Instruction/ maintenance manual of the product HP 50g HP (Hewlett-Packard)
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HP 5 0g gr aphing calc ulator user ’s manual H Ed it io n 1 HP part number F22 2 9AA-90001.
Notice REG ISTER Y OUR PRODU CT A T: ww w .register .hp.com THI S MANU AL AND ANY EX AMPLES CONT AI NED HEREIN ARE PRO VIDED “ AS IS” AND ARE SUBJECT TO CHANGE WITHOUT NO TI CE.
Pre face Y ou hav e in y our hands a compact sy mbolic and numer ical computer that w ill fac ilitate calc ulation and mathe matical analy sis of pr oblems in a var iety of disc iplines, f rom eleme ntar y mathemati cs to advanced engineering and sc ience sub jects.
Page TOC-1 T able of Contents Chapter 1 - Getting started Basic Ope rations , 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 in the stack , 2- 1 Creating arithmetic expressions, 2-1 Creating algebraic expressions, 2-4 Using the Equation Writer (EQ W) to create expressions , 2-5 Creating arithm.
Page TOC-3 Available units, 3-9 Attaching units to numbers, 3-9 Unit prefixes, 3-10 Operations with units, 3-11 Unit conversions, 3-12 Physical constants in the calculator , 3-13 Defining and using fu.
Page TOC-4 The PROOT function, 5-9 The QUOT and REMAINDER func tions, 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, division, 7-2 Functions applied to lists, 7-4 Lists of complex numbers , 7-4 Lists of algebraic objects , 7-5 The MTH/LIST menu , 7-5 The SEQ function.
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 NORM.
Page TOC-7 Chapter 12 - Multi-variate Calculus Applications Partial derivati ves , 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 Gett in g st art ed This c hapter pr ov ides basi c infor mation about the oper ation o f your calc ulator . It is designed to famili ari z e yo u with the basi c operati ons and settings bef or e you perfor m a calculati on.
Page 1-2 b . Insert a new CR203 2 lithium bat tery . Make sur e its positiv e (+) side is facing up . c. Replace the plate and push it to the ori ginal place. After installing the batter ies, pr ess $ to turn the p o wer o n. Wa rn i ng : When the low battery icon is displa yed , you need to r eplace the batteri es as soon as possible .
Page 1-3 Contents of the calculator ’s displa y T urn yo ur cal c ulato r on o nce mo r e. At t he top of th e dis pla y y ou w ill hav e two line s of infor mation that desc ribe the s ettings of the calculator .
Page 1-4 These si x functi ons form the f irst page of the T OOL menu . This menu has actually e ight entr ies arr anged in t w o pages. The second page is av ailable by pr essing the L (NeXT menu) k ey . This k ey is the third k ey fr om the left in the thir d r ow of k ey s in the k ey board .
Page 1-5 F or ex ample , the P key , key (4,4 ) , has the follo w ing six f unctio ns associated with it: P Main functi on, to ac tiv ate the S YMBolic menu „´ Le f t-shift functi on, to acti vat e.
Page 1-6 Of the six f unctions ass ociat e d w ith a k ey onl y the firs t four ar e shown in the ke yboar d itself . The f igure in ne xt page show s these four labels for the P ke y .
Page 1-7 Operating Mode The ca lc ulator off ers tw o operating mode s: the Alg eb r a ic mode , and the Reverse P ol ish N ota tion ( RPN ) mode . The def ault mode is the Algebr aic m o d e ( a s i .
Page 1-8 Y ou could also ty pe the expr essio n directl y into the displa y w ithout using the equation w riter , as f ollow s: R!Ü3.*!Ü5.- 1/3.*3.™ /23.Q3+!¸2.5` to obtain the same result . Change the oper ating mode to RPN b y fir st pre ssing the H butto n.
Page 1-9 Let's try some other sim ple operatio ns befor e trying the mor e complicat ed expr essi on used earlier f or the algeb r aic oper ating mode: Note the positi on of the y and x in the last tw o operati ons.
Page 1-10 T o select between the AL G v s. RPN operating mode , y ou can a lso s et/ clear s ys tem flag 9 5 thr ough the follo w ing k e ystr ok e sequence: H @FLAGS! 9˜˜ ˜˜ ` Number F ormat and dec imal dot or comma Changing the numbe r form at allow s yo u to cus tomi z e the wa y real numbers ar e displa yed b y the calculator .
Page 1-11 Pr ess the ri ght arr ow k e y , ™ , to highlight the z er o in front o f the option Fix . Pr ess the @ CHOOS soft menu k ey and , using the up and dow n arr ow keys, —˜ , select , say , 3 dec imals.
Page 1-12 K eep the number 3 in fr ont of the Sc i . (T his number can be c hanged in the same fashi on that we c hanged the Fix e d number of decimals in the e xample abo ve). Pr ess the !!@@OK#@ so ft men u k e y r etu rn t o t he c alc ul at or d isp la y .
Page 1-13 Pr ess the !!@@OK#@ so ft men u k e y r e tur n t o th e ca lc ula to r di spl a y . T he n um ber now is sho wn as: Becaus e this number has thr ee fi gures in the integer part, it is sho wn w ith four si gnifi cativ e figur es and a z er o pow er of ten, while using the Engineer ing format .
Page 1-14 Angle Measure T rigonometr ic fu nctions, f or e xample , req uire ar guments r eprese nting plane angles . The calc ulator pro vi des three diff eren t Angle Measure modes f or wor ki ng wi th an gl e s, n a me ly: • Degr ees : T her e are 360 degr ees ( 360 ° ) in a co mp le t e ci rcum fe ren ce.
Page 1-15 soft men u ke y to complete the oper ation . For e xample , in the follo wing scr een , the P olar co or dinate mode is selected: Selec ting CA S set tings CA S stands fo r C omputer A lgebr aic S ys tem. T his is the mathematical core of the calculator w her e the s ymboli c mathema ti cal op er ations and func tions are pr ogrammed .
Page 1-16 Non-Rati onal o pti ons above). Unselected options w ill show no chec k mark in the underline pr eceding the option of inter est (e.g ., the _Numeri c, _Appr ox , _Comple x, _V erbos e, _St ep /S tep, _Inc r P ow options abov e) .
Page 1-17 Selec ting Displa y modes The calc ulator displa y can be cu stomi zed to your pr ef erence b y selecting differ ent displa y modes. T o see the optional displa y settings use the follo w ing: •F i r s t , p r e s s t h e H button to activ ate the CAL CULA T OR MODE S in put fo rm.
Page 1-18 Selec ting the displa y font Fi r st, p r es s t h e H button to activate the CAL CUL A T O R MODE S i nput fo rm. W ithin the CAL CULA T OR MODE S input for m, pr ess the @@DISP@ soft menu k ey t o display the DISP L A Y MODE S input for m.
Page 1-19 Selecting properties of the Stack Fi r st, p re s s th e H but ton to activ ate t he CAL CULA T OR MOD E S input for m. W ithin the CAL CUL A T OR MODES inpu t form , pre ss the @@DISP@ soft menu k ey ( D ) to display the DISPLA Y MODES in put for m.
Page 1-20 Selecting properties of the equation writer (E QW ) Fi r st, p r es s t h e H button to activate the CAL CUL A T O R MODE S i nput fo rm. W ithin the CAL CULA T OR MODE S input for m, pr ess the @@DISP@ soft menu k e y to display the DISPLA Y MODE S input f orm .
Page 2-1 Chapter 2 Intr oduc ing the calc ulat or In this chapte r we pr esent a number o f basic oper ations of the calc ulator including the us e of the E quation W riter and the manipulati on of data obje cts in the calc ulator .
Page 2-2 Notice that , if y our CAS is set to EXA CT (see Appendi x C in user ’s guide) and y ou enter y our expr essi on using integer numbers f or integer v alues, the r esult is a s ymboli c quantity , e.g ., 5*„Ü1+1/7.5™/ „ÜR3-2Q3 Bef ore pr oduc ing a re sult, y ou w ill be asked t o change to Appr ox imate mode .
Page 2-3 If the CAS is s et to Exact , you w ill be ask ed to appro ve c hanging the CAS setti ng to Appr ox . Once this is done , you w ill get the same result a s bef ore . An alter nativ e wa y to ev aluate the expr essi on enter ed earlie r bet w een quote s is b y using the option …ï .
Page 2-4 Creating algebraic e x pr essions Algebr aic e xpres sions include n ot only number s, but also v aria ble names. As an ex ample , we w ill enter the follo w ing algebraic e xpr ession: W e set the calculat or operating mode to A lgebrai c, the CA S to Ex act , and the display to Te x t b o o k .
Page 2-5 Using the Equation W riter (EQW) to create ex p re s s i o ns The equati on wr iter is an extr emely po w er f ul tool that not only let y ou enter or see an equati on, but als o allow s yo u to modify and wor k/apply functi ons on all or part of the equation.
Page 2-6 Suppose that y ou w ant to replace the quan tit y betw een parenthes es in the denominator (i.e ., 5+1/3) with (5+ π 2 /2). Fir st , we u se the delet e ke y ( ƒ ) delete the c urr ent 1/3 .
Page 2-7 F irst , we need to highlight the entire f irst ter m by using either the r ight arr ow ( ™ ) or the upper arr ow ( — ) ke ys , repeatedl y , until the entire e xpres sion is hi ghlighted , i .e., s ev en times, produc ing: Once the e xpressi on is highligh ted as show n abov e , type +1/ 3 to add the fr action 1/3 .
Page 2-8 ~„y———/~‚tQ1/3 This r esults in the output: In this e xample w e used se ver al low er -case English letter s, e .g., x ( ~„x ), se v er al Gr ee k l e tt er s , e .g ., λ ( ~‚n ), and even a combinati on of Greek and English le tters, namel y , ∆ y ( ~‚c~„y ) .
Page 2-9 Subdirectories T o store y our data in a w ell or ganiz ed direct or y tr ee yo u may w ant to cr eate subdir ector ies under the HOME dir ectory , and more subdir ectori es w ithin subdirec tori es, in a hier arc hy o f direct ories similar t o folders in modern co mputers .
Page 2-10 T o unlock the upper -case lock ed ke yboar d, pr ess ~ . T r y the f ollow ing ex er cis es: ~~math` ~~m„a„t„h` ~~m„~at„h` The calc ulator dis play w ill sho w the follo wing (l e.
Page 2-11 The fo llow ing are the k eys trok es for ente ring the remaining var iables: A12: 3V5K~a 12` Q: ~„r/„Ü ~„m+~„r™™ K~q` R: „Ô3‚í2‚í1™K~r` z1: 3+5*„¥K~„z1` (Accep t cha nge to Com pl ex mode if asked). 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 ocedu r e: 3V5³~a12`K Here is a w ay to enter the contents of Q: Q: ~„r/„Ü ~„.
Page 2-13 Chec king v ariables contents The si mp les t way to ch eck a va riab le co nte nt i s by pres si ng th e sof t men u k ey label f or the var iable .
Page 2-14 This pr oduces the f ollow ing scr een (A lgebraic mode in the left , RPN in the rig ht ) Notice that this time the contents of pr ogr am p1 are lis ted in the scr een .
Page 2-15 Y ou can us e the PURGE command t o erase mor e than one v aria ble by plac ing their names in a list in the ar gument of P URGE . F or ex ample , if now we wan te d to pu rg e va ria bl es R and Q , simultaneously , w e can try the follo wing e xer cis e.
Page 2-16 UNDO and CMD functions F unctions UNDO and CMD are us eful for r ecov er ing r ecent commands, or to r ev ert an operati on if a mistak e was made . The se functi ons are ass oci ated w ith the HIS T k ey : UNDO re sults fr om the k ey str ok e sequ ence ‚¯ , whi le CMD re sults fr om the k ey str ok e seque nce „® .
Page 2-17 Ther e is an alter nativ e wa y to access these menus as soft MEN U keys, by sett ing sy stem f l ag 117 . (F or infor mation on F lags see Chapt ers 2 and 2 4 in the calc ulator’s user ’s guide) .
Page 2-18 Pr ess B to sel ect the MEMOR Y soft me nu ( ) @@MEM@ @ ). T h e di s pl a y n o w sho ws: Pr ess E to sele ct the DIR E CTOR Y sof t menu ( ) @ @DIR@@ ) The ORDER command is not sho wn in this sc reen . T o f ind it we us e the L key to fi n d i t : T o a c tiv ate the ORD ER command w e pres s the C ( @ORDER ) soft menu ke y .
Page 3-1 Chapter 3 Calculations with real numbers This c hapter demons trates the use of the calc ulator for ope ratio ns and functi ons rel ated to real n umbers. T he user should be acq uainted with the k ey boar d to iden tify ce rtain functi ons av ailable i n the ke ybo ard (e .
Page 3-2 6.3#8.5- 4.2#2.5* 2.3#4.5/ • P arentheses ( „Ü ) can be us ed to gr oup oper ations, a s well as to enclose argum ents of fun ctions. In AL G mode: „Ü5+3.2™/„Ü7- 2.2` In RPN mode , you do not need the par enthesis, calc ulatio n is done dir ectly on the s tack: 5`3.
Page 3-3 • The po w er function , ^, is availa ble through the Q key . Wh en calc ulating in the s tack in AL G mode, ente r the base ( y ) fo llow ed by the Q k ey , and then the e xponent ( x ), e .g . , 5.2Q1.25` In RPN mode, ente r the number firs t, then the f unction , e.
Page 3-4 2.45`‚¹ 2.3`„¸ • Thr ee tri gonometr ic functi ons are r eadily a vailable in the k ey board: sine ( S ), co si ne ( T ), and tangent ( U ).
Page 3-5 Real number functions in th e MTH menu The MT H ( „´ ) menu include a number of mathemati cal func tions mostl y applicable to r eal numbers . With the defa ult setting of CHOOSE bo xes for sy s tem fl ag 1 17 (see Chap ter 2 ) , th e MTH men u shows th e foll ow i ng fu nct ions : The f unctions ar e gr ouped by th type of argument (1.
Page 3-6 F or e xample , in AL G mode, the k ey str ok e sequence to calc ulate , say , tanh( 2 .5 ) , is the fo llow ing : „´4 @@OK @@ 5 @@OK@@ 2.5` In the RPN mode , the ke ys trok es to perfo rm this calculati on are the follo wing: 2.
Page 3-7 F inally , in o rder to s elect, for e xample , the hy perboli c tangent (tanh) functi on, simpl y press @ @TANH@ . F or ex ample , to calculat e tanh(2 . 5) , in the AL G mode, w hen using SO F T menus over CHOOSE box es , f ollo w this pr ocedur e: „´ @@HYP@ @ @TANH@ 2.
Page 3-8 Option 1. T ools.. cont ains functi ons used to operate on units (discu ssed later ) . Opti ons 2. L e n g t h . . t h r o u g h 17 .Viscosity .. contai n menus w ith a number of u nits f or each o f the quantities desc ribed . F or ex ample , selec ting option 8.
Page 3-9 Pr essing on the appropr iate soft men u ke y will open the sub-menu of units fo r that partic ular selecti on. F or ex ample, f or the @) SPEED sub-men u, the fo llow ing units are a vailable: Pr essing the so ft menu k ey @) UNITS w ill ta k e you back to the UNIT S menu.
Page 3-10 5‚Û8 @@OK@@ @@OK@@ Notice that the under scor e is enter e d aut omaticall y when the RPN mode is acti ve . The k ey str oke sequence s to enter units when the SO FT m en u option is select ed, in both AL G and RPN modes, ar e illustr ated ne xt.
Page 3-11 123‚Ý~„p~„m Using UB ASE (type the name) to con vert to the def ault unit (1 m) results in: Operations w it h units Her e are some cal culatio n ex amples using the AL G operating mode .
Page 3-12 Additi on and subtracti on can be performed , in AL G mode, w ithout using par entheses, e .g., 5 m + 3 200 mm, can be enter ed simpl y as 5_m + 3 200_mm ` .
Page 3-13 Ph ysical constants in the calculator The calc ulator’s ph y sical const ants are con tained in a constants libr ar y acti vated w ith the command CONLIB.
Page 3-14 If w e de -select the UNIT S option (pr ess @UNITS ) only the v alues are sho wn (English units select ed in this case) : T o copy the va lue of Vm to the stac k, select the vari able name , and pres s @²STK , then, press @QUIT@ .
Page 3-15 Defining and using functions Users can de fine their o wn f unctions b y using the DEFINE com mand av ailable thought the ke ystr ok e sequence „à (assoc iated w ith the 2 ke y).
Page 3-16 r elativ ely simple and consists of tw o par ts , contained between the pr ogram containers This is to be in terpr eted as say ing: enter a v alue that is temporar ily assigned to the name x.
Page 4-1 Chapter 4 Calculations with complex numbers This c hapter sho ws e xamples o f calcul a ti ons and applicati on of func tions to comple x number s. Definitions A comple x number z is a number z = x + iy , whe re x and y ar e r eal number s, and i is the imaginary unit def ined by i ² = –1.
Page 4-2 Pr ess @@OK @@ , t w ice, to r etu rn to the stack. Entering comple x numbers Com plex numbe rs in the calculat or can be enter ed in e ither of the tw o Carte sian representations, na mely , x+iy , or (x,y) . The re su lts in the calculat or will be sho wn in the or der ed-pair for mat, i .
Page 4-3 P olar repr esentation of a complex number The polar r epres entation of the comple x number 3. 5-1.2i, enter ed abov e, is obta ined by changing th e coor di nate sy stem to cylindrical or pol ar (using func tion CYLIN). Y ou can find this f unction in the catalog ( ‚N ).
Page 4-4 Sim ple o per ati ons w ith comp le x nu mber s Com plex number s can be combined using the f our fundamental oper ations ( +-*/ ). The r esults f ollow the rules of algebr a w ith the cav eat that i2= -1 . Oper ations w ith complex number s are similar to tho se with r eal numbers .
Page 4-5 The f irst men u (options 1 thr ough 6) sho ws the f ollow ing f unctions: Example s of appli cations o f these f unctio ns are sho wn next in RECT coor dinates. R ecall that, f or AL G mode , the function mu st pr ecede the argumen t, w hile in RPN mode, y ou enter the ar gument f irst , and then select the func tion.
Page 4-6 CMP LX m enu in k ey board A second CMP LX menu is accessible by u sing the righ t -shift option assoc iat ed with the 1 k ey , i .e., ‚ß .
Page 4-7 Function DROITE: equation o f a straight line F unction DROITE tak es as ar gument t w o complex number s, say , x 1 + iy 1 and x 2 +iy 2 , and r eturns the equati on of the strai ght line, sa y , y = a + bx, that contains the po ints (x 1 , y 1 ) and (x 2 , y 2 ) .
SG49A.book Page 8 Friday, September 16, 200 5 1:31 PM.
Page 5-1 Chapter 5 Algebraic and arithmetic oper ations An algebr aic object , or simply , algebr aic , is an y number , var iable name or algebrai c expr essi on that can be oper ated upon , manip ulat ed, and combined accor ding to the ru les of algebr a.
Page 5-2 Simple operations w it h algebr aic objec ts Algebr aic ob jects can be added , subtrac ted, m ultiplied, div ided (e xcept b y z er o) , r aised to a po wer , us ed as arguments f or a var iety of standar d functi ons (exponenti al, logarithmi c, tr igonometry , h yperboli c, etc .
Page 5-3 @@A1@@ * @@A 2@@ ` @@A1@@ / @@A2@@ ` ‚¹ @@A1@@ „¸ @@A2@@ The same re sults are obtai ned in RPN mode if using the f ollo wing keyst rokes : Functions in the AL G menu The A L G (Alg ebrai c) menu is a vailable b y using the k e ystr oke s equence ‚× (ass oci ated w ith the 4 ke y).
Page 5-4 T o complete the oper ation pr ess @@OK@ @ . Here i s t he h elp screen for fun ctio n COL LECT : W e noti ce that, at the bottom of the sc reen , the line See: EXP AND F A CT OR suggests links t o other help fac ility entri es, the f unctions E XP AND and F A CT OR.
Page 5-5 F or ex ample , for f unction S UBS T , w e find the f ollow ing CA S help fac ility entry: Operations wi t h tr anscende ntal functions The calc ulator off ers a number of fu nctions that can be used to r eplace e xpressi ons containing logar ithmic and e xponential func tions ( „Ð ), as well as trigonometric functions ( ‚Ñ ).
Page 5-6 Info rmation and e xample s on these commands ar e a vailable in the help fac ility of the calc ulator . F or e xample , the desc ri ption of E XPLN is sho wn in the left-hand side , and the .
Page 5-7 Functions in the ARITH M E TIC menu The ARI THMETIC menu is tr igger ed thr ough the ke ystr oke comb ination „Þ (assoc iated with the 1 k ey).
Page 5-8 Po l y n o m i a l s P oly nomials ar e algebr aic expr es sions consisting of one or mor e terms containing dec rea sing po wers of a gi ven v ari able. For ex ample , ‘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 PROOT f unc t io n Gi ven an ar ra y containing the coeffi c i ents of a pol ynomial , in decr easing or der , the functi on PROO T pro vi des the r oots of the poly nomial . Example , from X 2 +5X+6 =0, P ROO T([1, –5, 6]) = [2 . 3 .].
Page 5-10 F A CT OR(‘(X^3-9*X)/(X^2 -5*X+6)’ )=‘X*(X+3)/(X- 2)’ The SIMP2 function F unction S IMP2 , in the ARITHME TIC men u, t akes as ar guments two number s or polyn omials, r epre senting the numer ator and denominator of a r ational fr action , and retur ns the simplified n umerator and de nominator .
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 pres s µ„î` (or , si mpl y µ , in RPN mode) yo u will get: ‘(X^6+8*X^5+5*X^4-50*X^3 .
Page 5-12 Refe renc e Additi onal informati on, def initions , and ex amples of algebr aic and arithme tic oper a ti ons are pr esent ed in Chapter 5 of the calc ulator’s us er’s guide .
Page 6-1 Chapter 6 Solution to equations Assoc iated w ith the 7 ke y there ar e two menu s of equation -sol ving functi ons, the S ymboli c SOL V er ( „Î ) , and the NUMer ical S oL V er ( ‚Ï ). Fo llow ing, w e pr esent some o f the functi ons contained in these men us.
Page 6-2 the fi gure to the le ft. A fter apply ing IS OL, the r esult is show n in the fi gure to the ri ght: The f irst ar gument in IS OL can be an e xpre ssion , as show n abov e , or an equation .
Page 6-3 The f ollo wing e xamples sh ow the us e of functi on SOL VE in AL G and RPN modes (Us e Comple x mode in the CA S): The scr e en shot s ho wn above displays two solut ions. In the f irst one , 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 tio n SOL VEV X The f unction S OL VEVX solv es an equati on for the defa ult CAS var iable co nta in ed in th e rese r ved variab le na me VX . By d efau lt, th is va riab le is set to ‘X’ . Ex amples, using the AL G mode with VX = ‘X’ , a r e show n below : In the fir st case S OL VEVX could not find a solu tion.
Page 6-5 sc reen shots sh ow the RPN st ack bef ore and afte r the applicatio n of ZERO S to the tw o ex amples abov e (Use Complex mode in the CAS): The S ymbolic S olve r functions pr esen ted abov e produ ce solutions to rati onal equations (mainl y , polynomi al equations).
Page 6-6 w ith ex amples for the numeri cal sol ver appli cations. It em 6. MSL V (Multiple equation SoL V er) w i ll be prese nted later in page 6 -10 .
Page 6-7 Pr ess ` to retur n to stack . The s tack w ill show the f ollo wing r esults in AL G mode (the s ame result w ould be sho wn in RPN mode): All the soluti ons are comple x numbers: (0.4 3 2 , -0.3 8 9) , (0.4 3 2 , 0.3 8 9) , (- 0.7 66 , 0.6 3 2) , (-0.
Page 6-8 Generating an algebraic e xpression f or th e pol ynomial Y ou can us e the calculator to ge nerate an algebr aic e xpre ssion f or a poly nomial gi ven the coeff ic ients or the r oots of the pol ynomial . The r esulting expr essi on will be gi v en in terms of the de fault CA S vari able X.
Page 6-9 Solv ing equations with one unknow n through NUM.SL V The calculator's NUM .SL V menu pr ov ides item 1. Sol ve equation .. so lve diffe rent ty pes of equati ons in a single vari able , including non-linear algebrai c and transcende ntal equations .
Page 6-10 T he e qu ati on we st or ed i n v ar ia bl e E Q i s al r ead y l oad ed i n th e Eq fiel d i n the SO L VE E QU A TION in put for m. Also , a fiel d labeled x is pr ov ided . T o solv e the equation all y ou need to do is highlight the fi eld in front o f X: b y using ˜ , and pres s @SOLVE@ .
Page 6-11 In AL G mode, pr ess @ECHO t o copy the e xample to the stack , pre ss ` to run the e x a m ple. T o see all the ele ments in the solution y ou need to acti vate the line edito r by pr essin.
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Page 7-1 Chapter 7 Ope r atio ns w ith l ist s L ists are a type o f calculator ’s object that can be us eful f or data pr ocessing. This c hapter pr esents e xamples of operatio ns with list s. T o get started w ith the e xamples in this C hapter , w e use the Appr o ximate mode (S ee Chapter 1).
Page 7-2 Addition, subtr action, multiplication, div ision Multiplicati on and div ision of a list b y a single number is distr ibuted acr oss the list , for e xample: Subtr action of a single n umber.
Page 7-3 The di v ision L4/L3 w ill produce an inf inity e ntr y becau se one of the elements in L3 is z er o, and an e rr or message is r eturned . If the lists in vol ved in the operati on hav e differ ent lengths , an err or mess age (Inv alid Dimensions) is pr oduced.
Page 7-4 Functions applied to lists Real n u mber f unctions fr om the ke yboar d (ABS , e x , LN, 10 x , L OG, S IN, x 2 , √ , CO S, T AN, A SIN, A COS , A T AN, y x ) as well as those fr om the MTH / HYPERB OLIC menu (SINH, CO SH, T ANH, A SINH, A CO SH, A T ANH) , and MTH/REAL menu (%, etc .
Page 7-5 Lists o f alg ebr aic objec ts The f ollo wing ar e e xamples of lis ts of algebrai c objec ts with the fun ction SIN appli ed to them (selec t Exact mode f or these e xampl es -- See Chapter 1): Th e M T H/ LI ST m e nu The MTH men u pro vi des a number of func tions that ex clu siv ely to lis ts.
Page 7-6 Example s of applicati on of these f unctions in AL G mode are sh ow n next: S ORT and REVLI ST can be combined t o sort a list in decr easing or der: If y ou are w orking in RPN mode , enter the list on to the stac k and then select the ope ratio n you w ant.
Page 7-7 Th e S EQ fu n c ti on The SE Q functi on, a vailable thr ough the command catalog ( ‚N ), tak es as argume nts an expr ession in te rms of an index , the name of the inde x, and starting ,.
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Page 8-1 Chapter 8 Ve c t o r s This Ch apter pr ov ides e xamples o f enteri ng and operating w ith vec tors, both mathematical v ectors o f many e lements, as w ell as ph ysical v ector s of 2 and 3 components .
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 cto rs u 2 = [1, 2] , u 3 = [-3, 2, -2] , v 2 = [3,-1] , v 3 = [1, -5, 2] Stored in to variables @@@u2@@ , @@@u3@@ , @@@v2@@ , and @@@v3@@ , respec tiv ely .
Page 8-3 Using the M atri x W riter (MTR W ) to enter v ec tors V ectors can also be e ntered b y using the Matr ix W r iter „² (thir d ke y in the fo ur th r ow o f ke y s fro m the top of the k ey board).
Page 8-4 @+ROW@ @- ROW @+COL@ @-COL@ @GOTO@ The @+ROW@ ke y will add a r ow f ull of z ero s at the location of the se lected cell of th e spr eadsheet.
Page 8-5 Simple operations w it h v ec tors T o illustr ate operati ons wi th vect ors we w ill use the v ector s u2 , u3, v2 , and v3, sto r ed in an earlier e xerc ise. Also , stor e vector A =[-1,- 2 ,- 3,- 4,-5] to b e used in the f ollow i ng e xe rc ises.
Page 8-6 Multiplication by a s calar , and div ision b y a scalar Multiplicati on by a scalar or di vi sion by a scalar is s traigh tforwar d: Absolute v alue func tion The ab solute value f unction ( ABS), when appli ed to a vector , produ ces the magnitude of the ve ctor .
Page 8-7 Magnitud e The magnitude of a v ector , as discus sed earlier , can be found w ith functi 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 ). Example s of applicati on of functi on ABS w ere sho wn a bov e.
Page 8-8 Examples of cr oss pr od ucts of on e 3-D vector w it h one 2-D vector , or v ice ve rsa, ar e pr esented ne xt: Attemp ts to ca lculate a c ross product of v e ctors of len gth oth er th an .
Page 9-1 Chapter 9 M atr ices and linear alg ebr a This c hapter sho ws e xamples of cr eating matri ces and oper ations w ith matri ces, inc luding linear algebra appli cations.
Page 9-2 If y ou hav e selected the t extbook displa y option (using H @) DISP! and che cki ng off Textbook ), the matri x will loo k like the one sho wn abo ve . Other w ise, the display will sho w: The displa y in RPN mode w ill look very similar to these .
Page 9-3 Ope r atio ns w ith m atr ic es Matri ces, lik e other mathematical obj ects, can be added and su btracted . The y can be multiplied by a scalar , or among themselv es, and r aised to a r eal pow er . An important operati on for linear algebr a applicati ons is the inv erse o f a matr ix .
Page 9-4 Addition and subtr ac tion F our ex amples ar e show n below using the matr ices stor ed abov e (AL G mode). In RPN mode , tr y the f ollow ing ei ght ex amples: Mult ipl icat ion Ther e are a number o f multiplication oper ations that inv olv e ma tr ices .
Page 9-5 Matrix -vector multiplication Matri x -vector m ultiplication is po ssible only if the number of columns of the matri x is equal t o the length of the v ector . A couple o f ex amples of matr ix - vec tor multiplicati on follo w: V ector-matr i x multiplicatio n, on the other hand , is not def ined.
Page 9-6 T erm-b y-term multiplication T erm-by- term mul tiplica tion of t wo matrices of th e same dimen sions is possib le through t he use of function HAD A MARD.
Page 9-7 The identity matri x The i dentity matri x has the pr opert y that A ⋅ I = I ⋅ A = A . T o ver if y this pr opert y w e prese nt the follo w ing exam ples using the matri ces stor ed earli er on.
Page 9-8 Characteri zing a matri x (The matr ix NORM menu) The matr ix NORM (NORMALI ZE) menu is acces sed through the k ey strok e sequ ence „´ . This men u is descr ibed in detail in Chapter 10 of the calculator ’s user’s guide . Some of thes e functions ar e desc ribed ne xt.
Page 9-9 Solution of linear s ystems A s ys tem of n linear eq uations in m var iables can be wr 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 , a .
Page 9-10 2x 1 + 3x 2 –5x 3 = 13, x 1 – 3x 2 + 8x 3 = -13, 2x 1 – 2x 2 + 4x 3 = -6 , can be wr itten as the matri x equation A ⋅ x = b , if This s y stem has the same n umber of equations as of unkno wns, 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 soluti on was f ound as show n next . Sol utio n wi th the in v erse matr i x The s olution to the s yste m A ⋅ x = b , w here A is a squar e matri x is x = A -1 ⋅ b .
Page 9-12 Refe renc es Additi onal informati on on cr eating matri ces, matr ix oper ations, and matr ix applicati ons in linear algebra is p r es ent ed in Chapters 10 and 11 of the calculator ’s user’s guide .
Page 10-1 Chapter 10 Gr aph ics In this cha pter we intr oduce some of the gr aphics capa bilities of the calc ulator . W e w ill pre sent gr aphics o f functi ons in Cartesian coor dinates and polar coor dinates, par ametri c plots, gra phics of coni cs, bar plots, scatterplots , and fast 3D plots .
Page 10-2 P lot ting an e xpression of the for m y = f(x) As an e xample , let's plot the f unction , • First , enter the PL O T SETUP env ironment by pressing, „ô . Mak e sur e that the option F unction is select ed as the TYPE , and that ‘X’ is selec ted as the independent var iable ( INDEP ).
Page 10-3 •P r e s s ` to retur n to the PL O T - FUNCTION w indow . The expr essi on ‘Y 1(X) = EXP(-X^2/2)/ √ (2* π ) ’ w ill be highlighted. Pr ess L @@@OK@@@ to r eturn to normal calc ulator display . • Enter the PL O T WINDO W env ironmen t by enter ing „ò (pres s them simultaneou sly if in RPN mode) .
Page 10-4 Gen er ating a table of v alues for a function The com bin at ions „õ ( E ) and „ö ( F ), pr esse d simultaneousl y if in RPN mode, let ’s the user pr oduce a table of va lues of func tions.
Page 10-5 • With the option In hi ghlight ed, pr ess @@@OK@@@ . The ta ble is expanded so that the x -incr ement is no w 0.2 5 rather than 0. 5 . Simpl y , what the calc ulator does is to m ultiply the or iginal inc reme nt, 0. 5, b y the z oom fac tor , 0.
Page 10-6 • K eep the def ault plot windo w r anges to read: •P r e s s @ERASE @DRAW to dr aw the thr ee -dimensional surface . The r esult is a w iref rame pic ture of the surface with the r efer ence coor dina te s yst em sho wn at the lo wer le f t co rner of the sc reen .
Page 10-7 • When done , pr ess @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 re turn to normal calculat or display . T r y 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 .
SG49A.book Page 8 Friday, September 16, 200 5 1:31 PM.
Page 11-1 Chapter 11 Calculus Applications In this Chapt er we dis cuss a pplications o f the calculator ’s functio ns to oper ations r elated to Calc ulus , e.
Page 11-2 Fu nc t io n lim is enter ed in AL G mode as lim(f (x),x=a) to calculate the limit . In RPN mode , enter the functi on fir st, then the e xpres sion ‘ x=a’ , and finally f unction lim . Example s in AL G mode ar e sho wn ne xt, including some limits t o infinity , and one -si ded limits.
Page 11-3 Functions DERI V and DERVX The function D ERIV is used to tak e d er ivativ es in terms of any indep endent var iable , while the functi on DERVX tak es deri vati ve s with r espect to the CAS defau lt variabl e V X (t ypic ally ‘X’ ) .
Page 11-4 P lease notice that f unctions S IGMA VX and SIGMA ar e designed f or integr ands that inv olv e some s ort of integer functi on like the f actor ial (!) functi on sho wn abo ve . Their r esult is the so -called discr ete der iv ativ e, i . e .
Page 11-5 Infinite series A func tion f(x) can be expanded in to an infinite se rie s around a poin t x=x 0 by u sing a T ay lor’s ser ies, namel y , , wher e f (n) (x) r epre sents the n- th der iv ativ e of f(x) w ith re spect to x , f (0) (x) = f(x).
Page 11-6 ser ies) or an e xpres sion of the fo rm ‘ var iable = va lue’ indicating the po int of e xpansion of a T aylor se ries , and the order of the s eri es to be produced .
Page 12-1 Chapter 12 Multi-variate Calculus Applications Multi-var iate calc ulus r ef ers to func tions o f two or mor e var iables . In this Chapte r we disc uss basi c concep ts o f multi- v ari ate calculus: partial deri vati v es and multiple integr als.
Page 12-2 T o d e fine the func tions f(x,y) and g(x ,y ,z) , in AL G mode, us e: DEF(f(x,y)=x*C OS(y)) ` DEF(g(x,y ,z)= √ (x^2+y^2)*SIN(z) ` T o t y pe the deri vati ve s ymbol us e ‚¿ . The de rivative , fo r ex ample, w ill be enter ed as ∂ x(f(x ,y)) ` in AL G mode in the scr een.
Page 13-1 Chapter 13 V ec tor Anal ysis Applications This c hapter desc ribes the use of fu nctions HE S S, DIV , and CURL , for calc ulating operati ons of vec tor analy sis.
Page 13-2 Div ergence Th e div er genc e of a v ect or fu nctio n, F (x,y ,z) = f( x ,y ,z ) i + g(x,y ,z) j +h(x ,y ,z) k , is def ined by taking a “ dot-product ” of the del oper ator w ith the functi on, i .e ., . F unction DIV can be used to calc ulate the div erg ence of a vector f ield .
Page 14-1 Chapter 14 Differential Equations In this Chapter w e pre sent ex amples of so lving or dinary differe ntial equati ons (OD E) us ing calculator f unctions . A differ 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 ODE • the char acter istic equation of the ODE Both of these inputs must be gi ven in ter ms of the def ault independent var iable for the calc ulator’s CA S (t y picall y X) . T he output f rom the funct ion is the general solu tion of the ODE .
Page 14-3 Fun c ti on DESO L VE The calc ulator pro vi des functi on D E SOL VE (Differ ential E quation S OL VEr) to solv e certain types of diff erential equati ons. The f unction r equires as input the differ ential eq uation and the unkno wn f u nc tion , and retur ns the solution to the equation if a vailable .
Page 14-4 ‘ d1y(0 ) = -0. 5’ . Changing to these Ex act expr essions f acilitates the solution. Pr ess µµ to simplify the r esult. Use ˜ @EDIT to s ee this r esult: i. e. , ‘ y(t) = -((19* √ 5*SI N( √ 5*t) - (14 8*COS( √ 5*t)+8 0*CO S(t/2)))/190)’ .
Page 14-5 Compar e these e xpressi ons with the one gi ven earli er in the definition o f the La place transfo rm, i .e ., and yo u will noti ce that the CAS def ault var iable X in the equati on wr iter sc reen r eplaces the var iable s in this de finition .
Page 14-6 Fo urier series f or a quadratic function Determine the coeff ic ients c 0 , c 1 , and c 2 for the f unction g(t) = (t-1) 2 +(t -1), w ith peri od 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 ou r ier series with three ele ments will be written as g(t) ≈ R e[(1/3) + ( π⋅ i+2)/ π 2 ⋅ ex p (i ⋅π⋅ t)+ ( π⋅ i+1)/(2 π 2 ) ⋅ exp (2 ⋅ i ⋅π⋅ t)].
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Page 15-1 Chapter 15 Pr obabilit y Distr ibutions In this Chapte r we pr ov ide e xamples o f applicatio ns of the pre-defined pr obability distributi ons in the calculator . T h e MTH/P ROB ABI LI TY .. sub-menu - par t 1 The MTH/P ROB ABILI T Y .. sub-men u is acces sible through the k ey str oke sequ ence „´ .
Page 15-2 • PERM(n ,r): Calc ulates the number o f permutati ons of n items tak en r at a time • n!: F actor ial of a positi ve integer . For a no n -integer , x! r eturns Γ (x+1), whe re Γ (x) is the Gamma functi on (see Chapter 3). The fact orial s ymbol (!) can be enter ed also as the ke ystr oke combinati on ~‚2 .
Page 15-3 T h e MTH/P ROB menu - part 2 In this secti on w e disc uss f our continuou s proba bility distri butions that ar e commonl y used f or proble ms relate d to statisti cal infer ence: the nor mal distr ibution, the S tudent’s t distr ibution , the Chi-s quare ( χ 2 ) dis tribution , and the F-dis tributi on.
Page 15-4 The Chi-squar e distribution The Chi -s qua re ( χ 2 ) distributi on has one paramete r ν , kno wn as the degr ees of fr eedom. T he calculato r pr o vi des for v alues of the upper -tail (c umulativ e) distr ibution func tion f or the χ 2 -distributi on using UTPC gi ven the value o f x and the parameter ν .
Page 16-1 Chapter 16 Statistical Applications The calc ulator pr ov ides the follo wing pr e -progr ammed statisti cal features accessible thr ough the k ey str ok e combination ‚Ù (the 5 key) : Entering data Applicati ons numbered 1, 2 , and 4 in the list abov e requir e that the data be av ailable as columns of the matr ix Σ D A T .
Page 16-2 Calculating singl e-variable statistics After entering the column v ector into Σ DA T, p re s s ‚Ù @@@OK@@ to sel ect 1. Singl e-var .. The fo llow ing input f orm w ill be pr o vided: The f orm lists the dat a in Σ DA T , sho ws that column 1 is s elected (ther e is only one column in the c urr ent Σ D A T) .
Page 16-3 Obtaining frequenc y distributions The app lic at ion 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 fr equency dis tribution s for a set o f data. T he data must 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 f unction S T O Σ (see e xample abo ve). Next , obtain single - var iable inf ormati on using: ‚Ù @@@OK@@@ . The r esults are: This information i ndicates tha t our data ranges fr om -9 to 9 .
Page 16-5 F it ting data to a function y = f(x) The pr ogram 3. F it da ta.. , a vailable as opti on number 3 in the S T A T menu , can be used to f it linear , logar ithmic, e xponential , and po w er func tions to data sets (x , y), stored in column s of the Σ D A T matri x.
Page 16-6 Le vel 3 sh ow s the form o f the equation . Lev el 2 sho ws the sample corr elation coeff ic ient , and lev el 1 show s the cov ariance of x -y .
Page 16-7 •P r e s s @@@OK@@@ to obtain the follo wing r esults: Confidence inter v als The a pplication 6. Conf Inter val can be acces sed by u sing ‚Ù— @@@OK@@@ . The a ppl ica tion offe rs th e fol lowing op tion s: These options are to be interpre te d as follo ws: 1.
Page 16-8 4. Z -INT : p 1− p 2 .: Confi dence inter v al for the diff erence of tw o pr opor tions , p 1 -p 2 , for lar ge samples w ith unkno wn populatio n varia nc es. 5. T- I N T: 1 µ .: Single sample confi dence interval fo r the population mean, µ , f or small samples with unkno wn populati on var iance.
Page 16-9 The gr aph sho ws the st anda r d normal dis tribution pdf (probability density functi on) , the locatio n of the cr itical points ± z α/2 , the mean value ( 2 3 .
Page 16-10 2. Z - Te s t : µ1−µ2 .: Hy pothesis testing f or the differ ence of the population means, µ 1 - µ 2 , with either kno wn populati on var iances, or f or large samples w ith unkno wn populati on var iances .
Page 16-11 Then , we r ejec t H 0 : µ = 150 , against H 1 : µ ≠ 150. The test z v alue is z 0 = 5 .6 5 68 54. The P -value is 1. 54 × 10 -8 . The cr itical v alues of ± z α /2 = ± 1.9 5 9 9 64, cor r esponding to c riti cal ⎯ x range of {14 7 .
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Page 17-1 Chapter 17 Numbers in Differ ent Bases Beside s our dec imal (base 10, digits = 0 -9) number s y stem, y ou can w ork w ith a binary s yste m (base 2 , digits = 0,1), an octal s y stem (bas e 8, digits = 0 - 7) , or a hex adec imal sy stem (base 16, di gits =0 -9 ,A-F) , among others .
Page 17-2 W riting non-dec imal numbers Numbers in non-decimal s yst ems, r eferr ed to as bin ar y i nteg ers , are w ritt en pr eced ed b y the # s ymbol ( „â ) in the calc ulator . T o select the cur rent base to be us ed for binary integer s, c hoose eithe r HEX (adec ima l), DEC (imal), OCT (al) , or BIN (ary) in the B ASE me nu .
Page 18-1 Chapter 18 Using SD car ds The calc ulator has a memor y car d slot into whic h you can insert an SD flash car d for backing up calc ulator objects , or for do wnloading objects fr om other source s. The SD car d in the calculator w ill appear as port numbe r 3 .
Page 18-2 4. When the for m atting is finished , the HP 50g display s the message "FORMA T FINISHED . PRE SS ANY KEY T O EXIT". T o ex it the sy stem menu , hold dow n the ‡ key , press and r elease the C ke 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 eigh t charac ters, it w ill appear in 8.
Page 18-4 P urging all objects on t he SD card (b y refo rm at t in g) Y ou can pur ge all objec ts fr om the SD card b y re formatting it . When an SD car d is inserted, @FORMA a ppears an additional menu it em in File Manager . Selecting this opti on r efor mats the entire card , a proces s whic h also delete s ev ery object on the card .
Page 19-1 Chapter 19 Equation L ibrary The E quati on Libr ar y is a collecti on of equati ons and commands that enable y ou to solv e simple sc ience and engineer ing pr oblems. The libr ary consists o f more than 3 00 equations gr ouped into 15 t echnical sub jects containing mo re than 100 pr oblem titl es.
Page 19-2 No w use this equation s et to answ er the questi ons in the follo w ing ex ample . Step 4: Vi ew the fi ve eq uations in the Pr ojectile Moti on set . All fi ve ar e used inter changeably in or der to solv e for missing v ariables (see the ne xt ex ample) .
Page 19-3 0 *!!!!!!X0!!!!!+ 0 *!!!!!!Y0!!!!!+ 50 *!!!!!!Ô0!!!!!+ L 65 *!!!!!!R!!!!!+ Step 3: Sol ve f or the ve locity , v 0 . (Y ou solv e for a v ariable b y pres sing ! and then the var iable ’s menu k ey .
Page 19-4 Refe renc e F or additional details on the E quation Libr ary , see Chapter 2 7 in the calculator’s u ser’s guide . SG49A.book Page 4 Friday, September 16, 200 5 1:31 PM.
Pa g e W - 1 Limited W arr ant y HP 50g gr aphing calculator ; W arr anty period: 12 months 1. HP warr ants to y ou, the end-user customer , that HP har dw are , accessor ies and supplie s will be f ree fr om defects i n materials and wor kmanship after the date of purc hase , for the per iod spec ified abo ve .
Pa g e W - 2 REMEDIES . EX CEPT A S IND ICA TED ABO VE , IN NO EVENT WILL HP OR IT S S UPPLIER S BE LIABLE FOR L OS S OF DA T A OR FOR DIRE CT , SPE C IAL , INCIDENT AL, CO NSEQUENT IAL (INCL UDING L OS T PROFI T OR D A T A), OR O THER DAMA GE , WHE THER BA SED IN CONTRACT , T OR T , OR O THER WISE .
Pa g e W - 3 Ser v ice Euro pe Count ry : Te l e p h o n e n u m b e r s Au stri a +4 3-1-3 60 2 7 71203 B e l g i u m + 32-2-7 1 262 1 9 Denmar k +4 5-8- 2 33 2 844 Eas te rn Eu rop e c ou nt rie s +.
Pa g e W - 4 L.A me ri ca Co untry : Te l e p h o n e n u m b e r s Argentina 0- 81 0-5 5 5- 5 5 20 Br azil S a o Pa u l o 37 47-7 79 9 ; RO T C 0 -80 0 -15 77 51 Mex ico Mx C i t y 5 258 - 9922; RO T.
Pa g e W - 5 Regulat or y inf ormation Feder al Communications Commission N otice This equipme nt has been tested and found t o comply with the limits fo r a Clas s B digital de v ice , pursua nt to P art 15 of the FC C Rule s.
Pa g e W - 6 Or , call 1 -8 0 0 - 4 7 4 - 6836 F or questi ons regar ding this FC C declar ation , contact: Hew lett -P ack ard C ompany P . O . Bo x 6 9 2000, Mail Sto p 510101 Houston , T ex as 77 2 6 9- 20 00 Or , call 1 - 28 1 - 5 1 4 - 3333 T o identify this produc t, r efer t o the par t , ser ies, or model n umber found on the product.
Pa g e W - 7 Japane se Notice 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 の装置.
An important point after buying a device HP (Hewlett-Packard) HP 50g (or even before the purchase) is to read its user manual. We should do this for several simple reasons:
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