Manuale d’uso / di manutenzione del prodotto 39gII del fabbricante HP
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hp 39g+ graphing calculator user’s guide H Edition 2 Part Number F2224-90001.
Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT NOTICE.
Contents i Contents Preface Manual conventions ................ ................ ................. ............. P-1 Notice ......... ............. ................ ................. ................ .......... P-2 1 Getting started On/off, cancel operatio ns .
ii Content s 3 Function aplet About the Fu nction aplet ....... ................. ................ ............. ... 3-1 Getting started with the Function aplet ... ................ ............. 3-1 Function aplet intera ctive analysis . ............
Contents iii 9 Inference aplet About the Inference a plet ................... ................ ................ .... 9-1 Getting started with the Infere nce aplet ..................... .......... 9-1 Importing sample statistics from the Statistics a plet .
iv Content s 12 Variables and memory management Introduction ........ ................ ................. ................ ............. . 12-1 Storing and recalling variables ..... ................ ................ ........ 12-2 The VARS menu ........
Contents v 16 Programming Introduction ..... ................. ................ ................ ............. ..... 16-1 Program catalog .......... ................ ................ ................ .. 16-2 Creating and editing pro grams ............
vi Content s Reference information Glossary... ................. ............. ................ ................ ............. R-1 Resetting the hp 3 9g+ .............. ................ ................ ............. R-3 To erase all memory and reset defaults .
Preface P-1 Preface The hp 39g+ is a feature-rich graphing calculator. It is also a powerful mathematics learning tool. The hp 39g+ is designed so that you can use it to explore mathematical functions and their proper ties. You can get more information on the hp 39g+ from Hewlett-Packard’s Calcula tors web site.
P-2 Pre face Notice This manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibit ed by law, Hewlett-Packard Company makes no.
Getting started 1-1 1 Get ting star ted On/off, cancel operations To turn on Press to turn on the calculator. To cancel When the calculator is on, the key cancels the current operation. To turn off Press OFF to turn the calculator off. To save power, the calc ulator turns itself off afte r several minutes of inactivity.
1-2 Getting started The display To adjust the contrast Simultaneously press and (or ) to increase (or decrease) the contrast. To clear the display • Pres s CANCEL to clear the edit line . • Pres s CLEAR to cle ar the edit line and the display history .
Getting started 1-3 Annunciators . Annunciators are sy mbo ls that appear above the title bar and give you important status information. The keyboard Menu keys Annunciator Description Shift in effect for next keystroke. To cancel, press again. α Alpha in effect for next keystroke.
1-4 Getting started • On the calculator k e y boar d, the top r o w of k e y s ar e called menu k e ys . T heir meanings depend on the conte xt—that’s w h y the ir tops ar e blank . The menu k ey s ar e sometime s called “ s oft k ey s ” . • The bottom line o f the displa y sho ws the labels f or the menu k e ys ’ c urr ent meanings .
Getting started 1-5 Entry/Edit keys The entry and edit keys are: K ey Meaning ( CANCEL ) Cancels the current operation if the calculator is on by pressing . Pressing , then OFF turns the calculator off. Accesses the function printed in blue above a key.
1-6 Getting started Shifted keystr okes There are two shift keys that you use to access the operations and characters printed above the keys: and . CHARS Displays a menu of all avai lable characters. To type one, use the arrow keys to highlight it, and press .
Getting started 1-7 HELPWITH The hp 39g+ built-in help is available in HOME only. It provides syntax help for bu ilt-in math functions. Access the HELPWITH command by pressing SYNTAX and then the math key for which you require syntax help.
1-8 Getting started • Pr essing takes y o u to the beginning of the MA TH menu . See “Math functions by category” on page 11-2 for details of the math functions. HINT When using the MA TH menu , or an y menu on the hp 3 9g+, pr essing an alpha ke y tak es y ou str aight to the fir st menu optio n beginning with that alpha c har acter .
Getting started 1-9 • If there ar e tw o columns, the left column sho ws gener al categor i es and the r ight column sho w s spec if ic co ntents within a catego ry . Highlight a gener al category in the left column , then highli ght an item in the r ight column .
1-10 Getting started Mode settings You use the Modes input form to set the modes for HOME. HINT Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting selected in Modes is the ang le setting used in both HOME and current aplet.
Getting started 1-11 Number Format The number format mode you set is the number format used in both HOME and the current aplet. Standard . Full-precision display. Fixed . Displays results rounded to a number of decimal places. Example: 123.456789 becomes 123 .
1-12 Getting started Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedur e is the same for changing number format and decimal mark modes. 1. Pres s MODES to open the HOME MODES input form.
Getting started 1-13 • Copi ed fr om another calculator . Aplets a re store d in the Aple t library. See “Aplet library” on page 1-16 for further information. You can modify configuration settings for the graphical, tabular, and symbolic views of the aplets in the following table.
1-14 Getting started A great many more teaching ap lets can be found at HP’s web site and other web sites created by educators, together with accompanying documentation, often with student work sheets. These can be downloaded free of charge and transferred to the hp 39g+ using the separately supplied Connectivity Kit.
Getting started 1-15 A button is provided to evaluate the student’s knowledge. Pressing displays a target qu adratic graph. The student must manipulate the equation’s parameters to make the equation match the target graph. When a student feels that they have correctly chosen the parameters a button evaluates the answer and provide feedback.
1-16 Getting started Pressing displays the equation at the top of the screen. The equation is controlled by the graph. Pressing the and keys moves from parameter to parameter. Pressing the or key changes the parameter’s values. The default angle setting for this aplet is radians.
Getting started 1-17 Plot view Pre ss to display the aplet’s Plot vi ew . In this vi e w , the functi ons that y ou hav e de fined ar e display ed gr a phically . See “About the Plot view” on page 2-5 for further information. Numeric view Press to display the aplet’s Numeric view.
1-18 Getting started Overlay Plot view The VIEWS menu contains the Overlay Plot view. Select Overlay Plot Plots the current expression(s) without erasing any pre-exis ting plot(s). See “Other views for scaling and splitting the graph” on page 2-14 for further information.
Getting started 1-19 Numeric Setup Press SETUP - NUM . Sets parameters for building a table of numeric values. Symbolic Setup This view is only available in the Statistics aplet in mode, where it plays an important role in cho osing data models. Press SETUP - SYMB .
1-20 Getting started • Pres s to e valuat e the expr e ssio n y ou hav e in the edit line (w her e the blinking cur sor is). An expr essi on can contain numbers , func tions , and vari ab le s.
Getting started 1-21 Explicit and implicit multiplication Implied multiplication takes place when two operands appear with no operator in between. If you enter AB , for example, the result is A*B . However, for clarity, it is better to include the multiplication sign where you expect multiplication in an expression.
1-22 Getting started Algebraic precedence order of evaluation Functions within an expression are evaluated in the following order of precedence. Functions with the same precedence are evaluated in order from left to right. 1. Ex pressions within parenthe ses.
Getting started 1-23 When you highlight a previous input or resu lt (by pressing ), the and menu labels appear. To copy a previous line Highlight the line (press ) and press . The number (or expression) is co pied into the ed it line. To reuse the last result Press ANS (last answer) to put the last result from the HOME display into an expression.
1-24 Getting started HINT When you retrieve a number from ANS , you obtain the result to its full precision. When you retrieve a number from the HOME’s display history, you obtain exactly what was displayed. Pressing evaluates (or re-evaluates) the last input, whereas pressing ANS copies the last result (as ANS ) into the edit line.
Getting started 1-25 Accessing the display history Pressing enables the highlight bar in the display history. While the highlight bar is active, the following menu and keyboard keys are very useful: Clearing the display history It’s a good habit to cl ear the display history ( CLEAR ) whenever you have finish ed working in HOME.
1-26 Getting started 2 . Select Number Format , pre ss to display the options , and highli ght Fraction . 3 . Pres s to select the Number For mat option, then mov e to the prec ision v alue field . 4. Enter the prec isi on value that y ou w ant to use , and pre ss to set the prec isi on .
Getting started 1-27 • Prec ision set to 1: • Prec ision set to 2 : • Prec ision set to 3: • Prec ision set to 4 Fraction calculations When entering fractions: • Y ou use the ke y to separate the numerator part and the denominator par t of the fr action .
1-28 Getting started 2. E n t e r t h e c a l c u l a t i o n . 32 3 45 7 8 Note: Ensur e y ou ar e in the HOME v ie w . 3 . Evaluate the calc ulati on. Converting decimals to fractions To convert a decimal value to a fraction: 1. Set the number for mat mode to Fraction .
Getting started 1-29 Complex numbers Complex results The hp 39g+ can return a comp lex number as a result for some math functions. A comp lex number appears as an ordered pair ( x, y ), where x is the real part and y is the imaginary part. For example, entering returns (0,1).
1-30 Getting started Catalogs and editors The hp 39g+ has several cata logs and editors. You use them to create and manipulate objects. They access features and stored values (numbe rs or text or other items) that are independent of aplets. • A catalog lists items, w hich y ou can delete or tr ansmit , fo r e xam ple an aple t .
Aplets and their views 2-1 2 Aplets and th eir vie ws Aplet views This section examines the options and func tionality of the three main views for the Functio n, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views.
2-2 Aplets and their views – For a Function definition , e nt er an ex pr essi on to def ine F(X) . The only independent variab le in th e exp re ss io n is X. – Fo r a P arametr ic definition , e nt er a pair of expr es sio ns to def ine X(T) and Y(T) .
Aplets and their views 2-3 Evaluating expressions In aplets In the Symbolic view, a variable is a symbol only, and does not represent one specif ic value. To evaluate a function in Symbolic view, press . If a function calls another function, then resolves all references to other functions in terms of their independent vari able.
2-4 Aplets and their views In HOME You can also evaluate any expression in HOME by entering it into the edit line and pressing . For example, define F4 as below. In HOME, type F4(9) and press . This evaluates the expression, substituting 9 in place of X into F4 .
Aplets and their views 2-5 About the Plot view After entering and selecting (check marking) the expression in the Symbolic view, press . To adjust the appearance of the graph or the interval that is displayed, you can change the Plot view settings. You can plot up to ten expressions at the same time.
2-6 Aplets and their views Plot view settings The plot view settings are: Those items with space for a checkmark are settings you can turn on or off. Press to display the second page. Field Meaning XRNG, YRNG Specifies the minimum and maximum horizontal ( X ) and vertical ( Y ) values for the plotting window.
Aplets and their views 2-7 Reset plot settings To reset the default values for all plot settings, press CLEAR in the Plot Setup view. To reset the default value for a field, highlight the field, and press . Exploring the graph Pl ot v i ew gi v e s y ou a se l ec t io n of k ey s an d m e nu k ey s to explore a graph further.
2-8 Aplets and their views Trace a graph You can trace along a function using the or key which moves the cursor along the graph. The display also shows the current coordinate position ( x, y ) of the cu rsor. Trace mode and the coordinate disp lay are automatically set when a plot is drawn.
Aplets and their views 2-9 To jump directly to a value To jump straight to a value rather than using the Trace function, use the menu key. Press , then enter a value. Press to jump to the value. To turn trace on/off If the menu labels are no t displayed, press first.
2-10 Aplets and their views Y-Zoom In Divides vertical sc ale only, using Y-factor. Y-Zoom Out Multiplies vertical scale only, using Y-factor. Square Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Zoom, X- Zoom, or Y-Zoom.
Aplets and their views 2-11 ZOOM examples The following screens show the effects of zooming options on a plot of . Plot of Zoom In : In Un-zoom : Un-zoom Note: Press to move to the bottom of the Zoom list. Zoom Out : Out Now un- zoom. X-Zoom In : X-Zoom In Now un- zoom.
2-12 Aplets and their views X-Zoom Out : X-Zoom Out Now un-zoom. Y-Zoom In: Y-Zoom In Now un-zoom. Y-Zoom Out: Y-Zoom Out Zoom Square: Square To box zoom The Box Zoom option lets you draw a box around the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle.
Aplets and their views 2-13 5 . Press to zoom in on the bo x ed ar ea . To set zoom factors 1. In the P lot v ie w , pr e ss . 2. P r e s s . 3. Se l e c t Set Factors... and pr es s . 4. Enter the z oom factors . Ther e is one z oom factor fo r the horiz onta l scal e ( XZOOM ) and one for the v ertical scal e ( YZOOM ).
2-14 Aplets and their views Other views for scaling and splitting the graph The preset viewing options menu ( ) contains options for drawing the plot using certain pre-defined configurations.
Aplets and their views 2-15 Split the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Pr ess . Select Plot-Detail and pr es s . The graph is plot ted t wice . Y ou can now z oom in on the r ight si de . 2. P r e s s , select the z oom method and press or .
2-16 Aplets and their views 2 . T o move up and dow n the ta ble , use the and c ursor k e y s . These k eys mo v e the tr a.ce po int le ft or ri ght along the plo t , and in the table , the corr es ponding value s are highlighte d. 3 . T o move between f unctions , use the and c ursor k e y s to mo v e the curs or fr om o ne graph to another .
Aplets and their views 2-17 Setting up the table (Numeric view setup) Press NUM to define any of the table settings. Use the Numeric Setup input form to configure the table. 1. Hi ghlight the f ield t o edit. U se the arr o w k e y s to mo v e from fiel d to fie ld.
2-18 Aplets and their views Reset numeric settings To reset the default values for all table settings, press CLEAR . Exploring the table of numbers NUM view menu keys The following table details the menu keys that you use to work with the table of numbers.
Aplets and their views 2-19 The display on the right is a Zoom In of the display on the left. The ZOOM factor is 4. HINT To jump to an independ ent variable value in the table, use the arrow keys to place the cursor in the independent variable column, then ente r the value to jump to.
2-20 Aplets and their views 5 . Enter the independent values in the left-hand column. T ype in a number and press . Y ou do not have to enter them in order , because the function can rear r ange them. T o inser t a number between tw o othe rs, use . Clear data Press CLEAR , to erase the data from a table.
Aplets and their views 2-21 Example: plotting a circle Plot the circle, x 2 + y 2 = 9 . First rearrange it to read . To plot both the positive and negative y values, you need to define two equations as follows: and 1. In the Funct ion aplet , spec if y the functi ons .
2-22 Aplets and their views 5 . Display the func tions in n umeri c f orm ..
Function aplet 3-1 3 Function aplet About the Function aplet The Function aplet enables you to explore up to 10 real-valued, rectangular functions y in terms of x .
3-2 Function aplet Define the expressions 2 . T her e ar e 10 functi on de finiti on f ields on the F unction aplet’s S ymbolic v ie w s cr een . T hey ar e labeled F1(X) to F0(X). Highlight the f uncti on def initio n fi eld y ou w ant to u se , and ente r an e xpr e ssi on .
Function aplet 3-3 Change the scale 6. Y ou ca n change the sca le to see more or less of your gra phs. In this e x ample , c hoos e Auto Scale . (S ee “VIEW S menu opti ons ” on page 2 -14 fo r a descrip tio n of Auto Sc al e) . Select Auto Scale Trace a graph 7 .
3-4 Function aplet Analyse graph with FCN functions 9. Display the Plot view menu. From the Plot view menu, you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based ap lets).
Function aplet 3-5 12 . Choose the linear f uncti on w hos e inter sec tion w ith the quadr atic f unctio n y ou w ish to f ind. The coo r dinates of the intersec tion po int ar e display ed at the bottom of the screen .
3-6 Function aplet 15 . Mov e the c urs or to by pr e ssing the or key . 16. Pre ss to accept using F2(x) = (x + 3) 2 – 2 as the other boundar y for the integr al. 17 . Choos e the end v alue for x . 2 Th e cu rso r jum ps t o x = –2 on the linear functi on .
Function aplet 3-7 HINT The Root and Extremum functions return one value only even if the fun ction has more than one root or extremum. The function finds the value closest to the position of the cursor. You need to re-locate the cursor to find other roots or extrema that may exist.
3-8 Function aplet To navigate around a table 2 4. Mov e to X = –5 .9 . 6 times To go directly to a value 2 5 . Mov e direc tly to X = 10. 1 0 To access the zoom options 2 6. Z oom in on X = 10 b y a factor o f 4. Note: NUMZOOM has a setting of 4 . In To change font size 2 7 .
Function aplet 3-9 Function aplet interactive analysis From the Plot view ( ), you can use the functions on the FCN menu to find roots, intersection s, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets). See “FCN functions” on page 3- 10.
3-10 Function aplet FCN functions The FCN functions are: Function Description Root Select Root to find the root of the current function nearest the cursor. If no root is fo und, but only an extremum, then the result is labeled EXTR: instead of ROOT: .
Function aplet 3-11 Shading area You can shade a selected area between functions. This process also gives yo u an approximate measurement o f the area shaded. 1. Open the Function aplet . T he Func tion aplet opens in the S y mbolic v ie w . 2 . S elect the e xpr essions w ho se c urve s y ou w ant to study .
3-12 Function aplet Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. 1. Open the Functi on aple t. Select Function 2 . Hi ghlight the line y ou w ant to u se , and ent er the expr essi on. ( Y ou can press to delete an e xis ting line , or CLEAR to clear all lines .
Parametric aplet 4-1 4 Pa r a m e t r i c a p l e t About the Parametric aplet The Parametric aplet allows you to explore parametric equations. These are equations in which both x and y are defined as functions of t .
4-2 Parametric aplet Set angle measure 3 . Set the angl e measure to degrees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT The P lo t Setup in put f orm has tw o f ie lds not inc luded in the Functi on aplet , TRNG and TSTEP .
Parametric aplet 4-3 Overlay plot 8. Plot a triangle graph over the existing circle graph. PLOT 120 Select Overlay Plot A tria ngle is display ed r ather than a c ir cle ( w ithout c hanging the equati on) because the c hanged v alue of TSTEP ensur es that points being plotted are 120 ° apart inst ead of near l y continuous .
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Polar aplet 5-1 5 Po l a r a p l e t Getting started with the Polar aplet Open the Polar aplet 1. Open th e P olar aplet. Select Polar L ik e the F uncti on aplet , the P olar aplet opens in the S y mbolic vi e w . Define the expression 2 . De fine the po lar equati on .
5-2 Polar aplet Explore the graph 5 . Display the P lot v ie w menu k e y labels . Th e Plo t vi ew op t i on s av ailable ar e the same as those fo und in the F unctio n aplet. See “Explor ing the gr aph ” on page 2 - 7 for f urther informati on.
Sequence aplet 6-1 6 Sequence aplet About the Sequence aplet The Sequence aplet allows you to e xplore sequences. You can define a sequence named, for example, U1: • in terms of n • in terms of U1 ( n –1) •i n ter ms o f U1 ( n –2) • in terms o f another sequence , f or ex ample , U2 ( n ) • in an y combinati on of the abo v e .
6-2 Sequence aplet Define the expression 2 . Def ine the Fibonacc i sequence , in whi ch eac h ter m (after the fir st tw o) is the sum of the pr eceding tw o terms: , , for . In the S y mbolic v i e w of the Seq uence aplet , hi ghlight the U 1 (1) field and begin def ining y our sequence .
Sequence aplet 6-3 Select Cobweb Display the table 6. Display the table of values f or this ex ample ..
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Solve aplet 7-1 7 Solv e aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable . You define an equation or expression in the symbolic view, then supply values for all the variables except one in the numeric view.
7-2 Sol ve aplet should be solved using matrices or graphs in the Function aplet. Getting started with the Solve aplet Suppose you want to find th e acceleration needed to increase the speed of a car from 1 6.67 m/sec (60 kph) to 27.78 m/sec (100 kp h) in a distance of 100 m.
Solve aplet 7-3 4. Enter the values f or the kno wn v ar iable s. 2 7 7 8 1 6 6 7 1 0 0 HINT If the Decimal Mark setting in the Modes input form ( MODES ) is set to Comma, use instead of . Solve the unknown variable 5. Solv e f or the unkno w n var ia ble ( A ).
7-4 Sol ve aplet 6. Plot the eq uation f or v ar iable A . Sele ct Auto Scale 7 . T race along the graph repr e senting the left side o f the equati on until the c urso r nears the inter secti on . 20 times Note the v alue of A displa y ed near the bottom left corner of the scr een .
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7-6 Sol ve aplet Interpreting results After Solve has returned a solution, press in the Numeric view for more information. You will see one of the following three messages.
Solve aplet 7-7 If Solve could not find a solution, you will see one of the following two messages. HINT It is important to check the information relating to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets to zero.
7-8 Sol ve aplet where X is distance, V 0 is initial velocity, T is time, and A is acceleration. This is actually two equations, Y = X and Y = V 0 T + (AT 2 ) / 2 . Since this equation is quadratic for T , there can be both a positive and a negative solution.
Solve aplet 7-9 5. Move the cursor near the positive (r ight-side) intersection. This cursor value will be an initial guess for T . Pres s until the c ursor is at the intersec tion. The t wo po in t s o f inters ecti on sho w that ther e ar e two so lution s for this eq uation .
7-10 Solve apl et Using variables in equations You can use any of the real variable names , A to Z and θ . Do not use variable nam es defined for other type s, such as M 1 (a matrix variable).
Statistics aplet 8-1 8 Statist ic s ap let About the Statistics aplet The Statistics aplet can store up to ten data sets at one time. It can perform one- variable or two-vari able statistical analysis of one or more sets of data. The Statistics aplet starts with the Numeric view which is used to enter data.
8-2 Statistics aplet Open the Statistics aplet 1. Open the Statisti cs aplet and c lear e x isting data b y pres sing . Select Statistics Th e St a ti s ti cs ap l et starts in the Numer ical view .
Statistics aplet 8-3 Choose fit and data columns 4. Select a fit in the S y mboli c setup v ie w . SETUP - SYMB Select Linear Y o u c a n c rea t e up t o five ex p lo ra t io n s of t wo - va ri ab l e data, named S1 to S5 . I n t h i s exa m p le, we wi ll cre a t e just o ne : S1 .
8-4 Statistics aplet Setup plot 8. Change the plotting range to e nsur e all the data points ar e plotted (and select a differ ent po int mark , if yo u wi s h ) . SETUP - PLOT 7 100 400 0 Plot the graph 9 . P lot the gr aph . Draw the regression curve 10.
Statistics aplet 8-5 Predict values 13 . T o find the pr edi ct ed sales f ig ur e if adv ertising w er e to go up to 6 minute s: S ( to highligh t Stat-Two ) (to highli ght PREDY ) 6 14. Retur n to the P lot v ie w . 15 . Jump to the indi cated po int on the r egr essi on line .
8-6 Statistics aplet Entering and editing statistical data The Numeric view ( ) is used to enter data into the Statistics aplet. Each column represents a variable named C0 to C9 . After entering the data, you must define the data set in the Symbolic view ( ).
Statistics aplet 8-7 Example You are measurin g the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 170c m, 175cm, 180cm. 1. Open the Statistics aplet. Select Statistics 2 .
8-8 Statistics aplet 3 . Find the mean of the sample. Ensur e the / menu k ey label reads . Pr es s to see the statistic s calculated fr om the sample data in C1 . Note that the title o f the colu mn of stat isti cs is H1 . Ther e ar e 5 data set de finiti ons a vailable for one- var iable stat is tics: H1–H5 .
Statistics aplet 8-9 To continue our example, supp ose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded. Instead of entering all the new data in C1 , we shall simply add another column, C2 , that holds the frequencies of our five data points in C1 .
8-10 Statistics aplet 5 . Move the hi ghlight bar into the r ight column o f the H1 def inition and replace the frequency value o f 1 w ith the name C2 . 2 6 . Return to the n umer ic v ie w . 7 . Ente r the fr equenc y data sho w n in the abo v e table .
Statistics aplet 8-11 Edit a data set In the Numeric view of the Statistics aplet, highlight the data value to change. Type a new va lue and press , or press to copy the value to the edit line for modification. Press after modifyi ng the value on the edit line.
8-12 Statistics aplet Defining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or “fit”, to use for the regression analysis of each two-variable data set. There are three ways to select a regression model: • Accept the d efault option to fit the data to a str aight line.
Statistics aplet 8-13 To define your own fit 1. In Numeric v ie w , mak e sur e is set . 2 . Display the S ymbolic v ie w . 3 . Highlight the F it expr essi on ( Fit1 , etc.) f or the desired data set . 4. T ype in an e xpr ess ion and pr ess . The independent variable must be X , and the expr ession mus t not contain an y unkno w n var ia bles.
8-14 Statistics aplet When the data set contains an odd number of values, the data set’s median value is no t used when calculating Q1 and Q3 in the table above.
Statistics aplet 8-15 Plotting You c an plot: • histogr ams ( ) • box -a nd-whisk er plots ( ) • scat ter p lots ( ) . Once you have entere d your data ( ), defined your data set ( ), and defined your Fit mode l for two- variable statistics ( SETUP - SYMB ), you can plot your data.
8-16 Statistics aplet 3 . F or an y plot , but espec iall y fo r a histogr am, adj ust the plottin g scale and range in the P lot Setup vie w . If you find histogr am bars too fat or too thin , you can adj ust them b y adju sting the HWIDTH setti ng. 4.
Statistics aplet 8-17 To connect the data points as they are plotted, checkmark CONNECT in the second page of the Plot Setup. This is not a regression curve. Fitting a curve to 2VAR data In the Plot view, press . This draws a curve to fit the checked two-variable data set(s).
8-18 Statistics aplet HINT In order to access the CORR and RE LERR variables after you plot a set of statistics, you must press to access the numeric view and then to display the correlation values. The values are stored in the variables when you access the Symbolic view.
Statistics aplet 8-19 • The co rr ec t or menu labe l on (Numer ic view ) . • The cor r ect f it (r egre ssi on model) , if the data set is tw o -v ar i able . • Only the data sets to compute or plot are chec kmark ed (S ymbolic v ie w). • The cor r ect plo tting range .
8-20 Statistics aplet Calculating predicted values The functions PREDX and PREDY estimate (predict) value s for X or Y given a hypothetical value for the other. The estimation is made based on the curve that has been calculated to fit the data a ccording to the specified fit.
Statistics aplet 8-21 You can type PREDX and PREDY into the edit line, or you can copy these function names from the MATH menu under the Stat-Two category. HINT In cases where more than one fit curve is displayed, the PRED Y function uses the most recently calculated curve.
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Inference aplet 9-1 9 Inference aplet About the Inference aplet The Inference capabilities include calculation of confidence intervals and hy pothesis tests based on the Normal Z-distribution or Student’s t-distribution.
9-2 Inferenc e aplet Inference aplet’s SYMB view keys The table below summarizes the options available in Symbolic view. If you choose one of the hypoth esis tests, you can choose the alternative hypothesis to test against the null hypothesis.
Inference aplet 9-3 Select the inferential method 2. Select the Hypothesis Test infer ential method. Select HYPOTH TEST 3. Define the type of test. Z–Test: 1 µ 4. Select an alternative hypothesis. µ< µ0 Enter data 5. Enter the sample statistics and population parameters.
9-4 Inferenc e aplet By default, each field already contains a value. These values constitute the ex ample database and are explained i n the feature of this aplet. Display on-line help 6. To display the on-line help, press 7. To close the on-line help, press .
Inference aplet 9-5 A calculator produces the following 6 random numbers: 0.529, 0.295, 0.952, 0.2 59, 0.925, and 0.592 Open the Statistics aplet 1. Open the Statistics aplet and reset the current settings. Select Statistics The Statistics aplet opens in the Numeric view.
9-6 Inferenc e aplet Open Inference aplet 6. Open the Infere nce aplet and cle ar current setti ngs. Select Inference Select inference method and type 7. Select an inference method. Select CONF INTERVAL 8. Select a distribution statistic type. Select T-Int: 1 µ Set up the interval calculation 9.
Inference aplet 9-7 Import the data 10. Import the data from the Statistics aplet. Note: The data from C1 is displayed by default. Note: Press to see the statistics before importing them into the Numeric Setup view. Also, if there is more than one aplet b ased on the Statistics aplet, you are prompted to choose one.
9-8 Inferenc e aplet Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are base d on statistics of samples of the populations. The hp 39g+ hypothesis tests use the Normal Z-distribution or Student’s t-distribution to calculate probabilities.
Inference aplet 9-9 Results The results are: Two-Sample Z-Test Menu name Z-Test: µ 1– µ 2 On the basis of two samples, each from a separate population, this test measures t he strength of the evidence for a selected hypothesis against the null hypothesis.
9-10 Inference apl et Results The results are: One-Proportion Z-Test Menu name Z-Test: 1π On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.
Inference aplet 9-11 Inputs The inputs are: Results The results are: Two-Proportion Z-Test Menu name Z-Test: π 1 – π 2 On the basis of statistics from two samples, each from a different population, the Two-Proportion Z-Test measures the strengt h of the evide nce for a selected hypothesis against the null hypothesis.
9-12 Inference apl et Inputs The inputs are: Results The results are: One-Sample T-Test Menu name T-Test: 1 µ The One-sample T-Test is used when the population standard deviation is not know n. On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis agains t the null hypothesis.
Inference aplet 9-13 Inputs The inputs are: Results The results are: Field name Definiti on Sample mean. Sx Sample standard de viation. n Sample size. µ0 Hypothetical population mean. α Significance level. x Result Description Test T T-Test statistic.
9-14 Inference apl et Two-Sample T-Test Menu name T-Test: µ 1 – µ 2 The Two-sample T-Test is used when the population standard deviation is not know n. On the basis of statistics from two samples, each sample from a different population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.
Inference aplet 9-15 Results The results are: Confidence intervals The confide nce interval calc ul ations that the hp 39g+ can perform are based on the Normal Z-distribution or Student’s t-distribution.
9-16 Inference apl et Results The results are: Two-Sample Z-Interval Menu name Z-INT: µ1 – µ2 This option uses the Normal Z- distribution to calculate a confidence interval for the difference between the means of two populations, µ 1 – µ 2 , when the population standard deviations, σ 1 and σ 2 , are known.
Inference aplet 9-17 One-Proportion Z-Interval Menu name Z-INT: 1 π This option uses the Normal Z-distribution to calculate a confidence interval for the proportion of successes in a population for the case in which a sample of size, n , has a number of successes, x .
9-18 Inference apl et Results The results are: One-Sample T-Interval Menu name T-INT: 1 µ This option uses the Student’s t-distribution to calculate a confidence interval for m, the true mean o f a population, for the case in which the true population standard deviation, s, is unknown.
Inference aplet 9-19 Results The results are: Two-Sample T-Interval Menu name T-INT: µ 1 – µ 2 This option uses the Student’s t-distribution to calculate a confidence interval for the difference between the means of two populations, µ 1 – µ 2, when the population standard deviations, s1and s2 , are unknown.
9-20 Inference apl et Results The results are: Result Description Critical T Critical value for T. µ Min Lower bound for µ 1 – µ 2 . µ Max Upper bound for µ 1 – µ 2 .
Using the Finance Solve r 10-1 10 Using the Finance Solver The Finance Solver, or Finance aplet , is available by using the APLET key in your calculator. Use the up and down arrow keys to select the Finance aplet. Your screen should look as follows: Press the key or the soft menu key to activate the aplet.
10-2 Using the Finance Solv er Financial calculations involving compound interest include savings accounts, mo rtgages, pension funds, leases, and annuities. Time Value of Money (TVM) calculations, as the name implies, make use of the notion that a dollar today will be worth more than a dollar someti me in the future.
Using the Finance Solve r 10-3 modes: Begin mode and End mode. The following cash flow diagram shows lease payments at the beginning of each period. The following cash flow diagram shows deposits into an account at the end of each period.
10-4 Using the Finance Solv er Performing TVM calculations 1. Launch the F inanc ial Solv er as indicat ed at the beginning of this secti on . 2 . Use the arr o w k e y s to hi ghlight the diff er e nt fi elds and enter the kno wn v ar iables in the TVM calculati ons, pres sing the soft-menu ke y after ent ering eac h kno wn v alue .
Using the Finance Solve r 10-5 Example 1 - Loan calculations Suppose you finance the purcha se of a car with a 5-year loan at 5.5% annual interest, compounded monthly.
10-6 Using the Finance Solv er Example 2 - Mortgage with balloon payment Suppose you have taken out a 30-year, $ 150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repay ing the loan in a balloon payment. Find the size of the balloon payment -- the value of the mortgage after 10 years of payment.
Using the Finance Solve r 10-7 Calculating Amortizations Amortization calculations, which also use the TVM variables, determine the amounts applied towards principal and interest in a payment or series of payments. To calculate amortizations: 1. Start the F inance Sol v er as indicat ed at the beginning of t hi s sec tion.
10-8 Using the Finance Solv er 3 . Press the soft men u ke y to amorti z e the ne w batch of pa y ments. R epeat steps 1 thr ough 3 as often as needed. Example 4 - Amortization for home mortgage For the results of Example 3, show the amortization of the next 10 years of the mortgage loan.
Using mathematical fun ctions 11-1 11 Using mathematical func tions Math functions The hp 39g+ contains many math functions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as Prob.
11-2 Using mathem atical functions 2 . T he list of f uncti ons (on the r ight) appli es to the c urr entl y highli ghted catego ry (on the left) . Use and to sw itch between the category list and th e functi on list . 3 . Highlight the name of the f uncti on y ou w ant and pres s .
Using mathematical fun ctions 11-3 Keyboard functions The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. ,, , Add, Subtract, Multiply, Di vide. Also acc epts complex numbers, lists and matrices.
11-4 Using mathem atical functions 10 x Exponential (antilogarithm). Also accepts complex numbers. 10^ val u e Example 10^3 r etur ns 1000 Common logarithm. Also accepts complex numbers. LOG ( val ue ) Example LOG(100) r etur ns 2 ,, Sine, cosine, tangent.
Using mathematical fun ctions 11-5 ATAN Arc tangent: tan –1 x . Output range is from –90° to 90°, 2 π /2 to π /2, or –100 to 100 grad s. Inputs and outputs depend on the current an gle format. Also accepts complex numbers. ATAN ( valu e ) Example ATAN(1) ret u rn s 45 (Degrees mode).
11-6 Using mathem atical functions Takes the n th root of x . roo t NTHROOT val ue Example 3 NTHROOT 8 r etur ns 2 Calculus functions The symbols for differentiation and integration are available directly form the keyboard— and S respectively—as well as from the MATH menu.
Using mathematical fun ctions 11-7 TAYLOR Calculates the n th order Taylor polynomial of expression at the point where the given variable = 0. TAYLOR ( expr essi on, v ar iable , n ) Example TAYLOR(1 + sin(s1) 2 ,s1,5) w ith Radians angle measur e and F r acti on number f or mat (set in MODE S) r e turns 1+s1^2-1/3*s1^4 .
11-8 Using mathem atical functions Constants The hp 39g+ has an internal numeric representati on for these constants. e Natural logarithm base. Internally represented as 2.71828182846. e i Imaginary value for , the complex number (0,1). i MAXREAL Maximum real number.
Using mathematical fun ctions 11-9 TANH H yperbolic tangent. TANH ( valu e ) ALOG Antilogarithm (exponential). Th is is more accurate than 10^x due to limitations of the power function. ALOG ( valu e ) EXP Natural exponential. This is more accurate than due to limitations of the power function.
11-10 Using mathematical functions RECURSE Provides a method of defini ng a sequence without using the Symbolic view of the Seque nce aplet. If used with | (“where”), RECURSE will step through the evaluation.
Using mathematical fun ctions 11-11 POLYEVAL Polynomial evaluati on. Evaluates a polynomial with the specified coefficients for the value of x . POLYEVAL([ coeff ic ien ts ] , va l ue ) Example Fo r x 4 +2x 3 –25x 2 –26x+120 : POLYEVAL([1,2,-25,-26,120],8) ret u rn s 3432 .
11-12 Using mathematical functions Probability functions COMB Number of combinations (without regard to order) of n things taken r at a time: n!/(r!(n-r)) . COMB (n, r) Example COMB(5,2) r etur ns 10 . T hat is, ther e are t en differ ent w ay s that f i ve things can be comb ined two at a time .
Using mathematical fun ctions 11-13 UTPF Upper-Tail Snedecor’s F Probability given numerator degrees of freedom and denominator degrees of fre edom (of the F distribution), evaluated at value . Returns the probability that a Snedecor 's F random variable is greater than value.
11-14 Using mathematical functions FNROOT Function root-finder (like the Solve aplet). Finds the value for the given variable at which expression most nearly evaluates to zero. Uses guess as initial estimate. FNROOT ( e xpres sion , v ari able , gues s ) Example FNROOT(M*9.
Using mathematical fun ctions 11-15 MAX Maximum. The greater of two values. MAX ( val ue 1 , val ue 2 ) Example MAX(210,25) r etur ns 210 MIN Minimum. The lesser of two values. MIN ( val ue 1 , val ue 2 ) Example MIN(210,25) ret u rn s 25 MOD Modulo. The remainder of value1 / value2 .
11-16 Using mathematical functions ROUND Rounds value to decimal places . Accepts complex numbers. ROUND ( valu e , places ) Round can also round to a number of significant digits as showed in example 2. Examples ROUND(7.8676,2) r etur ns 7.68 ROUND (0.
Using mathematical fun ctions 11-17 Symbolic functions The symbolic functions are used for symbolic manipulations of expression s. The variables can be formal or numeric, but the re sult is usually in symbolic form (not a number).
11-18 Using mathematical functions QUOTE Encloses an expression that should not be evaluated numerically. QUOTE( exp re ss io n ) Examples QUOTE(SIN(45)) F1(X) stor es the expr essi on SIN( 4 5) r ather than the value of SIN(4 5 ). Another method is to enclos e the expr essi on in single quotes.
Using mathematical fun ctions 11-19 ≥ Greater than or equal to. Returns 1 if true, 0 if false. val u e1 ≥ va l ue 2 AND Comp ares value1 and value2 . Returns 1 if they are both non-zero, otherwise returns 0. val u e1 AND va l ue 2 IFTE If expression is true, do the trueclause ; if not, do the falseclause.
11-20 Using mathematical functions SEC Sec ant: 1/cos x . SEC ( val ue ) Symbolic calculations The hp 39g+ has the ability to perform symbolic calculations, for example, symbolic integration and differentiation. You can perform symbolic calculations in HOME and in the Function aplet.
Using mathematical fun ctions 11-21 Symbolic calculations in the Function aplet You can perform symbolic operations in the Functi on aplet’s Symbolic view. For example, to find the derivative of a function in the Functi on aplet’s Symbolic view, you define two functions and define the second function as a derivative of the first function.
11-22 Using mathematical functions 3 . Show the r esult . To find derivatives in the Function aplet’s Symbolic view To find the derivative of the fu nction in the Function aplet’s Symbolic view, you define two functions and define the second function as a der ivati ve of the first function.
Using mathematical fun ctions 11-23 To find the indefinite integral using formal variables F or ex ample , to find the ind efinite integral of use: 1. Enter the functi on. 0 S1 3 X 5 X 2 . Sho w the re sult f ormat . 3 . Press to close the sho w w i ndo w .
11-24 Using mathematical functions The ‘extra’ constant of 6.4 results from the substitution of into ( x –2 ) 5 /5 , and should be disregarded if an indefinite integral is required.
Variables and me mory management 12-1 12 V ariables and memory manag ement Introduction The hp 39g+ has approximately 232K of user memo ry. The calculator uses this memory to store variables, perform computations, and store history. A v a r i a b l e i s a n o b j e c t t h a t y o u c r e a t e i n m e m o r y t o h o l d data.
12-2 Variables and memory managem ent Storing and recalling variables You can store numbers or expressions from a pr evious input or result into variables. Numeric Precision A number stored in a variable is always stored as a 12- digit mantissa with a 3-digit exponent.
Variables and me mory management 12-3 5 . Enter a name for the v ar iable . A 6. P re ss to stor e the r esu lt . The results of a calculation can also be stored directly to a variable. For example: 2 5 3 B To recall a value To recall a variable’s value, type the name of the variable and press .
12-4 Variables and memory managem ent The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organised by category. For each variable category in the left column, there is a list of variables in the right colu mn.
Variables and me mory management 12-5 5 . Choose w hether to place the v ari able name or the var ia ble va lue on the command line . – Press to indicate that you w ant the var ia ble’s co ntents to appear on the command line. – Press to indicate that yo u wan t the var ia ble’s name t o appear on the command line .
12-6 Variables and memory managem ent 4. Enter data for L2 . 55 48 86 90 77 5. P re s s to access HO ME . 6 . Open the varia ble menu and se lect L1. 7 . Cop y it to the command line . Note: Because the option is highli ghted , the v ari able ’s name , rather than its conten ts, is copi ed to the command line .
Variables and me mory management 12-7 Home variables It is not possible to store data of one type in a variable of another type. For example, yo u use the Matrix catalog to create matrices. You can crea te up to ten matrices, and you can store these in variables M0 to M9.
12-8 Variables and memory managem ent Aplet variables Aplet variables store values that are unique to a particular aplet. These include symbolic expres sions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections.
Variables and me mory management 12-9 6 . T o cop y the value o f the var i able int o the edit line , pr ess and pres s . Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory.
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Matrices 13-1 13 M atrices Introduction You can perform matrix calc ulations i n HOME and in programs. The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas.
13-2 Matr ices Creating and storing matrices You can create, edit, delete, send, and receive matrices in the Matrix catalog. To open the Matrix catalog, press MATRIX .
Matrices 13-3 To create a matrix in the Matrix Catalog 1. Press MATRIX to open the Matri x Catalog. T he Matri x cat alog lists the 10 a vailable matr ix var iables , M0 to M9 . 2 . Hi ghlight the matr i x v ar iable name y ou want to use and pres s .
13-4 Matr ices A matrix is listed with two dimensions, even if it is 3×1. A vector is listed with the number of elements, such as 3. To transmit a matrix You can send matrices between calculators just as you can send aplets, programs, lists, and notes.
Matrices 13-5 To display a matrix • In the Matri x catalog ( MATRIX ), highlight the matri x name and pr ess . • In HOME , enter the name of the matr ix v ar iab le and pres s . To display one element In HOME, enter matrixname ( row,column ). For example, if M2 is [[3,4],[5,6]] , then M2(1,2) returns 4 .
13-6 Matr ices To store one element In HOME, enter, value matrixname ( row, column ). For example, to change the element in the first row and second column of M5 to 728, then display the resulting matrix: 728 M 512 M5 . An attempt to store an element to a row or column beyond the size of the matrix results in an error message.
Matrices 13-7 3 . Add the matri ces that you c re a t e d. M1 M2 To multiply and divide by a scalar For division by a scalar, enter the matrix first, then the operator, then the scalar. For multiplication, the order of the operands does not matter. The matrix and the sc alar can be real or complex.
13-8 Matr ices To divide the two matrices M1 and M2 that you created for the previous example, press the following keys: M1 M2 To invert a matrix You can invert a square matrix in HOME by typing the matrix (or its variable name) and pressing x –1 . Or you can use the matrix INVERSE command.
Matrices 13-9 4. Create a ne w matri x . Select Real matrix 5 . Enter the equation coeffi c ients. 23 4 11 1 4 12 In this ex ample , the matrix yo u cr eat ed is listed as M2 . 6 . Return to HO ME and enter the calc ulati on to left-multipl y the constants v ec tor b y the in ve rse o f the coeff ic i ents matr i x .
13-10 Matri ces • F unctio ns al wa y s pr oduce and displa y a r esult . T he y do not change an y stor ed var ia bles, suc h as a matri x vari ab l e. • F unctio ns hav e ar guments that ar e enclo sed in parenthes es and separ ated by comma s; for e x ample , CROSS ( vecto r 1 , vec to r2 ) .
Matrices 13-11 DET Determinant of a square matrix . DET ( matri x ) DOT Dot Product of two arrays, matrix1 matrix2 . DOT ( matri x1, matri x2 ) EIGENVAL Displays the eigenvalue s in vector form for matrix . EIGENVAL ( matri x ) EIGENVV Eigenvectors and Eige nvalues for a square matrix .
13-12 Matri ces calculation for each element substitutes the current row number for I and the current column number for J. MAKEMAT ( ex p re ss io n , rows , columns ) Example MAKEMAT(0,3,3) r etur ns a 3×3 z er o matri x , [[0,0,0],[0,0,0],[0,0,0]] .
Matrices 13-13 SVD Singular Value Decomp osition. Factors an m × n matrix into two matrices and a vector: {[[ m × m square orthogonal ]],[[ n × n square orthogonal ]], [ real ]}. SVD ( matri x ) SVL Singular Values. Returns a vector containing the singular values of matrix.
13-14 Matri ces Reduced-Row Echelon Form The following set of equations can be written as the augmented matrix which can then stored as a real matrix in any matrix variable. M1 is used in this example. You can use the RREF function to change this to reduced row echelon form, storing it in any matrix variable.
Lists 14-1 14 L ists You can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matr ices, all enclosed in braces. A list may, for example, contain a sequence of real numbers such as {1,2,3} .
14-2 Lists 3. E nter t he values you want i n th e l ist, pressi ng after each one. V alues can be r eal or comple x number s (or an expr ession). If you enter a calculati on , it is ev aluated and the re sult is inserted in the list . 4. When done, pr ess LIST to see the List catalog, or pres s to retur n to HOME .
Lists 14-3 List edit keys When you press to create or change a list, the following keys are available to you: Create a list in HOME 1. Enter th e list on the edit line. Start and end the list w ith br aces (the shift ed and k e y s) and separate each element w ith a comma.
14-4 Lists Displaying and editing lists To display a list • In the List catalog , highli ght the list name and pr ess . • In HOME , enter the name of the lis t and pr ess . To display one element In HOME, enter listname ( element# ). For example, if L2 is {3,4,5,6}, then L2(2) returns 4 .
Lists 14-5 To insert an element in a list 1. Open the List catalog. LIST . 2. P r e s s or to highligh t the name of the list y ou w ant to edit (L1, etc.) and pr e ss to displa y the list contents . New elements are inserted above the highlighted positio n.
14-6 Lists Deleting lists To delete a list In the List catalog, highli ght the list name and press . You are prompted to confirm that you want to delete the contents of the highlighted list variable. Press to delete the contents. To delete all lists In the List catalog, press CLEAR .
Lists 14-7 • If Dec imal Mark in Modes is set to C omma , use peri ods to separ ate ar guments . F or e x ample , CONCAT(L1.L2) . Common operators like +, –, ×, and / can take lists as arguments. If t here are two ar guments and both are lists, then the lists must have the same length, since the calculation pairs the elements .
14-8 Lists MAKELIST Calculates a sequence of elements for a new list. Evaluates expression with variable from begin to end values, taken at increment steps. MAKELIST( expression , va ria b le , begin , end , incr ement ) The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression.
Lists 14-9 SIZE Calculates the number of elements i n a list. SIZE( list ) Also works with matrices. Σ LIST Calculates the sum of all elements in list.
14-10 Lists 2 . In HOME , stor e L1 into C1. Y ou w ill then be able to see the list data in the Nu meri c v ie w of the S tatis tics aple t. L1 C1 3 . Start the Statisti cs aplet , and selec t 1-var ia ble mode (pre ss , if nece ssary , to display ) .
Notes and sketches 15-1 15 Notes and sk etches Introduction The hp 39g+ has text and picture editors for entering notes and sk etches. • E ach aplet has its ow n independent Note vie w and Sk etch view . Note s and sk etc hes that y ou cr eate in these vi ew s are assoc i ated with the aplet.
15-2 Notes and sketches Note edit keys Key Me a n i n g Space key for text entry. Displays next page o f a multi-page note. Alpha-lock for letter entry. Lower-case alpha-lock for letter entry. Backspaces cursor and deletes character. Deletes current character.
Notes and sketches 15-3 Aplet sketch view You can attach pictures to an aplet in its Sketch view ( SKE TCH ). Y our wor k is automati cally s av ed w ith the aplet . Pr ess an y other v ie w k e y or to ex it the Sketc h vi ew Sketch keys To dra w a line 1.
15-4 Notes and sketches To draw a box 1. In Sk etch v i ew , press and mo v e the c ursor to wher e y ou want an y corner of the box to be . 2. P r e s s . 3 . Mov e the c urs or to mark the opposite corner fo r the bo x. Y ou can adju st the si z e of the bo x b y mo v ing the cu rs or.
Notes and sketches 15-5 To label parts of a sketch 1. Press and type the te xt on the edit line . T o lock the Alpha shift on, pr ess (for upper cas e) or (fo r lo w er case). T o make the label a smaller c har ac ter si z e, turn o ff befor e pr essing .
15-6 Notes and sketches To import a graphics variable You can copy the contents of a graphics v ariable into the Sketch view of an aplet. 1. Open the Sketch v ie w of the aplet ( SKETCH ). The gr aphic w ill be copi ed here . 2 . Pr ess , . 3 . Highlight Graphic , then pr ess and highligh t the name of the var i able ( G1 , etc.
Notes and sketches 15-7 4. W rite y our note . See “Note edit k e y s ” on page 15- 2 for mor e infor mation o n the entry and editing of notes. 5 . When yo u are finished, pr ess or an aplet key to e x it Notepad . Y our w or k is automati cally s av ed .
15-8 Notes and sketches To import a note You can impo rt a note from the Notepad into an aplet’s Note view, and vice versa. Suppose you wan t to copy a note named “Assignments” fr om the Notepad into the Function Note view: 1. In the Functi on aplet , displa y the Note v ie w ( NOTE ).
Programming 16-1 16 Pr ogr amming Introduction This chapter describes how to program using the hp 39g+. In this chapter you’ll learn abo ut: • using the Pr ogr am catalog to cr eate and edit progr ams • progr amming commands • stor ing and r etr ie v ing v ari ables in pr ogr ams • progr amming v ar iables .
16-2 Programming Example RUN GETVALUE: RUN CALCULATE: RUN " SHOW ANSWER " : This program is separated into three main tasks, each an individual program. Within each program, the task can be simple—or it can be di vided further into other programs that perform smaller tasks.
Programming 16-3 Program catalog keys The program catalog keys are: Key M e a n i n g Opens the highlighted program for editing. Prompts for a new program name, then opens an empty program. Transmits the highlighted program to another hp 39g+ or to a disk drive.
16-4 Programming Creating and editing programs Create a new program 1. Pres s PROGRM to open the Progr am catalog . 2. P r e s s . The hp 3 9g+ prompts yo u fo r a n am e.
Programming 16-5 2 . On the le ft, u se or to highlight a command category , then pres s to access the commands in the category . Select the command that y ou want . 3 . Press to paste the command into the pr ogr am editor . Edit a program 1. Press PROGRM to open the Progr am catalog.
16-6 Programming Editing keys The editing keys are: Key M e a n i n g Inserts the character at the editing point. Inserts space into text. Displays previous page of the program. Displays next page of the program. Moves up or down one line. Moves right or left one character.
Programming 16-7 Using programs Run a program From HOME, type RUN program_name. or From the Program catalog, highlight the program you want to run and press Regardless of where you star t the program, all programs run in HOME. What you see will differ slightly depending on where you started the program.
16-8 Programming Copy a program You can use the following procedure if you want to make a copy of your work before edit ing—or if you want to use one program as a template for another. 1. Pres s PROGRM to open the Progr am catalog . 2. P r e s s . 3 .
Programming 16-9 Delete a program To delete a program: 1. Press PROGRM to open the Progr am catalog . 2 . H ighligh t a pr ogr am to delete , the n pr ess . Delete all programs You can delete all programs at once. 1. In the Progr am catalog , pr es s CLEAR .
16-10 Programming 4. D ev elop a pr ogr am that uses the SE TVIEWS command to modify the aplet’s VIEW S menu . The menu options pr ovi de links to a ssoc iat ed pr ogr ams. Y ou can spec ify an y other pr ogr ams that y ou w ant transfer red w ith the aplet.
Programming 16-11 Save the aplet 1. Open the Func tion aplet and sa v e it as “EXP ERIMENT ” . The new a plet appear s in the Aplet library . Select Function EXP ERIMENT 2 . Cr eate a pr ogram called EXP .ME1 w ith contents as shown . This progr am conf igur es the plot ra nges, then runs a progr am that allo ws y ou to set the angle for mat .
16-12 Programming 6 . Open the Progr am catalog and c r eate a pr ogr am named “EXP .S V” . Include the follow ing code in the progr am . E ach en try line after the command SETVIEW S is a tri o t.
Programming 16-13 ’ ’ ’ ’ ;’ ’ EXP.ANG’ ’ ;0 ; The pr ogram EXP .ANG is a smal l ro utine that is called by other pr ogr ams that the aplet use s. T his entry spec if ies that the progr am EXP.ANG is transfer r ed when the aplet is tr ansf err ed , but the space in the fir st quot es ensur es that no e ntry appears on the menu .
16-14 Programming Aplet commands CHECK Checks (selects) the correspon ding function in the current aplet. For example, Check 3 would check F3 if the current aplet is Function. Then a checkmark would app ear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view.
Programming 16-15 options us e , or the pr ogr am that def ines the a plet’s VIEW S menu . • Y ou can incl ude a “Start ” option in the VIE W S menu to spec ify a progr am that y ou wa nt to run automati cally w hen the aplet starts. T his pr ogr am typically sets up the aplet’s initial configur ation.
16-16 Programming ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected. All programs that are identified in the aplet’s SETVIEW S command are transferred when the aplet is transmitted. ViewNumber V iewNumber is the number of a view to start after the program finishes running.
Programming 16-17 View numbers The Function aplet views are numbered as fo llows: UNCHECK Unchecks (unselects) the corresponding function in the current aplet. For example, Uncheck 3 would uncheck F3 if the current aplet is Function. UNCHECK n : Branch commands Branch commands let a program make a deci sion based on the result of one or more tests.
16-18 Programming IF... THEN... ELSE... END Executes the true-clause sequence of commands if the test- clause is true, or the false-clause sequ ence of commands if the test-clause is false.
Programming 16-19 RUN Runs the named program. If your program name contains special characters, such as a space, then you must enclose the file name in double quotes (" "). RUN " pr ogr am name " : or RUN pr ogra mname : STOP Stops the current program.
16-20 Programming ERASE Clears the display ERASE: FREEZE Halts the program, freezing the cu rrent display. Execution resumes when any key is pressed. LINE Draws a li ne from (x1, y1) to ( x2, y2 ) . LINE x1; y1; x2 ; y2: PIXOFF Turns off the pixel at the specified coordinates (x,y) .
Programming 16-21 → DISPLAY Displays gr aphic from graphicname in the display. → DISPLAY gr aphicname : → GROB Creates a graphic from expression , using font_size , and stores the resulting graphic in graphicname .
16-22 Programming → PLOT Puts graph from graphi cname into the Plot view display. → PLOT graphi cname : REPLACE Replaces portion of graphic in graph icname1 with graphicname2 , s tarting at position .
Programming 16-23 WHILE… REPEAT… END While ... Repeat ... End is a loop command that repeatedly evaluates test-clause and executes loop-clause sequence if the test is true. Because the test-clause is executed before the loop-clause, the loop-clause i s not executed if the test is initially false.
16-24 Programming DELCOL Delete Column. Deletes the specif ied column from the specified matrix . DELCOL name ; c olumn_number : DELROW Delete Row. Deletes the specified row from the specified matrix. DELROW name ; row _ n u m b e r : EDITMAT Starts the Matrix Editor and displays the specified matrix.
Programming 16-25 SUB Extracts a sub-object— a portion of a list, matrix, or graphic from object —and stores it into name . start and end are each specified using a list with two numbers for a matrix, a number for vector or li sts, or an ordered pair, ( X,Y ), for graphic s.
16-26 Programming CHOOSE Creates a choose box, which is a box containing a list of options from which the user choo ses one. Each option is numbered, 1 through n . The result of the choose command is to store the number of the option chosen in a variable.
Programming 16-27 Examples 5.152000 X DATE( sets the date to May 15, 2000). 10.1500 X TIME (sets the time to 10:15 am). EDITMAT Matrix Editor. Opens the Matrix editor for the specified matrix. Returns to the program when user presses EDITMAT matri xname : The EDITMAT command can also be used to create matrices.
16-28 Programming Example INPUT R; "Circular Area"; "Radius"; "Enter Number";1: MSGBOX Displays a message box containing textitem. A text item consists of any number of expre ssions and quoted string s of text. The expressions are evaluated and turned into strings of text.
Programming 16-29 Stat-One commands DO1VSTATS Calculates S TATS us ing datasetname and stores the results in the corresp onding variables: N Σ , Tot Σ , Mean Σ , PVar Σ , SVar Σ , PSDev, SSDev, Min Σ , Q1, Median, Q 3, and Max Σ . Datasetname can be H1, H2, .
16-30 Programming Storing and retrieving variables in programs The hp 39g+ has both Home variables and Aplet variables. Home va riables are used for real numbers, complex numbers, graphics, lists, and matrices. Home variables ke ep the same va lu es in HOME and in aplets.
Programming 16-31 Coord Function Parametric Polar Sequence Solve Statistics Turns the coordinate-display mode in Plot view on or off. From Plot view, use the Menu mean key to toggle coordinate display on an off. In a program, type 1 X Coord —to turn coor dinate dis play o n (def ault).
16-32 Programming Hwidth Statistics Sets the width of histogram bars. From Plot Se tup in 1VAR stats set a value for Hwidth or In a program, type n X Hwidth Indep All Aplets Defines the value of the inde pendent variable used in tracing mode. In a program, type n X Indep InvCross All Aplets Toggles between solid crosshairs or inverted crosshairs.
Programming 16-33 Nmin / Nmax Sequence Defines the minimum and maxi mum independent variable values. Appears as the NRNG fields in the Plot Setup input form. From Plot Setup, enter values for NRNG . or In a program, type X Nmin X Nmax whe re Recenter All Aple ts Recenters at the crosshairs locations when zooming.
16-34 Programming Simult Function Parametric Polar Sequence Enables you to choose between simultaneous and sequential graphing of all selected expressions. From Plot Setup, check (or uncheck) _ SIMULT or In a program, type 1 X Simult —for simu ltaneous gr aphing .
Programming 16-35 Tmin / Tmax Parametric Sets the minimum and maxi mum independent variable values. Appears as the TRNG field in the Plot Setup input form. From Plot Setup, enter values for TRNG . or In a pr ogr am , ty pe X Tmin X Tmax whe re Tracing All Aple ts Turns the tracing mode on or off in Plot vi ew.
16-36 Programming Xtick All Aplets Sets the distance between ti ck marks for the horizontal axis. From the Plot Setup input form, enter a value for Xtick . or In a program, type n X Xtick whe re Ytick All Aplets Sets the distance between tick marks for the vertical axis.
Programming 16-37 Xzoom All Aple ts Sets the horizontal zoom factor. From Plot-ZOOM-Set Factors, enter the value for XZOOM . or In a program, type n X XZOOM whe re Yzoom All Aple ts Sets the vertical zoom factor. From Plot-ZOOM-Set Factors, enter the value for YZOOM .
16-38 Programming R1...R9, R0 Polar Can contain any expression. Independent vari able is θ . Example '2*SIN(2* θ )' X R1( θ ) U1...U9, U0 Sequence Can contain any expression. Independent vari able is N. Example RECURSE (U,U(N-1)*N,1,2) X U1(N) E1.
Programming 16-39 Numeric-view variables The following aplet variabl es control the Numeric view. The value of the variable appl ies to the current aplet only. C1...C9, C0 Statistics C0 through C9 , for columns o f data. Can contain lists. Enter data in the Nu meric view or In a program, type LIST X C n whe re n = 0, 1, 2, 3 .
16-40 Programming Except in the Solve aplet, the value of Format takes effect only after the current aplet is saved with a new name. Until then, HFormat is in effect. Example Scientific X Format or 3 X Format NumCol All Aplets except Statistics aplet Sets the column to be highlighted in Numeric view.
Programming 16-41 NumStep Function Parametric Polar Sequence Sets the step size (increment value) for an independent varia ble in Num eric view . From Num Setup, enter a value for NUMSTEP . or In a program, type n X NumStep whe re NumType Function Parametric Polar Sequence Sets the table format.
16-42 Programming Note variables The following aplet variable is available in Note view. NoteText All Aplets Use NoteText to recall text previously entered in Note view. Sketch variables The following aplet vari ables are available in Sketc h view. Page All Aplets Sets a page in a sketch set.
Extending aplets 17-1 17 Extending aplets Aplets are the application environments where you explore different classes of m athematical operations. You can extend the capability of the hp 39g+ in th e .
17-2 Ext endi ng aple ts 1. Open the Solve aplet and sav e it under the n e w name . Solve | T R I A N G L E S 2 . Ent er th e fo ur form u la s: θ O H θ A H θ OA AB C 3 . Decide w hether yo u w ant the aplet to oper ate in Degr ees , Radi ans, or Gr ads .
Extending aplets 17-3 Using a customized aplet To use the “Triangles ” aplet, simply select the appropriate formula, change to the Numeric view and solve for the missing variable. Find the length of a ladder leaning against a vertical wall if it forms an angle of 35 o with the horizontal and extends 5 metres up the wall.
17-4 Ext endi ng aple ts Annotating an aplet with notes The Note view ( NOTE ) attaches a note to the current aplet. See Chapter 15, “Notes and sketches”. Annotating an aplet with sketches The Sketch view ( SKET CH ) attaches a picture to the current aplet.
Extending aplets 17-5 To transmit an aplet 1. Connect the P C or aple t disk dr i ve t o the calc ulator b y cable or align the two calc ulator s ’ infr ar ed ports b y matching up the tr iangle mar ks on the r ims of the calc ulator s. P lace the calc ulators n o mor e than 2 inche s (5 cm) apar t.
17-6 Ext endi ng aple ts To sort the aplet list In the aplet library, press . Select the sorting scheme and press . • Chronologically pr oduces a chr onological order based on the date an a plet was last used . (The last- used aplet appe ars first , and so on.
Reference inform ation R-1 R Re fere nce infor mation Glossary aplet A small application, limited to one topic. The built-in aplet types are Function, Parametric, Polar, Sequence, Solve, and Statistics. An aplet can be filled with the data and solutions for a specific problem.
R-2 Reference information list A set of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in braces. Lists are commonly used to enter statistical data and to evaluate a function with multiple values. Created and manipulated b y the List editor and catalog.
Reference inform ation R-3 Resetting the hp 39g+ If the calculator “locks up” and seems to be stuc k, you must reset it. This is much like resetting a PC. It cancels certain operations, restores ce rtain conditions, and clears temporary memory locations.
R-4 Reference information If the calculator does not turn on If the hp 39g+ does not tu rn on follow the steps below until the calculator turns on. You may find that the calculator turns on before you have completed the procedure. If the calculator still does not turn on, please contact Customer Support for further information.
Reference inform ation R-5 To install the main batteries a. Slide up the battery compartment cover as illustrated. b. Insert 3 new AAA(LR03) batteries into the main compartment. Make sure each batte ry is inserted in the indicated direction. To install the backup battery a.
R-6 Reference information Variables Home variables The home variables are: Category Available name Complex Z1 ... Z9 , Z0 Graphic G1 ... G9 , G0 Library Function Parametric Polar Sequence Solve Statistics User-named List L1 .
Reference inform ation R-7 Function aplet variables The function aplet variables are: Category A v ailable name Plot A xes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Xcro.
R-8 Reference information Parametric aplet variables The parametric aplet variables are: Category Available name Plot Axe s Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing T.
Reference inform ation R-9 Polar aplet variables The polar aplet variables are: Category A v ailable names Plot A xes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θ step Tracing.
R-10 Reference information Sequence aplet variables The sequence aplet variables are: Category Available name Plot Axe s Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcro.
Reference inform ation R-11 Solve aplet variables The solve aplet variables are: Category Available name Plot A xes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtic.
R-12 Reference information Statistics aplet variables The statistics aplet variables are: Category Available name Plot Axe s Connect Coord Grid Hmin Hmax Hwidth Indep InvCross Labels Recenter S1mark S.
Reference inform ation R-13 MATH menu categories Math functions The math functions are: Category Available name Calculus TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL π Hyperb .
R-14 Reference information Matrix COLNORM COND CROSS DET DOT EIGENVAL EIGENVV IDENMAT INVERSE LQ LSQ LU MAKEMAT QR RANK ROWNORM RREF SCHUR SIZE SPECNORM SPECRAD SVD SVL TRACE TRN Polynom.
Reference inform ation R-15 Program constants The program constants are: Tests < ≤ = = ≠ > ≥ AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category Av ailable name (Continued) Category Available name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlot Cobweb Stairstep S1.
R-16 Reference information Program commands The program commands are: Category Command Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE.
Reference inform ation R-17 Status messages Message Meaning Bad Argument Type Incorrect input for this operation. Bad Argument Value The value is out of range for this operation. Infinite Result Math exception, such as 1/0 . Insufficient Memory You must recover some memory to continue operation.
R-18 Reference information No Equations Checked You must enter and check an equation (Symbolic view) before evaluating this function. (OFF SCREEN) Function value, root, extremum, or intersection is not visible in the current screen. Receive Error Problem with data reception from anot her ca lculator.
Limiting Warranty W-1 Li mi t i n g W arra n t y hp 39g+ Graphing Calculator; Warranty period: 12 months 1. HP warr ants to you , the end-user c ustomer , that HP hard w ar e , accessor ies and su pplies w ill be fr ee fr om defec ts in mater ials and w or kmanship after the date of pur cha se , for the per iod spec if ied abo v e .
W-2 Limiting Warranty 6 . HP MAKES NO O THER EXPRE S S W ARRANTY OR CONDIT ION WHE THER WRI TTEN OR ORAL. T O THE EXTENT ALL OWED B Y L OCAL L A W , ANY IMPLIED W ARRANTY OR CONDI TION OF MERCHANT ABI.
Limiting Warranty W-3 Service Europe Countr y : T elephone numbers Austr i a +43-1-36 0 2 77120 3 Belgium +3 2 - 2- 712 6 219 D e n m a r k + 45 - 8 -2 33 284 4 Ea st e r n Eu ro p e countr ies +4 20 .
W-4 Limiting Warranty P lease logon to http://www .hp.com for the lat est se r vice a n d s u p p o r t in f o r m at i o n . L.Ame r ica Country : Telephone numbers Ar gentina 0 -810 -55 5-5 5 20 Bra.
Limiting Warranty W-5 Regulatory information This section contains information that shows how the hp 39g+ graphing calculator comp lies with regulations in certain regions. Any modifications to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the 39g+ in these regions.
W-6 Limiting Warranty Disposal of Waste Equipment by Users in Private Household in the European Union This s y mbol on the pr oduc t or on its pack aging indicates that this pr oduct m u s t n o t b e d i s p o s e d o f w i t h y o u r o t h e r household waste .
Index I-1 Index A absolute value 11-5 add 11-3 algebraic entry 1-19 alpha characters typing 1-6 alphabetical sorting 17-6 angle measure 1-10 in statistics 8-12 setting 1-12 animation 15-5 creating 15-.
I-2 Index chronological sorting 17-6 circle drawi ng 15-4 clearing aplet 17-3 characters 1-22 display 1-22 display history 1-25 edit line 1-22 lists 14-6 plot 2-7 cobweb graph 6-1 coeffici ents polyno.
Index I-3 definition of 11-6 in Function aplet 11-22 in Home 11-21 determinant square matrix 13-11 differentiation 11-6 display 16-20 adjusting contrast 1-2 annunciator line 1-2 capture 16-20 clearing.
I-4 Index gamma 11-12 intersection point 3-5 math menu R-13 slope 3-5 syntax 11-2 tracing 2-8 Function aplet 2-21 , 3-1 function variables area 16-30 axes 16-30 connect 16-30 fastres 16-31 grid 16-31 .
Index I-5 I i 11-8 implied multiplication 1-21 importing graphics 15-6 notes 15-8 increasing display contrast 1-2 indefinite integral using symbolic variables 11-23 independent values adding to table .
I-6 Index logarithmic fit 8-13 functions 11-3 logical operators AND 11-19 equals (logical test) 11-18 greater than 11-18 greater than or equal to 11-19 IFTE 11-19 less than 11-18 less than or equal to 11-18 NOT 11-19 not equal to 11-18 OR 11-19 XOR 11-19 logistic fit 8-13 loop commands BREAK 16-23 DO.
Index I-7 variables 13-1 matrix functions 13-10 COLNORM 13-10 COND 13-10 CROSS 13-10 DET 13-11 DOT 13-11 EIGENVAL 13-11 EIGENVV 13-11 IDENMAT 13-11 INVERSE 13-11 LQ 13-11 LSQ 13-11 LU 13-11 MAKEMAT 13.
I-8 Index order of precedence 1-21 overlaying plots 2-16 , 4-3 P π 11-8 paired columns 8-11 parametric variables axes 16-30 connect 16-30 grid 16-31 in menu map R-8 indep 16-32 labels 16-33 recent er.
Index I-9 precede nce 1-22 predicted values statistical 8-20 print contents of display 16-25 name and contents of variable 16-25 object in history 16-25 variables 16-25 probability functions ! 11-12 C.
I-10 Index interac tive 3-10 n th 11-6 variable 16-33 root-finding displaying 7-7 interac tive 3-9 operatio ns 3-10 variables 3-10 S S1mark-S5mark variables 16-33 scaling automatic 2-14 decimal 2-10 ,.
Un punto importante, dopo l’acquisto del dispositivo (o anche prima di acquisto) è quello di leggere il manuale. Dobbiamo farlo per diversi motivi semplici:
Se non hai ancora comprato il HP 39gII è un buon momento per familiarizzare con i dati di base del prodotto. Prime consultare le pagine iniziali del manuale d’uso, che si trova al di sopra. Dovresti trovare lì i dati tecnici più importanti del HP 39gII - in questo modo è possibile verificare se l’apparecchio soddisfa le tue esigenze. Esplorando le pagine segenti del manuali d’uso HP 39gII imparerai tutte le caratteristiche del prodotto e le informazioni sul suo funzionamento. Le informazioni sul HP 39gII ti aiuteranno sicuramente a prendere una decisione relativa all’acquisto.
In una situazione in cui hai già il HP 39gII, ma non hai ancora letto il manuale d’uso, dovresti farlo per le ragioni sopra descritte. Saprai quindi se hai correttamente usato le funzioni disponibili, e se hai commesso errori che possono ridurre la durata di vita del HP 39gII.
Tuttavia, uno dei ruoli più importanti per l’utente svolti dal manuale d’uso è quello di aiutare a risolvere i problemi con il HP 39gII. Quasi sempre, ci troverai Troubleshooting, cioè i guasti più frequenti e malfunzionamenti del dispositivo HP 39gII insieme con le istruzioni su come risolverli. Anche se non si riesci a risolvere il problema, il manuale d’uso ti mostrerà il percorso di ulteriori procedimenti – il contatto con il centro servizio clienti o il servizio più vicino.
