usto mi z e the wa y real number s ar e display ed by the calc ulator .
Page 1-11 Pr es s the r ight ar ro w k e y , ™ , to highlight the z er o in fr ont of the option Fix . Pr es s the @CHOOS so ft menu k ey and , using the up and do wn ar r ow keys, —˜ , select , say , 3 decimals .
Page 1-12 K eep the number 3 in fr ont of the Sc i . ( This number can be c hanged in the same f ashio n that w e c hanged the Fix e d number of dec imals in the e x ample abo ve). Pr es s the !!@@OK#@ s o ft me nu k e y r e tu rn to t he c alc u la to r di s p la y .
Page 1-13 Pr es s the !!@@OK#@ s o ft me nu k e y r e tur n t o th e ca lc ula to r d is p la y . T he n um ber no w is s ho w n as: Becau se this n umber has thr ee f igur es in the int eger part , it is sh o wn w ith fo ur signif icati ve f igur es and a z er o po w er of ten , w hile using the Engineer ing for mat .
Page 1-14 Angle M easure T r igonometr ic f unctions , f or e xample , r equir e ar guments r e pr esenting plane angles . The calc ulator pr ov ides thr ee differ ent A ngle Measur e modes f or wo rk i n g wi t h a n g l e s, n a m e l y: • Degr ees : Th er e ar e 360 degr ees ( 360 ° ) i n a c om p l e t e ci rcu m fe re n c e.
Page 1-15 soft men u k ey to complet e the oper ation . F or e x ample , in the fo llo w ing sc r een, the P olar coor dinate mode is selected: Selec ting CAS setting s CA S st ands f or C omputer A lgebr aic S y ste m.
Page 1-16 Non-Rati onal options abo v e) . Unselected options w ill sho w no chec k mark in the underline pr eceding the option of inte r est (e .g., the _Numer ic , _Appr o x , _Comple x , _V erbo se , _Step/St ep , _Incr P ow options abov e) .
Page 1-17 Selec ting Displa y modes T he calc ulator displa y can be cu stomi z ed to y our pr efer ence b y selec ting diffe r ent displa y modes. T o see the optional dis pla y settings u se the fo llo wing: •F i r s t , p r e s s t h e H button to acti vat e the CAL CULA T OR MODE S input f or m.
Page 1-18 Selec ting the display f ont Fi r s t , p re s s t h e H button to activ ate the C AL CUL A T OR MO D E S i nput f orm . Within the CAL CULA T OR MODE S input f orm , pr ess the @@DIS P@ soft menu k e y to displa y the D ISP LA Y MODE S input f orm .
Page 1-19 Selec ting pr operties of the Stac k Fi r s t , p re s s t h e H but ton to a cti vate the CAL CUL A T OR MOD E S i nput fo rm . Within the CAL CUL A T OR MODE S input for m, pr ess the @ @DISP@ soft menu k e y ( D ) to displa y the D ISP L A Y MODE S input fo rm .
Page 1-20 Selec ting pr oper ties of the equation writer (E QW ) Fi r s t , p re s s t h e H button to activ ate the C AL CUL A T OR MO D E S i nput f orm . Within the CAL CULA T OR MODE S input f orm , pr ess the @@DIS P@ soft menu k e y to dis play the DISP L A Y MODE S input f orm .
Page 2-1 Chapter 2 Intr oduc ing t he calc ulator In this cha pter w e pre sent a n umber of basi c operati ons of the calc ulator inc luding the use of the E quati on W riter and the manipulati on of data obj ects in the calc ulator .
Page 2-2 Notice that , if y our CA S is set to E X A CT (see Appendi x C in user ’s guide) and y ou enter y our expr essi on using integer number s fo r integer v alues, the r esult is a s ymboli c quantity , e. g ., 5*„Ü1+1/7.5™/ „ÜR3-2Q3 Bef or e pr oduc ing a r esult , y ou w ill be ask ed to c hange to Appr o x imate mode .
Page 2-3 If the CA S is set to Ex act , yo u w ill be ask ed to appr ov e changing the CA S sett in g to Appr ox . Once this is done , y ou w ill get the same r esult as bef ore . An alte rnati ve w ay t o e valuat e the e xpr essi on enter ed earli er between quot es is by u sing the opti on …ï .
Page 2-4 Creating algebr aic e xpressions Algebr aic e xpre ssi ons inc lude not onl y number s , but also v ari able names . As an e x ample , w e will ent er the fo llo w ing algebrai c e xpr ession: W e s et the calc ulator oper ating mode to A lgebrai c, the CA S to Exac t , and the displa y to Te x t b o o k .
Page 2-5 Using the Equation W riter (E QW ) to c reate ex p r e s s i o n s T he equation w rite r is an extr emel y po w erful t ool that not only le t y ou ent er or see an eq uation , but also allo ws y ou to modify and w ork/appl y func tions o n all or part of the equati on .
Page 2-6 Suppos e that y ou w ant to r eplace the quantity between par enthese s in the denominator (i .e ., 5+1/ 3) with (5+ π 2 /2) . F irs t , w e use the delet e k ey ( ƒ ) delete the c urr ent .
Page 2-7 F irst , w e need to hi ghlight the entir e fir st ter m b y using eithe r the ri ght arr o w ( ™ ) or the upper ar ro w ( — ) k ey s, r epeatedly , until the entir e e xpr essi on is highli ghte d , i .e. , se ven time s, pr oduc ing: Once the e xpr ession is hi ghlighted as sho w n abo v e , t ype +1/ 3 to add the fr action 1/3 .
Page 2-8 ~„y———/~‚tQ1/3 T his r esults in the output: In this e x ample w e us ed se ver al lo w er -case English letter s, e .g ., x ( ~„x ), se v er a l G r e ek le tt e rs , e .g ., λ ( ~‚n ) , and e v en a combinati on of Gr eek and English letter s, name ly , ∆ y ( ~‚c~„y ) .
Page 2-9 Subdirectories T o s tor e your dat a in a w ell or gani z ed dir e ctory tr ee yo u ma y w ant to c r eate subdir ector ies under the HOME dir ectory , and mor e subdir ector ie s w ithin subdir ector ies , in a hier ar ch y of dir ector ie s similar to f olders in modern co mput ers .
Page 2-10 T o unloc k the upper -case lock ed k e y board , pre ss ~ . T ry the f ollo wing e xe r c ises: ~~math` ~~m„a„t„h` ~~m„~at„h` T he calc ulator displa y w ill sho w the f ollo w in.
Page 2-11 The f ollo w ing are the k e ys tr oke s for ente r ing the r emaining var iables: A12: 3V5K~a12` Q: ~„r /„Ü ~„m+~„r™ ™K~q` R: „Ô3‚í2‚í1™ K~r` z1: 3+5*„¥K~„z1` (Acce p t cha n ge to Co mp l ex mode if ask ed ) . p1: å‚é~„r³„ì* ~„rQ2™™ ™K~„p1` .
Page 2-12 T o enter the value 3 × 10 5 i n t o A 1 2 , w e c a n u s e a s h o r t e r v e r s i o n o f t h e pr ocedur e: 3V5³~a12`K Her e is a wa y to enter the contents of Q: Q: ~„r/„Ü ~„.
Page 2-13 Chec king var iables contents Th e s i m p l es t way to che ck a va ria b l e c o nt e n t i s by p res s i n g t h e so f t m en u k e y label fo r the var iable .
Page 2-14 T his pr oduces the f ollo wing s cr een (A lgebr aic mode in the left , RPN in the rig h t ) Notice that this time the co ntents of pr ogr am p1 are listed in the s c r een. T o see the r emaining var iables in this dir ectory , pr es s L .
Page 2-15 Y ou can use the P URGE command to er ase mor e than one var iable b y plac ing their names in a list in the ar gument of P URGE . F or e x ample , if n ow we wa n t e d t o p u rg e va ri a b l es R and Q , simultaneousl y , w e can try the follo w ing ex erc ise .
Page 2-16 UNDO and CMD functions F unctions UNDO and CMD are u sef u l f or r ecov er ing r ecent commands, or to r ev er t an oper ation if a mist ak e was made . T hese f unctions ar e as soc iat ed w ith the HI S T k ey : UNDO re sults fr om the k e y st r ok e seq uence ‚¯ , w hile CMD r esult s fr om the k e y str ok e sequ ence „® .
Page 2-17 T her e is an alte rnati ve w ay to acces s thes e menu s as sof t ME N U keys, by set tin g sy stem flag 117 . (F or infor mation on F lags see Cha pter s 2 and 2 4 in the calc ulator ’s user ’s guide) .
Page 2-18 Pr ess B to sel ect the M EMOR Y sof t m enu ( ) @@MEM@ @ ). T he di s p la y n o w sho w s: Pr ess E to se lect th e D I RECT O R Y soft me nu ( ) @@DIR@ @ ) T he ORDER command is not sho wn in this sc reen .
Page 3-1 Chapter 3 Calculations with re al numbers T his chapt er demons tr ates the use o f the calc ulator for oper ations and func tions r elated to r eal numbers . The us er sho uld be acquainted w ith the k e ybo ar d to i dentify certain f uncti ons a v ailable in the k e y boar d (e .
Page 3-2 6.3#8.5- 4.2#2.5* 2.3#4.5/ • P arentheses ( „Ü ) can be used to gr oup ope r ations , as well as to enclose a rgument s of function s. In AL G mode: „Ü5+3.2™/„Ü7- 2.2` In RPN mode , y ou do not need the par enthesis , calc ulatio n is done dir ectl y on the stac k: 5`3.
Page 3-3 • T he po w er func tion, ^, is a vailable thr ough the Q key . W h e n calc ulating in the stac k in AL G mode , enter the ba se ( y ) f ollo w ed by the Q k ey , and then the e xponent ( x ), e .g ., 5.2Q1.25` In RPN mode, ent er the number f irst , then the functi on, e .
Page 3-4 2.45`‚¹ 2.3`„¸ • T hr ee tr igonome tr ic func tions ar e r ead ily a vailable in the k e yboar d: sine ( S ), c os i n e ( T ) , and tangent ( U ). Ar guments of the se f uncti ons ar e a ngles in either degr ees, r adians, gr ades .
Page 3-5 Real number functions in t he MTH menu Th e M T H ( „´ ) me nu inc lude a number of mathemati c al f uncti ons mostl y applicable t o r eal number s.
Page 3-6 F or e xample , in AL G mode , the k e ys tr ok e sequence t o calc ulate, sa y , tanh( 2 .5 ) , is the f ollo w ing: „´4 @@OK @@ 5 @@OK@@ 2.
Page 3-7 F inally , in or der to selec t , f or e x ample , the hy perboli c tangent (tanh) functi on, simpl y pr ess @@TANH@ . F or e x ample , to calc ulate ta nh(2 .5 ) , in the AL G mode , w hen using SO F T menus ove r CHOOSE bo xe s , f ollow this pr ocedur e: „´ @@HYP@ @@ TANH@ 2.
Page 3-8 Optio n 1. T ools.. cont ains f uncti ons u sed t o oper ate on units (disc uss ed later ) . Options 2. L e n g t h . . t h r o u g h 17 .V iscosity .. conta in menus w ith a number o f units fo r each of the quantiti es desc r ibed . F or e x ample , selec ting option 8.
Page 3-9 Pr es sing on the appr opri a te so ft menu k e y will open the sub-menu of units fo r that partic ular selec ti on . F or e x ample , for the @) SPEED su b-menu , the fo llo wing units ar e av ailable: Pr essing the so ft men u k ey @ ) UNITS w ill tak e you back to the UNIT S menu .
Page 3-10 5‚Û8 @@OK@ @ @@ OK@@ Notice that the unders cor e is enter e d au tomati call y w hen the RPN mode is acti ve . The k e y str oke s equences to enter units w hen the SO F T m e n u option is selec ted , in both AL G and RPN modes , ar e illustr ated next .
Page 3-11 123‚Ý~„p~„m Using UB ASE (type the name) to conv ert to the def ault unit (1 m) r esults in: Operations w ith units Her e ar e some calc ulation e xamples u sing the AL G operatin g mode .
Page 3-12 Additi on and subtr a cti on can be perfo rmed , in AL G mode, w ithout u sing par enthese s, e .g., 5 m + 3 200 mm, can be enter ed simply as 5_m + 3 200_mm ` .
Page 3-13 Ph ysical constants in the calculator T he calc ulator ’s ph ysi cal cons tants ar e contained in a cons tants libr ar y acti vated w ith the command CONLIB.
Page 3-14 If w e de -select the UNI T S option (pr es s @UNITS ) onl y the values ar e sho w n (English units selec ted in this case): T o cop y the value o f Vm to the stac k, s elect the v ari able name , and pr ess @²STK , then, press @QUIT@ .
Page 3-15 Defining and using func tions User s can def ine thei r o w n functi ons b y using the DEFIN E command av ailable thought the ke ystr ok e sequence „à (assoc iat ed with the 2 k e y) .
Page 3- 16 r elativ ely simple and consists o f two parts, contai ned between the pr ogram container s This is t o be inter pr eted as say ing: enter a v alue that is tempor aril y assigned to the nam.
Page 4-1 Chapter 4 Calculations with compl e x numbers T his cha pter sho ws e xample s of calc ulation s and applicati on of fu ncti ons to comp le x number s. Definitions A comple x number z is a number z = x + iy , wher e x and y ar e real number s , and i is the imaginary unit def ined by i ² = –1.
Page 4-2 Pr ess @@O K@@ , t wi ce, to r e turn to the sta ck . Entering comple x numbers Com p le x numbers in the calc ulator can be e nter ed in e ither of the tw o Car tesia n representations, nam ely , x+iy , or (x,y) . T he re sults in the calc ulator w ill be sho wn in the or dered-pair f ormat , i .
Page 4-3 P olar r epresentation o f a comple x number The polar r epr esentati on of the complex number 3 . 5-1.2i, enter e d abo v e , is ob tain ed by changing the c oor din ate sy stem to cylindri cal or pol ar (using f uncti on C YLIN) . Y ou can find this f unction in the catalog ( ‚N ) .
Page 4-4 Si mp le o per at io ns w ith co mple x nu mb er s Com ple x numbers can be comb ined using the f our fundament al oper ations ( +-*/ ) . T he re sults f ollo w the rule s of algebr a w ith the cav eat that i2= -1 . Oper atio ns w ith comple x numbers ar e similar to tho se w ith r e al number s .
Page 4-5 T he f irs t menu (opti ons 1 thr ough 6) sho ws the f ollo w ing f uncti ons: Ex amples of applic ations of these func tions are sho wn ne xt in RE CT coor dinates. R ecall that, f or AL G mode , the func tion mu st pr ecede the ar gument , while in RPN mode , y ou ente r the ar gument f irs t , and then select the fu ncti on .
Page 4-6 CMP LX menu in k e y boar d A second CMP L X menu is access ible by u sing the r ight- shift option ass oc iated w ith the 1 k e y , i .e ., ‚ß .
Page 4-7 F unc tion DROITE: equation o f a straight line F unction DROI TE tak es as ar gument two comple x numbers, sa y , x 1 + iy 1 and x 2 +iy 2 , and r etur ns the equati on of the str aight line , say , y = a + bx, that contains the po ints (x 1 , y 1 ) and (x 2 , y 2 ) .
SG49A.book Page 8 Friday, S eptember 16, 2005 1:31 P M.
Page 5-1 Chapter 5 Algebraic and ar ithm etic oper ations An algebr aic objec t , or simply , algebrai c , is an y number , var iable name or algebr aic e xpr es sio n that can be oper ated upon , manipulated , and comb ined accor ding to the r ules o f algebr a.
Page 5-2 Simple operations w it h alg ebr aic objects Algebr aic ob jec ts can be added, subtr acted , multipli ed , di vi ded (e x cept by z er o) , r aised to a po w er , used as ar guments f or a var iety of st andar d functi ons (exponen tial , logar ithmic , tr igonome tr y , h y perboli c, etc .
Page 5-3 @@A1@ @ * @@A2@@ ` @@A1@ @ / @@A2@@ ` ‚¹ @@A1@@ „¸ @@A2@@ T he same r esults ar e obtained in RP N mode if u sing the f ollo wi ng keyst ro kes : Functions in the AL G menu T he AL G (Alg ebr aic) men u is a vail able b y using the k e y str ok e sequ ence ‚× (assoc iat ed w ith the 4 k e y) .
Page 5-4 T o complete the oper ation pr ess @@ OK@@ . H e re i s t h e h el p scre en for fu n ct io n COL L ECT : W e noti ce that , at the bottom of the sc r een, the line See: EXP AND F A CT OR suggests l inks to other help f ac ility entr ie s, the f unctio ns EXP AND and F A CT OR .
Page 5-5 F or e x ample , for f unction S UB S T , w e find the f ollo wing CA S help fac ility entry: Operations w ith transcendental func tions T he calc ulator off ers a number of f uncti ons that can be used t o r eplace e xpr essions con taining logar ithmic and e xponential f uncti ons ( „Ð ), as well as trigonometric f unctions ( ‚Ñ ).
Page 5-6 Inf or mation and e x amples on the se commands ar e av ailable in the help fac ility of the calc ulator . F or ex ample , the de sc r ipti on of EXP LN is sh o w n in the left-hand side , an.
Page 5-7 F unc tions in the ARITH MET I C menu The ARI TH MET IC menu is tr igger ed thr ough the k e y str oke co mbinati on „Þ (asso c iated w ith the 1 k e y) .
Page 5-8 Po l y n o m i a l s P oly nomi als ar e algebrai c e xpr essi ons consisting of one or more ter ms containi ng decr easing po w ers of a gi v en var iable . F or e xam ple , ‘X^3+2*X^2 -3*X+2’ is a thir d-order pol y nomi al in X, while ‘S IN(X)^2 - 2’ is a second-or der poly nomial in S IN(X) .
Page 5-9 Th e PRO O T f u n c t i o n Gi ven an ar ra y containing the coeff ic i ents of a pol ynomi al , in decr easing or der , the functi on PR OO T pr ov ides the r oots of the pol ynomi al . Ex ample , fr om X 2 +5X+6 =0, P RO O T([1, –5, 6]) = [2 .
Page 5-10 F A CT OR(‘(X^3-9*X)/(X^2 -5*X+6)’ )=‘X*(X+3)/(X- 2)’ T he SI MP2 func tion F unction SIMP2 , in the ARITHME TIC men u , tak es as argume nts tw o number s or pol y nomi als, r epr esen ting the numer ator and denominator o f a r a tio nal fr action , and retur ns the simplified n umerato r and denominat or .
Page 5-11 FCOEF([2 ,1, 0, 3,–5,2 ,1,–2 ,–3,–5])=‘(X--5)^2*X^3*(X- 2)/( X-+3)^5*(X-1)^2’ If y ou pre ss µ„î` (or , si mply µ , in RPN mode) y ou w ill get: ‘(X^6+8*X^5+5 *X^4 -50*X^3.
Page 5-12 Refe re n c e Additi onal infor mation , def initions , and e xamples o f algebr aic and ar ithmeti c oper ation s ar e pr esented in C hapter 5 of the calc ulator’s u ser ’s guide .
Page 6-1 Chapter 6 Solution to equations Ass oc iated w ith the 7 k e y there ar e t wo me nus of equati on -sol v ing func tions , the S y mbolic S OL V er ( „Î ) , and the NUMeri cal SoL V er ( ‚Ï ) . F ollo wing , w e pr ese nt some o f the f u ncti ons contained in thes e menu s.
Page 6-2 the f igur e to the left . After a pply ing IS OL, the r esult is sho w n in the f igur e to the ri ght: T he fir st ar gument in IS OL can be an expr essi on, as sho wn a bov e , or an equation .
Page 6-3 T he fo llo wing e xample s sho w the use of f unction S OL VE in AL G and RPN modes (U se C omple x mode in the CA S): The scr een s hot show n above displ ay s t wo solution s. In t he first on e , β 4 -5 β = 1 2 5 , S O L V E p r o d u c e s n o s o l u t i o n s { } .
Page 6-4 Fun c t i on SO L V EV X T he functi on S OL VEVX sol v es an eq uation f or the def ault CA S v ari able co n t a i n e d i n t h e re se r ved va ria b l e n a me V X .
Page 6-5 sc reen sh ots sho w the RPN stac k bef or e and after the appli cation of ZERO S to the two e xamples abo ve (Use C omple x mode in the CAS): T he S ymboli c Solv er functi ons pre sente d abo v e pr oduce solutions t o r ational equations (mainl y , poly nomi al equations).
Page 6-6 w ith e xamples fo r the n umer ical sol v er applicatio ns. Item 6. MS L V (Multiple equation SoL V er ) w i ll be pr esen ted later in page 6 -10 .
Page 6-7 Pr ess ` to r eturn to st ack . The st ac k w ill sho w the follo w ing r esults in AL G mode (the same r esult w ould be sho w n in RPN mode) : All the solu tions ar e complex number s: (0. 4 3 2 , -0. 3 8 9) , (0.4 3 2 , 0.3 89 ) , (- 0.7 66 , 0.
Page 6-8 Generating an algebraic e xpression f or the poly nomial Y ou can use the calc ulator to gener ate an algebr aic e xpr essi on for a poly nomial gi ven the coe ffi ci ents or the r oots of the pol ynomi al . T he r esulting e xpr essi on wi ll be gi v en in ter ms of the de fa ult CA S v ar iable X.
Page 6-9 Solv ing equations with one unkno wn thr ough NUM.SL V T he calc ulator's NUM. S L V menu pr ov ides it em 1. Sol ve eq uation .. solve diffe r ent t y pes o f equati ons in a single v ar iable , inc luding non-linear algebr aic and tr anscendent al equati ons .
Page 6-10 T he eq uat i on w e s t or ed i n v ar i ab le E Q i s al r ead y lo ade d in t he Eq fie l d i n the S OL VE E Q U A TION inpu t fo rm . Also , a f ield labeled x is pr ov ided. T o sol v e the equation all y ou need to do is highlight the f ield in fr ont of X: by using ˜ , and pre ss @SOLVE@ .
Page 6-11 In AL G mode, pr ess @ECHO to cop y the e x ample to the s tack , pr es s ` to run the e x ample . T o see all the ele ments in the soluti on y ou need to acti vate the line editor b y pr es.
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Page 7-1 Chapter 7 Ope r at i on s w ith li sts L ists ar e a t ype o f calc ulator ’s obj e ct that can be us ef ul for dat a pr oces sing. T his chapt er pr esents e xamples o f oper a tio ns w ith lists. T o get started w ith the e xamples in this Chapte r , we use the A ppr ox imate mode (See C hapter 1) .
Page 7-2 Addition , subtr ac tion, multiplication, di vision Multipli cation and di visi on of a list b y a single number is distr ibuted acr os s the list , for e xample: Subtr action o f a single nu.
Page 7-3 T he di v isi on L4/L3 w i ll pr oduce an infinity entry becaus e one of the elements in L3 is z er o , and an err or mes sage is r eturned . If the lists in vol v ed in the oper atio n hav e differ ent lengths , an err or mess age (In valid Dime nsi ons) is pr oduced.
Page 7-4 Functions applied to lists Real n umber functi ons fr om the k e yboar d (ABS , e x , LN , 10 x , L OG , SIN, x 2 , √ , CO S, T AN, A SIN , A CO S, A T AN, y x ) as well as those fr om the M TH/ HYP ERBOLIC menu (S INH, C O SH, T ANH, A SINH, A C OSH , A T ANH) , and MTH/REAL men u (%, etc .
Page 7-5 L ists of algebraic objects T he f ollo wi ng ar e e xamples o f lists of algebr aic ob jec ts w ith the functi on SIN a pplied t o them (se lect Ex act mode fo r thes e e x amples -- See C hapter 1): Th e M T H / L I ST m e n u T he MTH menu pr ov ides a n umber of f uncti ons that e x c lusi vel y to lists .
Page 7-6 Ex amples of applic ation o f thes e func tions in AL G mode ar e sho w n next: S ORT and REVLI S T can be combined to sort a list in dec rea sing or der : If y ou ar e w or king in RPN mode , enter the lis t onto the s tac k and then selec t the oper ation y ou want .
Page 7-7 Th e S E Q f u n c t i o n T he SE Q functi on, a vailable thr ough the command catalog ( ‚N ), tak es as ar guments an e x pr ession in t erms o f an index , the name of the inde x , and s.
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Page 8-1 Chapter 8 Ve c t o r s T his Chapte r pr ov ides e xample s of ent er ing and oper ating w ith v ector s, both mathematical v ector s of man y elements , as well as ph ysi cal ve ctor s of 2 and 3 componen ts.
Page 8-2 Stor ing vectors into v ariables in the stack V e c t o r s c a n b e s t o r e d i n t o v a r i a b l e s . T h e s c r e e n s h o t s b e l o w s h o w t h e ve c to rs u 2 = [1, 2] , u 3 = [-3, 2, -2] , v 2 = [3,-1] , v 3 = [1, -5, 2] Stored i nto variable s @@@u 2@@ , @@@u3 @@ , @@@v2@@ , and @@@v3@@ , r especti ve ly .
Page 8-3 Using th e Ma tri x W riter (MTR W ) to enter vec tors V e ctor s can also be enter ed b y using the Matri x W rite r „² (thir d k e y in the f ourth ro w of k e ys f r om the t op of the k ey board).
Page 8-4 @+ROW@ @ -ROW @+COL@ @-COL@ @GOTO@ Th e @+ROW@ k ey w ill add a ro w full of z ero s at the location of the selec ted cell of the sp r eadsheet . Th e @- ROW ke y w ill delete the r o w corr esponding to the s elected cell o f the spr eadsheet .
Page 8-5 Simple operations w it h vectors T o illu str ate oper ations w ith vec tor s w e w ill us e the vect ors u2 , u3, v2 , and v3, stored in an ea rlier ex erc ise. Also , store v ector A =[ -1 ,- 2 ,-3 ,- 4,-5] to be used in the fo llo w ing ex er c ises .
Page 8-6 Multiplication b y a scalar , and div ision b y a scalar Multipli cation b y a scalar or di vi sion b y a scalar is str aigh tfo rwar d: Absolute v alue function T he absolu te v alue func tio n (AB S) , when appli ed to a v ector , pr oduces the magnitude of the v ect or .
Page 8-7 Ma gnitude T he magnitude of a v ector , as disc ussed ear lier , can be f ound w ith f uncti on A B S . T h i s f u n c t i o n i s a l s o a v a i l a b l e f r o m t h e k e y b o a r d ( „Ê ). Ex amples of applicati on of func tion AB S wer e sho w n abo ve .
Page 8-8 Exampl es of cross products of on e 3 -D vector with o ne 2 -D vector , or vice v ers a , ar e pr esented ne xt: Atte mpt s to c al culat e a cross product of vectors of l eng th oth er th an.
Page 9-1 Chapter 9 M atrices and linear algebr a T his chapt er sho ws e xample s of c reating matr ice s and oper ations w ith matr ices , including linear algebr a applicati ons .
Page 9-2 If y ou hav e select ed the te xtbook display opti on (using H @) DISP! and ch e ck i n g of f Textbook ) , the matri x wi ll look lik e the one show n abo v e . Other wise , th e display will sho w: T he displa y in RPN mode w ill look very similar to thes e .
Page 9-3 Ope r at i on s w ith ma tr ice s Matr ices , like other mathematical ob jec ts, can be added and su btr acted. T he y can be multipli ed b y a scalar , or among themsel ve s, and r aised to a r eal po wer . An important oper a tion f or linear algebr a appli cations is the in v erse o f a matr i x .
Page 9-4 Addition and subtr ac tion F our ex amples ar e show n below using the matr ices stor ed abo v e (AL G mode) . In RPN mode , tr y the follo w ing ei ght ex amples: Mul ti pl ica ti on T her e ar e a number of multipli cation oper ations that inv olv e matr ices .
Page 9-5 Matrix -v ector multiplication Matr i x - v ector m ultiplicati on is possible onl y if the number o f columns of the matr i x is equal to the length of the v ector . A couple o f ex amples o f matri x - ve ctor m ultiplicati on follo w: V e ctor -matr i x multiplicati on , on the other hand , is not def ined.
Page 9-6 T erm-b y-term multiplica tion T erm- by- term mu lt ip lica tion of t wo mat rices of t he sam e d im ens ions is possi bl e th r oug h th e use of function H ADAMAR D .
Page 9-7 T he identit y matri x T he ide ntity matri x has the pr oper ty that A ⋅ I = I ⋅ A = A . T o ve r ify this pr oper ty w e pr esent the f ollo w ing ex amples us ing the matri c es st or ed earli er o n.
Page 9-8 Char ac teri zing a matri x (The matr ix NORM menu) T he matri x NORM (NORMALI ZE) menu is acces sed thr ough the k ey str oke sequ enc e „´ . This men u is desc r ibed in de tail in Chapter 10 of the calc ulator’s us er’s gui de . Some o f these f uncti ons ar e des cr ibed next .
Page 9-9 Solution of linear s y stems A s ys tem of n linear equati ons in m var iab les can be w r itten as a 11 ⋅ x 1 + a 12 ⋅ x 2 + a 13 ⋅ x 3 + …+ a 1,m-1 ⋅ x m-1 + a 1,m ⋅ x m = b 1 ,.
Page 9-10 2x 1 + 3x 2 –5x 3 = 13, x 1 – 3x 2 + 8x 3 = -13, 2x 1 – 2x 2 + 4 x 3 = -6, can be wr it ten as the matr ix eq uation A ⋅ x = b , if T his s y stem has the same number o f equatio ns as of unkno w ns, and w ill be r e f e r r e d t o a s a s q u a r e s y s t e m .
Page 9-11 A solu tion w as found as sho wn ne xt . Sol uti on w ith the in v erse ma tr i x T he soluti on to the s yst em A ⋅ x = b , wher e A is a squar e matri x is x = A -1 ⋅ b .
Page 9-12 Refe re n c e s Additi onal informati on on cr eating matri ces, matr i x operati ons , and matri x appli cations in linear algebr a is pr es ented in Cha pter s 10 and 11 of the calculator ’s us er’s gui de .
Page 10-1 Chapter 10 Gr aph ics In this cha pter w e intr oduce some of the gr aphic s capab ilitie s of the calc ulator . W e w ill pr es ent gr aphic s of f unctions in C artesian coor dinates and polar coor dinates , parametr ic plots , gr aphi cs of coni cs, bar plots, scatter plots, and fa st 3D plots .
Page 10-2 P lot ting an e xpression o f the for m y = f(x) As an e xample , let's plot the f u ncti on , • F irst, enter th e PL O T S ETUP envir o nment by pressing, „ô . Mak e sur e that the option F uncti on is select ed as the TYPE , and that ‘X’ is selec ted as the independent v ar iable ( INDEP ).
Page 10-3 •P r e s s ` to r eturn t o the PL O T - FUNCTION w indo w . The e xpr essi on ‘ Y1(X) = EXP(- X^2/2)/ √ (2* π )’ will be highlig hted. Pr ess L @@@OK@@@ to r etur n to normal calc ulator display . • Enter the P L O T WINDO W en vir onment b y enter ing „ò (pre ss them simultaneou s l y if in RPN mode) .
Page 10-4 Gen er ating a table of v alues f or a func tion The c o m bi n a t ion s „õ ( E ) and „ö ( F ) , pressed simultaneousl y if in RPN mode , let’s the us er pr oduce a table o f value s of func tions .
Page 10-5 • W ith the option In hi ghligh ted , pr ess @@@OK@@@ . The t able is e xpanded so that the x -incr ement is no w 0.2 5 rather than 0. 5 . Simply , what the calc ulator does is t o multipl y the or iginal incr ement , 0. 5, b y the z oom fa ctor , 0.
Page 10-6 • K eep the def ault plot w indo w r anges to r ead: •P r e s s @ERASE @ DRAW to dr aw the thr ee -dimensio nal surface . The r esult is a w i r ef r ame pic tur e of the surface w ith the re fer ence coor dinate sy stem sho wn at the lo we r left corne r of the sc r een .
Page 10-7 • When done , pr es s @EXIT . •P r e s s @CANCL to r eturn to P L O T WINDO W . •P r e s s $ , or L @@@OK@@@ , to r eturn to normal calc ulator displa y . T ry also a F ast 3D plot f or the surface z = f(x ,y) = sin (x 2 +y 2 ) •P r e s s „ô , simultaneousl y if in RPN mode , to access the P L O T SETUP w indo w .
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Page 11-1 Chapter 11 Calculus Applications In this C hapter w e disc uss appli catio ns of the calc ulator’s f uncti ons to oper ations r elated to C alc ulus , e.
Page 11-2 Fu n c t io n lim is enter ed in AL G mode as lim(f (x),x=a) to calculate the limit . In RPN mode , ente r the func tion f irst , then the e xpr ession ‘ x=a’ , and f inally func tion lim. Ex amples in AL G mode ar e sho wn ne xt , inc luding some limits to inf inity , and one -sided limits .
Page 11-3 F unc tions DERI V and DER VX The function D ERIV is used to take deri vati ve s i n terms of any ind epen dent var iable , while the functi on D ER VX tak es deri vati ve s w ith r espect to the C AS d efa ul t va ria bl e V X ( t ypic a l ly ‘ X’ ) .
Page 11-4 P leas e noti ce that func tions S I G MA VX and SIGMA ar e designed f or integr ands that in v ol v e some s ort of integer func tion lik e the fact or ial (!) func tion sh o w n abo ve . The ir r esult is the so -called disc r ete der i v ati v e , i.
Page 11-5 Infinite ser ies A func tion f(x) can be e xpanded into an inf inite ser ies ar ound a point x=x 0 b y using a T a y lor’s se r ies , namely , , w here f (n) (x) r epr esen ts the n- th deri vati ve o f f(x) w ith r espec t to x , f (0) (x) = f(x) .
Page 11-6 ser ies) or an e xpre ssi on of the f or m ‘ var iable = v alue ’ indicating the poin t of e xpansion of a T ay lor ser ies , and the or der of the ser ies to be pr oduced .
Page 12-1 Chapter 12 M ulti-v ari ate Calc ulus Applications Multi-var iate calc ulus r ef er s to f uncti ons o f tw o or mor e var iable s. In this Chapt er w e disc uss basi c concepts of multi-v ar iate calc ulus: partial der i v ati ves and m ultiple integr als.
Page 12-2 T o de f ine the functi ons f(x ,y) and g(x ,y , z) , in AL G mode , use: DEF(f(x,y )=x*CO S(y)) ` D EF(g(x,y ,z)= √ (x^2+y^2)*SIN(z) ` T o t ype the der iv ativ e sy mbol use ‚¿ . Th e d e riva t ive , f or e xample , w ill be ente r ed as ∂ x(f(x ,y)) ` in A L G mode in the scr een.
Page 13-1 Chapter 13 V ec tor Anal y sis Applications T his chapt er desc ribes the us e of f uncti ons HE S S, DIV , and CURL , f or calc ulating oper ations of v ector anal y sis .
Page 13-2 Di ve rgence T he di v er ge nce o f a v ect or f unc ti on , F (x ,y ,z) = f(x,y ,z ) i + g(x,y ,z ) j +h(x ,y ,z) k , is de f ined by t aking a “ dot -produc t” o f the del oper ator w i th the func tion , i .e . , . F unction DIV can be used to calc ulate the di ve r gence of a v ecto r fi eld .
Page 14-1 Chapter 14 Differential Equations In this Chapte r we pr esen t e x amples of so l v ing or dinar y differ ential equati ons (ODE) using calc ulator functi ons. A diff er ential equati on is an equati on inv olv ing deri vati ve s of the independent var iable .
Page 14-2 • the ri ght-hand side of the OD E • the char acter isti c equation of the ODE Both of these inputs mus t be giv en in terms of the defa ult independent var iable f or the calc ulator ’s CAS (ty pi cally X). The output f r om the functi on is the general soluti on of the ODE .
Page 14-3 Fu n c ti o n DE SO L V E T he calculator pr o v ides f uncti on DE S OL VE (Differ ential E quation S OL VEr ) to sol v e certain t ype s of diff er enti al equations . The f unction r e quir es as input the differ enti al equatio n and the unkno wn f uncti on , and retur ns the soluti on to the equati on if av ailable .
Page 14-4 ‘ d1y(0 ) = -0. 5’ . Changing to these Ex act e xpres s ions f ac i litates the solut ion. Pr es s µµ to simplif y the re sult . Use ˜ @EDIT to see this r esult: i. e . , ‘ y(t) = -((19* √ 5*S IN( √ 5*t) -(148*CO S( √ 5*t)+8 0*C OS(t/2) ))/19 0)’ .
Page 14-5 Compar e these e xpr essions w ith the one gi v en earli er in the def initi on of the L aplace tr ansf orm , i .e ., and y ou w ill notice that the CA S defa ult v ar iable X in the equati on wr iter sc r e en r epla ces the v aria ble s in this de f inition .
Page 14-6 F our ier series f o r a quadr atic func tion Deter mine the co eff ic ients c 0 , c 1 , and c 2 f or the f uncti on g(t) = (t-1) 2 +(t - 1) , w ith per iod T = 2 .
Page 14-7 Th us , c 0 = 1/3, c 1 = ( π⋅ i+2)/ π 2 , c 2 = ( π⋅ i+1)/( 2 π 2 ). The F o urier seri es with three el ement s will be wr it ten as g(t) ≈ R e[(1/3) + ( π⋅ i+2)/ π 2 ⋅ ex p ( i ⋅π⋅ t)+ ( π⋅ i+1)/( 2 π 2 ) ⋅ ex p (2 ⋅ i ⋅π⋅ t)].
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Page 15-1 Chapter 15 Pr obabilit y Distributions In this Chapt er w e pr o v ide e x amples of appli cati ons of the pr e -defined pr obab ility distribu tions in the calc ulator . T he MTH/P R OB ABI LI TY .. sub-menu - par t 1 T he MTH/PR OB ABILI TY .
Page 15-2 • PERM(n ,r ) : Calc ulates the number o f perm utati ons of n items tak en r at a time • n!: F actor ial o f a positi ve inte ger . F or a non -integer , x! r etur ns Γ (x+1) , wh ere Γ (x) is the Gamma functi on (see C hapter 3). The f actor ial s ymbol (!) can be enter ed also as the ke ys tr ok e combinati on ~‚2 .
Page 15-3 T he MTH/P ROB menu - part 2 In this sec tio n w e dis c us s f our cont inuou s pr obabil ity distr ibuti ons that ar e commonl y us ed f or pr oblems r elated to s tatisti cal infer ence: the nor mal distr ibution , the Student ’s t distr i buti on , the Chi-squar e ( χ 2 ) distr ibuti on , and the F-dis tributi on .
Page 15-4 T he C hi-squar e distribution Th e C h i - sq u a re ( χ 2 ) distribu tion has one par ameter ν , know n as the degr ees of fr eedom. The calc ulator pr ov ides f or values o f the upper - tail (c umulati v e) distr ibution f uncti on f or the χ 2 -distr ibution using UTPC gi ven the value o f x and the par ameter ν .
Page 16-1 Chapter 16 Statistical Applications T he calc ulator pr ov ides the f ollo wing pr e -pr ogr ammed statis tical f eatur es access ible thr ough the k e y str ok e combinati on ‚Ù (the 5 k.
Page 16-2 Calculating singl e -v ar iable statistic s After enter ing the col umn vector into Σ DA T , p re s s ‚Ù @@@OK@@ to sele ct 1. Singl e - v ar .. The fo llo w ing input f or m w ill be pr ov ided: T he for m lists the data in Σ D A T , sho ws that column 1 is s elec ted (ther e is onl y one column in the c urr ent Σ D A T) .
Page 16-3 Obtaining frequenc y distr ibutions The ap p l ic a tio n 2. Frequenci es.. i n t h e S T A T m e n u c a n b e u s e d t o obtain f r equenc y distr ibuti ons f or a set of data . The data mu st be pr esent i n t h e f o r m o f a c o l u m n v e c t o r s t o r e d i n v a r i a b l e Σ DA T .
Page 16-4 Σ D A T , b y usi ng functi on ST O Σ (see e x ample abo ve) . Ne xt, obtain single - v ar ia ble infor mation us ing: ‚Ù @@@OK@@@ . The r esults are: This informat ion ind icates tha t our da ta ranges from -9 to 9 .
Page 16-5 F itting data to a func tion y = f(x) T he pr ogram 3. F it da ta.. , av ailable as option n umber 3 in the S T A T menu , can be used to f it linear , logar ithmic , exponenti al, and po w er func tions t o data sets (x , y) , stor ed in columns of the Σ D A T matr i x.
Page 16-6 Le ve l 3 sho ws the f or m of the equati on. L e v el 2 sho ws the sample corr elation coeff ic ient , and lev el 1 sho ws the co var iance of x -y .
Page 16-7 •P r e s s @@@OK@@@ to obtain the fo llo wing r esults: Confidence inter vals T he applicati on 6. Con f In ter val can be acces sed b y using ‚Ù— @@@OK@@@ . Th e ap p l ic at io n of fe rs t h e fol l ow in g o p t io ns : These opt ions ar e to b e i nterpre ted as follo ws: 1.
Page 16-8 4. Z -INT : p 1− p 2 .: C onf idence interval f or the differ ence of tw o pr oportions, p 1 -p 2 , for lar ge samples w ith unkno w n populatio n va rian c es. 5. T- I N T: 1 µ .: Single sample confi dence int erval f or the population mean , µ , f or small samples with unkno w n population v ariance .
Page 16-9 T he gr aph sho ws the s tandar d nor mal distr ibution pdf (pr o babi lity densit y func tion), the location of the c riti cal po ints ± z α/2 , the mean value ( 2 3 . 3) and the corr esponding interval limits ( 21.9 84 2 4 and 2 4.615 7 6 ) .
Page 16-10 2. Z - Te s t : µ1−µ2 .: Hy pothesis testing f or the differ ence of the populati on means, µ 1 - µ 2 , w ith either kno wn populati on v ari ances , or fo r lar ge samples w ith unkno wn populati on var iances .
Page 16-11 Then , we r ej ect H 0 : µ = 15 0, against H 1 : µ ≠ 15 0. The tes t z value is z 0 = 5 .6 5 6 8 54. T he P -v alue is 1. 54 × 10 -8 . T he cr iti cal v alues of ± z α /2 = ± 1.9 5 9 9 64 , cor r esponding t o cr itical ⎯ x r ange of {14 7 .
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Page 17-1 Chapter 17 Numbers in Differ ent Bases Besi des our dec imal (base 10, di gits = 0 -9) number s y ste m , y ou can w ork w ith a b inary s yst em (bas e 2 , digits = 0,1) , an octal s yst em (base 8 , digits = 0 - 7) , or a he x adec imal s y ste m (base 16, di gits=0 -9 ,A -F), among others .
Page 17-2 W r iting non -dec imal numbers Numbers in non-de c imal sy stems , r ef err ed to as bi n ar y i nte g e rs , ar e w r itten pr eceded by the # s y mbol ( „â ) in the calculator . T o select the c urr ent base to be u sed f or binary integers , choo se e ither HEX (adec imal) , D E C (imal) , OCT (al), or BIN (ary) in the BA SE menu .
Page 18-1 Chapter 18 Using SD car ds The calc ulator has a mem ory car d slot into w hic h y ou can insert an SD flash car d for backin g up calculat or objec ts, or f or do wnl oading objects fr om other sour ces . The SD car d in the calculat or w ill appear as port numb er 3.
Page 18-2 4. When the for matting is fin ished, the HP 5 0g display s the m essage "FORMA T FINISHED . PRE S S ANY KEY T O EXI T". T o ex it the sy stem menu , hold dow n the ‡ k e y , pr ess and r elease the C k e y and then r elease the ‡ key .
Page 18-3 N o t e t h a t i f t h e n a m e o f t h e o b j e c t y o u i n t e n d t o s t o r e o n a n S D c a r d i s longer than ei ght c har act ers , it w ill appear in 8.
Page 18-4 P urging all objects on t h e SD card (b y re fo rm at t i n g ) Y ou can pur ge all ob jects f r om the SD card b y r ef ormatting it . When an SD car d is inserted, @FO RMA appears an additi onal menu item in F ile Manager .
Page 19-1 Chapter 19 Equation L ibr ar y T he E quation L ibrary is a collectio n of equati ons and commands that enable y ou to sol v e simple sc ience and engineer ing pr oblems . T he libr ary consis ts of mor e than 300 equati ons grou ped into 15 tec hnical sub jects cont aining mor e than 100 pr oblem titl es .
Page 19-2 No w us e this equati on set to ans w er the questi ons in the follo w ing e x ample . Step 4: Vi e w the f i v e equati ons in the Pr oj ectile Moti on set . All f iv e ar e used inter changeabl y in order to s olv e for missing v ariable s (see the ne xt e xample).
Page 19-3 0 *!!!!!!X0!!!!!+ 0 *!!!!!!Y0!!!!!+ 50 *!!!!!!Ô 0!!!!!+ L 65 *!!!!!!R!!!!!+ Step 3 : S olv e for the v eloc ity , v 0 . (Y ou solv e for a v ar iable b y pre ssing ! and then the var iable ’s menu k ey .
Page 19-4 Refe re n c e F or additional det ails on the E quation L ibrary , see C hapter 2 7 in the calculator ’s us er’s gui de . SG49A.book Page 4 Friday, S eptember 16, 2005 1:31 P M.
Pa g e W - 1 L imited W arr ant y HP 50g gr aphing calculator ; W arr ant y per iod: 12 months 1. HP war r ants to y ou , the end-user c ustomer , that HP hard war e, accessor ies and suppli es w ill be fr ee fr om defects i n mater i als and w orkmanship after the date of pur c hase , for the per iod spec if ied a bov e.
Pa g e W - 2 REMEDIE S . EX CEPT A S INDICA TED ABO VE , IN NO EVENT WILL HP OR I T S S UPP LIERS BE LIABLE F OR L OS S OF D A T A OR FOR DIRE CT , SP E CIAL, INCIDENT AL , CO NSE QUENTIAL (INCL UD ING L O S T PR OFIT OR D A T A ) , OR O THER D AM A GE , WHETHER B ASED IN C ONT RA CT , T OR T , OR O THER WISE .
Pa g e W - 3 Ser vice Eur ope Co untry : Te l e p h o n e n u m b e r s A us tr ia + 4 3-1-3 6 0 2 7 71203 B e l g i u m + 32-2-7 1 262 1 9 Denm ark + 4 5-8- 2 3 3 2 844 Ea s t e r n Eu ro p e c o u n.
Pa g e W - 4 L.A me ri ca Co un try : Te l e p h o n e n u m b e r s Ar genti na 0- 8 1 0- 5 5 5 - 5 5 2 0 Br azil S a o Pa u l o 37 47-7 79 9 ; R O T C 0 -800 -15 77 51 Me x ico M x C i t y 5 258 - 9.
Pa g e W - 5 Regulat or y inf ormation F ederal Communications Commission Notice T his equipment has been tes ted and fo und to comply w ith the limits f or a C las s B di gital de v ice , pursu ant t o P art 15 of the FCC R ules .
Pa g e W - 6 Or , call 1 - 8 0 0 - 4 7 4 - 6836 F or questi ons r e gar ding this FCC dec larati on, contac t: Hew lett -P ac k ar d Compan y P . O . Bo x 6 9 2000, Mail S top 510101 Houston , T ex as 77 2 6 9- 2000 Or , call 1 -28 1 - 5 1 4 - 3333 T o identify this pr oduct , r ef er to the part , ser ies , or model number f ound on the pr oduct.
Pa g e W - 7 Japane se Not ice こ の装置は、 情報処理装置等電波障害自主規 制協議会 （VCCI） の基準 に 基づ く ク ラ ス B 情報技術装置 で す 。 こ の装.
An important point after buying a device HP HP 50g (or even before the purchase) is to read its user manual. We should do this for several simple reasons:
If you have not bought HP HP 50g yet, this is a good time to familiarize yourself with the basic data on the product. First of all view first pages of the manual, you can find above. You should find there the most important technical data HP HP 50g - thus you can check whether the hardware meets your expectations. When delving into next pages of the user manual, HP HP 50g you will learn all the available features of the product, as well as information on its operation. The information that you get HP HP 50g will certainly help you make a decision on the purchase.
If you already are a holder of HP HP 50g, but have not read the manual yet, you should do it for the reasons described above. You will learn then if you properly used the available features, and whether you have not made any mistakes, which can shorten the lifetime HP HP 50g.
However, one of the most important roles played by the user manual is to help in solving problems with HP HP 50g. Almost always you will find there Troubleshooting, which are the most frequently occurring failures and malfunctions of the device HP HP 50g along with tips on how to solve them. Even if you fail to solve the problem, the manual will show you a further procedure – contact to the customer service center or the nearest service center
