HP 39g+ Bedienungsanleitung

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 WITHO UT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WA RRANTY OF ANY KIND WITH REGA RD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTI ES OF MERCHANTABILITY, N ON-INFRINGEMENT AN D F[...]

Contents i Contents Preface Manual conventions ............. ............. ............. ............. .......... P-1 Notice ............ ............. .......... ............. ............. ............. ....... P-2 1 Getting started On/off, cancel o perations .. ............. ............. ............. ............. 1-1 The display .............[...]

ii Conten ts 3 Function aplet About the Function ap let .............. ............. .......... ............. ...... 3-1 Getting started w ith the Function aple t ......... ............. .......... 3-1 Function aplet intera ctive analysis ....... ............. ................. ...... 3-9 Plotting a pie cewise-defined function ........... .........[...]

Contents iii 9 Inference aplet About the Inference a plet ......... ............. ............. ............. ....... 9-1 Getting started with the Infere nce aplet .............. ............. .... 9-1 Importing samp le statistic s from the Statis tics aplet ............ .... 9-4 Hypothesis tes ts ...... ............. ............. ............. ..[...]

iv Conten ts 12 Variables and memory management Introduction ........... ............. .......... ............. ............. ........... 1 2-1 Storing and recalling variables ............... ............. ............. .... 12-2 The VARS menu ...... ............. ............. ............. ............. ........ 12-4 Memory Manager ...... .......[...]

Contents v 16 Programming Introduction .. ............. .......... ............. ............. ............. ........ 16-1 Program catalog ...... ............. ............. ............. ............. .. 16-2 Creating and editing p rograms ........ ............. ............. ........... 16-4 Using programs ............ ............. .............[...]

vi Conten ts Reference information Glossary ............. ............. .......... ............. ............. ............. ... R-1 Resetting the hp 39g+ ....... .......... ............. ............. ............. ... R-3 To erase all me mory and reset defaults ........ ............. .......... R-3 If the calculator do es not turn on ........ ...[...]

Preface P-1 Pr eface The hp 39g+ is a feature-rich graphing c alculator. 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 prop erties. You can get more information on the hp 39g+ from Hewlett-Packard’s Calcula tors web site. You can download customized aple[...]

P-2 Preface 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 express or implied warranty of any kind with regard to this manu al and specific ally disclaims the implied warranties and conditions of merchantabili[...]

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 ca lculator turns itself off after sev eral minutes of inactivity. All stored and displayed inf[...]

1-2 Getting started The display To adjust the contrast Simultaneously press and (or ) to increase (or decrease) the contrast. To clear the display • Pr ess CANCEL to c lear the edit line. • Pr ess CLEAR to c lear the edit line and the display history . Parts of the display Menu key or soft key labels. The la bels f or the menu k e ys ’ cur re[...]

Getting started 1-3 Annunciators . Annunciators are sy mbols that ap pear above the title bar and give you important status information. The keyboard Menu keys Annunciator Description Shift in effect for next keystrok e. To cancel, press again. α Alpha in effect for next keystroke. To cancel, press again. (( • )) Low battery power. Busy. Data is[...]

1-4 Getting started • On the calc ulator k ey boar d, the top r ow o f k e ys ar e called menu k ey s. The ir meanings depend on the conte xt—that’s w h y their to ps ar e blank. The menu k e y s ar e sometimes called “ s oft k e ys ” . • T he bottom line o f the displa y sho ws the labels f or the menu k ey s ’ curr ent meanings. Apl[...]

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. Returns to the HOME view, for performing calculations. Accesses the alphabetical characters prin[...]

1-6 Getting started Shifted keys trokes 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 . To select multiple character s, select each and press , then press . K e y M eaning (Cont[...]

Getting started 1-7 HELPWITH The hp 39g+ built-in help is availa ble 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. Example Pr ess SYNTAX Note: R emo ve the left par enthesis fr om built -in func tio ns such as sine , cosine [...]

1-8 Getting started • Pr essing tak es yo u to the beginning of the MA TH men u . 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+, pressing an alpha k e y tak es y ou str aight to the fir st menu opti on beginning w ith that alpha char acter . With [...]

Getting started 1-9 • If ther e are tw o c olumns , the left column sho ws gener al categor ies and the r ight column sho ws spec ifi c cont ents w ithin a categor y . Highli ght a gener al category in the left column, the n highligh t an item in the r ight column . The lis t in the ri ght column c hanges w hen a diffe r ent catego r y is hi ghli[...]

1-10 Getting started Mode settings You use the Modes inpu t 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 selecte d in Modes is the angle setting used in both HOME and current aplet. To further configure an aplet, you use the SET[...]

Getting started 1-11 Numb er 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 be comes 123.46 in Fixed 2 format . Scientific . Displays results with an exponent, one digit to the l[...]

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. Pr ess MODES to open the HOME MODES input form. T he cur sor (hi ghlight) is in the fir st f ield, A ngle Mea[...]

Getting started 1-13 • Cop ied fr om another calculator . Aplets are sto red in th e Aplet library. See “Aplet lib rary” 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. See “Aplet view configuration” on page 1-18 for further in[...]

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. Quad Explorer aplet The Quad[...]

Getting started 1-15 A button is provided to evaluate the student’s knowledge. Pressing displays a ta rget quadratic 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. An [...]

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. The angle setting can be changed to degrees by pressing . Aplet lib[...]

Getting started 1-17 Plot view Pr ess to display the aplet’s P lot vi ew . In this v ie w , the f uncti ons that y ou ha v e def ined ar e displa y ed gr aphicall y . See “About the Plot view” on page 2-5 for furth er information. Numeric view Press to display the aplet’s Numeric view. In this view, the functions that you have defined are d[...]

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-ex isting pl ot(s). See “Other views for scaling and splitting the graph ” on page 2-14 for further information. Note view Press NOTE to display the aplet’s note view. This note is t[...]

Getting started 1-19 Numeric Setup Press SETUP - NUM . Sets parameters for bui lding a table of numeric values. Symbolic Setup This view is only available in the Statistics aplet in mode, where it plays an important role i n choosing data models. Press SETUP - SYMB . To change views Each view is a separate environment. To change a view, select a di[...]

1-20 Getting started • Pr ess to e valuate the e xpre ssi on y ou hav e in the edit line (w here the blinking c urso r is) . An e xpressi on can contain n umbers , functi ons, and va riab l es. Example Calculate : Long results If the result is too long to fit on the display line, or if you want to see an expression in textbook format, press to hi[...]

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 clarit y, it is better to include the multiplication sign where you expect multiplication in an expression. It is clearest to enter AB as A[...]

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. E xpression s with in p arenthe ses. Nes ted p arenthe ses ar e ev aluated fr om inner to outer . 2 . Pr efi x functi ons, s[...]

Getting started 1-23 When you highlight a previous input or result (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 e dit line. To reuse the last result Press ANS (last answer) to put the last result from the HOME display into an expression. AN[...]

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 displaye d. Pressing evaluates (or re-evaluates) the last input, whereas pressing ANS copies the last result (as ANS ) into the edit line. Storing a va[...]

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 his tory ( CLEAR ) whenever you have finish ed working in HOME. It saves calcula[...]

1-26 Getting started 2 . Select Number Format , press to display the optio ns, and hi ghlight Fract ion . 3 . Pr ess to sele ct the Number F ormat option , then mo ve to the prec ision value fi eld. 4. Enter the prec ision v alue that yo u want to us e , and pr ess to set the pr ecisi on. Pr ess to r eturn to HOME . See “Setting fr action pr ec i[...]

Getting started 1-27 • Pr ec ision set to 1: • Pr ec ision set t o 2: • Pr ec ision set to 3: • Pr ec ision set t o 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 acti on. • T o en ter a mi xed f rac tion , for e xam ple , 1 1 / 2 , y ou enter it in[...]

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 i n the HOME v ie w . 3 . E valuat e the calc ulation . Converting decimals to fractions To convert a decimal value to a fraction: 1. Set the number for m at mode to Fraction . 2 . E ither r etr ie ve the v alue fr om the His tory , or e nter the v a[...]

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). To enter complex numbers Enter the number in either of these forms , wher[...]

1-30 Getting started Catalogs and editors The hp 39g+ has several cata logs and editors. You use them to create and manipulate object s. 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 , for e xam ple an aple t . • An editor let[...]

Aplets and their views 2-1 2 Aplets and t heir vie w s Aplet views This section examines the options an d functionality of the three main views for the Function, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views. About the Symbolic view The Symbolic view is the defining view for the Function, Parametric, Polar, and Seque nce[...]

2-2 Aplets and their views – For a F unc tion definiti on , en ter an e xpr essi on to def ine F(X) . T he only independent variab l e i n t h e ex p res s io n i s X. – Fo r a P arametric definiti on , en ter a pair of e xpr essi ons to def ine X(T) and Y(T) . The o nly independent v ari able in the e xpr es sions is T . – Fo r a Pol a r def[...]

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 reso lves all references to other functions in terms of their independent variable. 1. Ch oose the F un[...]

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 expres sion, substituting 9 in place of X into F4 . SYMB view keys The following table details the menu keys that you use to work with th[...]

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. Select the expressions you want to be plotted to[...]

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. F ield Meaning XRNG, YRNG Specifies the minimum and maximum horizontal ( X ) and vertical ( Y ) values for the plotting window. RES For function plots: Resolution; ?[...]

Aplets and their views 2-7 Reset plot settings To reset the default values for all plot settings, press CLEA R in the Plot Setup view. To reset the default value for a field, highlight the field, and pres s . Exploring the graph Pl o t v i ew g i v e s y o u a s e l e c ti o n o f ke y s a n d m e n u ke y s t o explore a graph further. The options[...]

2-8 Aplets and their views Trace a graph You can trace along a function using the or key which moves the cur sor along the graph. The display also shows the current coordinate position ( x, y ) of the cu rsor. Trace mode and the coordinate di splay are automatically set when a plot is drawn. Note: Tracing might not appe ar to exactly follow your pl[...]

Aplets and their views 2-9 To jump direc tly 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. • T urn o ff tr ace mode by pr essing . • T urn o n trace mode by pr essing .[...]

2-10 Aplets and their views Y-Zoom In Divides vertical scale only, using Y-factor. Y-Zoom Out Multipli es vertical scale only, using Y-factor. Square Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Zoo m, X-Zoom, or Y-Zoom.) Set Factors... Sets the X-Zoom and Y-Zoom factors for zooming in or zooming out. Includ[...]

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 -zoo m. X-Zoom In : X-Zoom In Now un -zoo m. Un-zoom Returns the display to the previous zoom, or if there has been only o[...]

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 dr aw a box aroun d the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle. 1. If necessary , pr ess to turn o n the menu -k [...]

Aplets and their views 2-13 5 . Pr ess to z oom in on the bo xe d ar ea . To set zoom factors 1. In the P lot v iew , pr ess . 2. P r e s s . 3. S e l e c t Set Factors... and pr es s . 4. Enter the z oom f actor s. T her e is one z oom facto r for the hori z ontal sc ale ( XZOOM ) and one f or the ve rtical sca le ( YZOOM ). Z ooming out m ultipli[...]

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. This is a shortcut for chan ging Plot view settings. For instance, if you have defined a trigonometric function, then you could select Tr ig to plot your func[...]

Aplets and their views 2-15 Split the screen The Plot-Detail view can give you two simultaneou s views of the plot. 1. Pr ess . Selec t Plot-Detail and pr ess . The graph is plot ted twice . Y ou can now z o om in on the r ight si de. 2. P r e s s , selec t the z oom method and pres s or . T his z ooms the r ight si de. Her e is an e x ample of spl[...]

2-16 Aplets and their views 2 . T o mo ve up and do wn the table , use the and c urso r k e y s. T hese k ey s mov e the tra .ce poin t left or r ight alo ng the plot , and in th e table , the corr esponding v alues ar e highlighted . 3 . T o mo ve between functi ons, u se the and c urso r k e ys t o mo ve the c ursor fr om one gr aph 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. H ighligh t the fi eld to edit . Use the arr ow k ey s to mov e from fie l d to fie l d. – If ther e is a number to enter , type it in and pr ess or . T o modify an ex ist[...]

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. Zoom within a table Zooming redraws the table of numbers in greater or lesser detail. ZOOM op[...]

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 inde pendent variable value in the ta ble, use the arrow keys to place the cursor in the independent variable column, then ente r the value to jum p to. Automatic recalculation You can enter any new value in the X c[...]

2-20 Aplets and their views 5 . Ente r the independent values in the le ft -hand column. T y pe i n a number and press . Y ou do not hav e to enter them in order , b ecause the function can r earr ange them. T o inser t a number between tw o oth ers, use . Clear data Press CLEAR , to erase the data from a table. “Build Your Own” menu keys F1 an[...]

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 F unction aple t , spec if y the func tio ns. Select Function 9 9 2 . R eset the gr aph setup t o the def ault s ettings . SE[...]

2-22 Aplets and their views 5 . Displa y the functi ons in numer ic f orm .[...]

Function aplet 3-1 3 F unc tion apl et About the Function aplet The Function aplet enables you to explore up to 10 real-valued, rectangu lar functions y in terms of x . For example . Once you have defined a function you can: • c r eate gr aphs to f ind r oots, in ter cepts, slope , signed ar ea, and e xtrema • cr eate tables to ev aluate functi[...]

3-2 Function aplet Define the expressions 2 . T here ar e 10 functi on def inition f ields on the F unction aplet’s S y mbolic v ie w sc r een . The y ar e labeled F1(X) to F0(X). Highligh t the func tion de f inition f ield y ou w ant to use , and e nter a n e xpr essi on . (Y ou can pr ess to delete an e xis ting line , or CLEAR to clear all li[...]

Function aplet 3-3 Change the scale 6 . Y ou can chan ge t he sca le to see mo r e or l ess of your gr aphs . In this e xam ple , choos e Auto Scale . (S ee “VIEW S menu options ” on page 2 -14 for a de script ion of Aut o Sc a le ) . Select Auto Scale Trace a graph 7 . T r ace the lin ear fu nctio n . 6 times Note: B y defa ult , the tr acer i[...]

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 Functi on aplet (and any Function-based ap lets). The FCN fun ctions act on the currently selected graph. S ee “FCN func[...]

Function aplet 3-5 12 . Ch oose the linear f unctio n wh ose in ter sec tion w ith the quadr atic functi on y ou w ish to f ind . T he coor dinates of the inters ecti on po int ar e display ed at the bottom of the scr een. Note: If ther e is more than one inter secti on (as in our e xam ple) , the coor dinates o f the inter sec tion po int c lose s[...]

3-6 Function aplet 15 . Mo v e the c urso r to b y pr essing the or key . 16 . Pr ess to accept u sing F2(x) = (x + 3) 2 – 2 as the other boundar y for the integr al. 17 . Choos e the end value for x . 2 Th e cu r so r ju mp s to x = –2 on the linear func tion . 18. Display the numerical value of the integral. Note: See “Shading ar ea” o n [...]

Function aplet 3-7 HINT The Root and Extremum functions return one value only even if the function has more than one root or extremum. The function finds the value closest to the position of the cursor. You need to re-l ocate the cursor to find other roots or extrema that may exist. Display the numeric view 20. Di spla y the numer ic v iew . Set up[...]

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 by a factor of 4. No te: NUMZOOM has a setting of 4 . In To change font size 2 7 . Displa y table n umbers in lar ge fo nt . To display the symbolic defin[...]

Function aplet 3-9 Function aplet interactive analysis From the Plot view ( ), you can use the functions on the FCN menu to find r oots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets). See “FCN functions” on pag e 3- 10. The FCN operations act on the currently sele cted graph. The r[...]

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 found, but only an extremum, then the result is labeled EXTR: instead of ROOT: . (The root-finder is also used in the Solve aplet. See also “Interpreting results” on page 7-6.)[...]

Function aplet 3-11 Shading area You can shade a selected area between functions. This process also gi ves you an appro ximate measurement of the area shaded. 1. Open the Functi on aplet. T h e F unction aplet opens in the S ymboli c v ie w . 2 . Selec t the e xpr essi ons w hos e curv es y ou wan t to stu dy . 3 . Pre ss to plot the functi ons. 4.[...]

3-12 Function aplet Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. 1. Open the F unctio n apl et. Sele ct Function 2 . Highlight the line y ou wa nt to us e , and ente r the e xpre ssion . (Y ou can press to delete an e x isting line , or CLEAR to clear all lines .) 2 CHARS ≤ 1 CHARS &g[...]

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 equ ations in which both x and y are defined as functions of t . They take the forms and . Getting started with the Parametric aplet The following example uses the parametric equations Note: This [...]

4-2 Parametric aplet Set angle measure 3 . Set the ang le meas ure to degr ees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT T he P lot Setu p input fo rm has tw o fie lds not inc luded in the Func tion aplet , TRNG and TSTEP . TRNG spec if ie s the r ange of t val u es. TSTEP specif ies th e step value between t value[...]

Parametric aplet 4-3 Overlay plot 8. Plot a triangle graph over the existing circle graph. PLOT 120 Sele ct Overlay Plot A tri angle is displa yed r ather than a c irc le (w ithout c hanging the equation) becaus e the c hanged value o f TSTEP ensur es that points be ing plot ted ar e 120 ° apart instead o f nearl y continuou s. Y ou ar e able to e[...]

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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 the P o lar aplet. Sele ct Polar L ik e the Func tion a plet , the P o lar aplet opens in the S ymboli c v ie w . Define the expression 2 . Def ine the polar equati on . 2 π 2 Specify plot settings 3 . Spec if y the plot settings . In this ex amp[...]

5-2 Polar aplet Explore the graph 5 . Display the P lot v ie w menu k ey labe ls. Th e Pl o t vi ew o p t i o n s av ailable ar e the same as those f ound in the F unction aplet . See “Explor ing the gra ph ” on page 2 - 7 fo r further infor mation . Display the numbers 6 . Dis play the t able of value s fo r θ and R1. Th e Nu m e ric vi ew op[...]

Sequence aplet 6-1 6 Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore sequences. You can define a sequence named, for example, U1 : • in terms of n • in terms o f U1 ( n –1) •i n ter ms of U1 ( n –2) • in ter ms of another sequence , for e xample , U2 ( n ) • in an y combination of the a bo ve . The Seq[...]

6-2 Sequence aplet Define the expression 2 . Define the F i bonacc i sequenc e , in whi c h each ter m (after the f irst tw o) is the sum of the pr eceding t w o terms: , , fo r . In the S ymboli c v iew o f the Sequence aplet , highligh t the U 1 (1) f ield and begin def ining y our sequence . 1 1 Note: Y ou can us e the , , , , and menu k e ys to[...]

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 aple t 7-1 7 Solv e aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable . You defi ne an equation or expression in the symbolic view, then supply valu es for all the variables except one in the nu meric view. Solve works only with real numbers. Note the differences between an equation and a[...]

7-2 Solve a plet 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 16.67 m/sec (60 kph) to 27.78 m/sec (100 kph) in a distan ce of 100 m. The equation to solve is: Open the Solve aplet 1. Open the Solv e aplet. S[...]

Solve aple t 7-3 4. Enter the v alues f or the know n var 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. Sol ve f or the unkno wn v ari able ( A ). T her ef ore , the acceler ation needed to inc r ease the speed of a car fr om 16.6 7 m[...]

7-4 Solve a plet 6. P lot the equati on for v ar iable A . Sel ect Auto Scale 7 . T r ace along the graph r epr esen ting the left side of the equati on until the c ursor nears the inter sec tion . 20 times Note the v alue o f A display ed near the bot tom left corner of the scr een. T he Plo t vi e w pr o v ides a con venie nt wa y to find an appr[...]

Solve aple t 7-5 Use an initial guess You can usually obtain a fa ster and more accurate solution if you supply an estimated valu e for the unknown variable before pressing . Solve starts looking for a solution at the initial guess. Bef ore plo tting, mak e sure the unkno w n var iable is highli ghted in the n umeri c vie w . Plo t the equati on to[...]

7-6 Solve a plet 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. Press to clear the message. Messa ge Con dition Zero The Solve aplet found a point where the value of the equation (or the root of the expression) is zero within the calculator?[...]

Solve aple t 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. Only by checking the information will you know that [...]

7-8 Solve a plet 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. However, we are concerned only with posi tive so lutions, since only positive distance mak[...]

Solve aple t 7-9 5. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial guess for T . Pr ess until the c urs or is at the inters ecti on. Th e t wo po i nt s o f inter sec tion sho w that ther e ar e t w o soluti ons f or this equati on . Ho w ev er , on ly p os i t ive va l u es fo r X m ak e sense , s[...]

7-10 Solve a plet 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 ty pes, such as M 1 (a matrix variable). Home variables All home variables (othe r than those for aplet settings, like Xmin and Ytick ) are globa l , which means they are shared throughout the diffe[...]

Statistics aplet 8-1 8 Statis tic s apl et About the Statistics aplet The Statistics aplet can store up to ten data sets at one time. It can perform one- variab le or two-variable statistical analysis of one or more sets of data. The Statistics aplet starts with the Numeric view which is used to enter data. The Symbol ic view is used to specify whi[...]

8-2 Statistics aplet Open the Statistics aplet 1. Open the St atisti cs aplet and c lear ex isting data b y pr essing . Select Statistics Th e S t at i s t ic s ap l e t starts in the Numer ical view . At an y time the Statisti cs aplet is conf igur ed for o nly one of t wo types of statist ical explorations: on e - var iable ( ) or t w o-v ari abl[...]

Statistics aplet 8-3 Choose fit and data columns 4. Se lect a fit in the S y mbolic setu p vi ew . SETUP - SYMB Sele ct Linear Y ou c a n c re a te up t o five ex p l o ra t io n s o f t wo - va ri ab l e data , named S1 to S5 . I n t h i s exa m p l e, we wi l l cre a t e jus t on e : S1 . 5 . Spec if y the columns that hold the dat a y ou w ant t[...]

8-4 Statistics aplet Setup plot 8. Change the plotting range t o ensur e all the data points ar e plot ted (and select a diff er ent point mar k, 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. Dr aw the r egr essi on curve (a c ur v e to f it the data points). T his dra ws the r egr es[...]

Statistics aplet 8-5 Predict values 13 . T o f ind the pr edi cted s a les f igur e if ad v ertising w er e to go up to 6 minute s: S ( to highli ght Stat-Two ) (to highli ght PREDY ) 6 14. Retur n to the P lot vi e w . 15 . Jum p to the indicat ed point on the r egr essi on line. 6 Observ e the pr edicted y -value in the le ft bottom corner of the[...]

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 ( ). HINT A data column must have at least four data points to provide vali d two-variable stat[...]

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, 1 70cm, 175cm, 180cm. 1. Open the Statistics apl et . Sele ct Statistics 2 . Enter t he measurement data. 160 16 5 17 0 17 5 180 Deletes the currently highlighted value.[...]

8-8 Statistics aplet 3 . Fi nd the mean of the sample. Ensur e the / menu k e y label r eads . Pr ess to see the statistic s calc ulated fr om the sample data in C1 . Note that the title o f the colu mn o f st atis ti cs i s H1 . T here ar e 5 data set de f initions a vailable for one -var iable sta ti st ics: H1–H5 . If data is entered in C1 , H[...]

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 . Disp[...]

8-10 Statistics aplet 5 . Mov e the highli ght bar into the r igh t column of the H1 def i nitio n and r epla ce the frequency v alue of 1 w ith the name C2 . 2 6 . R etur n to the numer ic v ie w . 7 . Ente r the fr equency data sho w n in the abo v e table . 5 3 8 2 1 8. Displa y the computed sta ti stics. The mean height is approxi mately 167.63[...]

Statistics aplet 8-11 Edit a data set In the Numeric view of the Statis tics aplet, highlight the data value to change. T ype a new value and press , or press to copy the value to the edit line for modification. Pr ess after modifying the value on the edit line. Delete data • T o delete a single data item, hi ghlight it and pr ess . T he value s [...]

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 Numer ic v ie w , make sur e is set . 2 . Di spla y the S ymboli c v ie w . 3 . Highli ght the F it expr essi on ( Fit1 , etc.) f or the desir ed data set. 4. T yp e in an e xpr es sion a nd pr es s . The independent variable must be X , and the e xpr ession mu st not cont ain any unkn o wn v aria [...]

8-14 Statistics aplet When the data set contains an odd number of values, the data set’s median value is no t us ed when calculating Q1 and Q3 in the ta ble above. For exa mple, for the following data set: { 3,5,7,8,15,16,17 } only the first three items, 3, 5, and 7 are used to calculate Q1, and only the last three ter ms, 15, 16, and 17 are used[...]

Statistics aplet 8-15 Plotting You can p lot: • histogr ams ( ) • bo x -and-whisk er plots ( ) • sca tte r pl ots ( ) . Once you have ente red your data ( ), defined your data set ( ), and defined your Fit mod el for two- variable statistics ( SETUP - SYMB ), you can plot your data. You can plot up to five scatter or box -and-whisker plots at[...]

8-16 Statistics aplet 3 . Fo r any plot , but espec iall y f or a histogr am, adj ust the plotti ng scale a nd r ange i n the Plot Setup v iew . If yo u find histogr am bars too fat or too thin, y ou can adju st them b y adj usting the HWIDTH setti n g. 4. Pr ess . If y ou hav e not adj ust ed the Plot S etup y ours elf , yo u can try sel e ct Auto[...]

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). See “To choose the fit” on page 8-12. The e xpre ssion in Fit2 sho ws[...]

8-18 Statistics aplet HINT In order to access the CORR and RELERR 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. Setting up the plot (Plot setup view) The Plot Setup view ( SETUP - PLOT ) set[...]

Statistics aplet 8-19 • T he cor r ect or menu labe l on (Numer ic vi ew ) . • T he corr ect fit (r egre ssion model), if the data set is tw o -v ar ia ble . • Only the data sets to compute or plot are chec kmark ed (S ymbolic v ie w) . • T he corr ect plotting r ange. T r y using A uto Scale (instead o f ) , or adju st the plotting par ame[...]

8-20 Statistics aplet Calculating predicted values The functions PREDX and PREDY estimate (predict ) values for X or Y given a h ypothetical 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. Find predicted values 1. In P lot v ie w , dra w the regr essi on c urve[...]

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 P RED Y function uses the most recently calculated curve. In order to avoid errors with th is function, uncheck all fits except the [...]

[...]

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. Based on the statistics from one or two samples, you can test hypotheses and find confidence intervals for the following quanti[...]

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 test s, you can choose the alternative hypothesis to test against the null hypothesis. For each test, th ere are three possible choices for an alternative hypothesis based on a quantitative [...]

Inference aplet 9-3 Select the inferential method 2. Select the Hypothesis Test inferential 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 stat istics and population parameters. setup-NUM The table below lists the fields in this view for our curren[...]

9-4 Inferenc e aplet By default, each field already contains a value. These values constitu te the example database and are expla ined in the feature of this ap let. Display on-line help 6. To display the on-line help, press 7. To close the on-line help, press . Display test results in numeric format 8. Display the test results in numeric format. T[...]

Inference aplet 9-5 A calculator produces the following 6 ran dom numbers: 0.529, 0.295, 0.95 2, 0.259, 0.925, a nd 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. Enter data 2. In the C1 column, enter the random number s produced by the c[...]

9-6 Inferenc e aplet Open Inference aplet 6. Open the Inference aple t and clear cu rrent settings . Select Inference Select inference method and type 7. Select an inference method. Select CONF INTER VAL 8. Select a distribution statistic type. Select T-Int: 1 µ Set up the interval calculation 9. Set up the interval calculation. Note: The default [...]

Inference aplet 9-7 Import the data 10. Import the data from the Statistics aplet. Note: The data from C1 is disp layed by default. Note: Press to see the statistics before importing them into the Numeric Setup view. Also, if there is more than one ap let based on the Statistics aplet, you are prompted to choose one. 11. Specify a 90% confidence in[...]

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 calc ulate 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 measu res the strength of the evidence for a selected hypothesis against the null hypothesis . The null hypothesis is that the mean of the two populations are equal (H 0 : µ 1= µ 2).[...]

9-10 Inferenc e aplet 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. The null hypothesis is that the proportion of su ccesses in the two populations is equal: H 0 : π = π 0 Y[...]

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 fr om two samples, each from a different population, the Two-Proportion Z-Test measures the stre ngth of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that[...]

9-12 Inferenc e aplet 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 i s not know n. On the basis of statistics from a single sample, this tes t measures the strength of the evidence for a selected hypothesis against the nu ll hypothesis. [...]

Inference aplet 9-13 Inputs The inputs are: Results The results are: Field name Definition 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. Prob Probability associated with the T-Test statistic. Critical T Boundary value of T assoc iated[...]

9-14 Inferenc e aplet Two-Sample T-Test Menu name T-Test: µ 1 – µ 2 The Two-sample T-Test is used when the population standard deviation i s 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. The [...]

Inference aplet 9-15 Results The results are: Confidence intervals The confi dence interv al calcul ations that the hp 39g+ can perform are based on the Normal Z-distribution or Student’s t-distribution. One-Sample Z-Interval Menu name Z-INT: µ 1 This option uses the Normal Z-distributio n to calculate a confidence interval for m, the true mean [...]

9-16 Inferenc e aplet 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. Inputs The inputs are: Results T[...]

Inference aplet 9-17 One-Proportion Z-Interval Menu name Z-INT: 1 π This option uses the Normal Z-distributio n to calculate a confidence interval for the proportion of successes in a population for the case in wh ich a sample of si ze, n , has a number of successes, x . Inputs The inputs are: Results The results are: Two-Proportion Z-Interval Men[...]

9-18 Inferenc e aplet Results The results are: One-Sample T-Interval Menu name T-INT: 1 µ This option uses the Student’s t-distribution to ca lculate a confidence interval for m, the true mean of a population, for the case in which the true population standard deviation, s, is unknown. Inputs The inputs are: n1 Sample 1 si ze. n2 Sample 2 si ze.[...]

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, s1 and s2, are unknown. Inputs The inputs are: Result D[...]

9-20 Inferenc e aplet Results The results are: Result Description Critical T Critical value for T. µ Min Lower bound for µ 1 – µ 2 . µ Max Upp er bound for µ 1 – µ 2 . ∆ ∆[...]

Using th e Finance So lver 10-1 10 Using the Finance Solver The Finance Solver, or Fin ance 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 m enu key to activate the aplet. The resulting screen shows the differen[...]

10-2 Using t he Finance Sol ver Financial calculations involvin g 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. A dollar today can be inv es[...]

Using th e Finance So lver 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. As these cash-flow diagrams imply, there are five TVM variables: PV 1 23 4 5 FV Capital iz e d value of lease [...]

10-4 Using t he Finance Sol ver Performing TVM calculations 1. Launc h the F inanc ial So lv er as indicated at the beginning of this secti on. 2 . Use the ar r o w ke ys to highligh t the diffe r ent f ields and enter the kno wn v ari ables in the TVM calc ulations , pr essing the soft -menu k e y af ter enter ing each kno wn value . Be sur e that[...]

Using th e Finance So lver 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. The purchase price of the car is $19,500, and the down payment is $3,000. What are the required monthly p a y m e n t s ? W h a t i s t h e l a r g e s t l o a n y o u c a n a f f o[...]

10-6 Using t he Finance Sol ver Example 2 - Mortgage with balloon payment Suppose you have taken o ut a 30-year, $150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repaying the loan in a b alloon payment. Find the size of the balloon payment -- the value of the mortgage after 10 years of payment. Solution. Th[...]

Using th e Finance So lver 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 indicated at the beginning of t h is sect ion. 2 . Set the f ollo w ing [...]

10-8 Using t he Finance Sol ver 3 . Pres s the soft menu k ey to amorti z e the new batch o f pay ments. Repeat st eps 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. First, press the soft menu key. Then, keeping 120 in the PAY[...]

Using mathemati cal functions 11-1 11 Using math ematical 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. on the MATH menu) contains functions for working with probabili[...]

11-2 Using math ematical functions 2 . The list o f func tions (on the r ight) appli es to the c urr entl y highligh ted category (on the left). Use and to sw itch between the categor y list and the func tion lis t . 3 . Highlight the name of the func tio n yo u wa nt and pr ess . This copi es the fu nctio n name (and an initial par enthesis, if ap[...]

Using mathemati cal functions 11-3 Keyboard functions The most frequently used functions are availa ble directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. ,, , Ad d, Subtract, Multiply, Di vide. Also ac cepts complex numbers, lists and matrices. va l ue 1 + va l u e 2 , etc. e x Natural exponential.[...]

11-4 Using math ematical functions 10 x Exponential (antilogarithm). Also accepts complex numbers. 10^ val u e Example 10^3 r eturns 1000 Common logarithm. Also accepts co mplex numbers. LOG ( val ue ) Example LOG(100) r eturns 2 ,, Sine, cosine, tangent. Inputs and outputs depend on the current angle format (Degrees, Radi ans, or Grads). SIN ( val[...]

Using mathemati cal functions 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 acce pts complex numbers. ATAN ( valu e ) Example ATAN(1) re t u rn s 45 (D egr ees mode) . Square. Also accept s complex numbers. va l ue 2 [...]

11-6 Using math ematical functions Takes the n th root of x . ro ot NTHROOT va lu e Example 3 NTHROOT 8 r eturns 2 Calculus functions The symbols for differentiation and integration are available directly form the k eyboard— and S respectively—as well as from the MATH menu. Differentiates expr ession with respect to the variable of differentiat[...]

Using mathemati cal functions 11-7 TAYLOR Calculates the n th order Taylor polynomial of expression at the point where the given variable = 0. TAYLOR ( e xpre ssion , v ari able , n ) Example TAYLOR(1 + sin(s1) 2 , s1,5) w ith R adians angle measur e and F rac tion n u mber f ormat (s et i n MODE S) r etur ns 1+s1^2-1/3*s1^4 . Complex number functi[...]

11-8 Using math ematical functions Constants The hp 39g+ has an internal numeric repr esentation 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. Internally represented as 9.99999999999 x 10 499 . MAXREAL MINREAL Minimum real nu[...]

Using mathemati cal functions 11-9 TANH Hyperbolic 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. EXP ( val u e ) EXPM1 Exponent minus 1 : . This is more[...]

11-10 Using mathe matical functions RECURSE Provides a method of defini ng a sequence without using the Symbolic view of the Seque nce aplet. I f used with | (“where”), RECURSE will step through the evaluation. RECURSE( seq uencename , ter m n , ter m 1 , term 2 ) Example RECURSE(U,U(N-1)*N,1,2) U 1(N) St or es a f actor ial-calculating f uncti[...]

Using mathemati cal functions 11-11 POLYEVAL Polynomial evaluation. Evaluates a polynomial with the specified coefficients for the value of x . POLYEVAL([ coeff ici ents ] , va l u e ) Example Fo r x 4 +2x 3 –25x 2 –26x+120 : POLYEVAL([1,2,-25,-26,120], 8) re t u r n s 3432 . POLYFORM Polynomial form. Creates a polynomial in v ariable1 from exp[...]

11-12 Using mathe matical functions Probability functions COMB Number of combination s (without regard to order) of n things taken r at a time: n!/(r!(n-r)) . COMB (n, r) Example COMB(5,2) r eturns 10 . T h at is, ther e are te n differ ent wa ys that fi ve things can be comb ined two at a time .! Factorial of a positive integer. For non-integers, [...]

Using mathemati cal functions 11-13 UTPF Upper-Tail Snedecor’s F Probability given numerator degrees of freedom and denominator degre es of freedom (of the F distribution), evaluated at value . Returns the probability that a Snedecor 's F random variable is greater than value. UTPF ( numerator , de nomina tor , val u e ) UTPN Upper-Tail Norm[...]

11-14 Using mathe matical functions FNROOT Function root-finder (lik e 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 x pr essi on , var iable , guess ) Example FNROOT(M*9.8/600-1,M,1) r eturns 61.2244897959 . FRAC Fractional part. FRAC ( val ue [...]

Using mathemati cal functions 11-15 MAX Maximum. The greater of two values. MAX ( val u e 1 , val u e2 ) Example MAX(210,25) r eturns 210 MIN Minimum. The lesser of two values. MIN ( val u e 1 , val u e2 ) Example MIN(210,25) re t u r n s 25 MOD Modulo. The remainder of value1 / value2 . va l ue 1 MOD va l u e 2 Example 9 MOD 4 r etur ns 1 % x perc[...]

11-16 Using mathe matical functions ROUND Rounds value to decimal places . Accepts complex numbers. ROUND ( val ue , places ) Round can also round to a number of significant digits as showed in example 2. Examples ROUND(7.8676,2) r eturns 7.68 ROUND (0.0036757,-3) r eturns 0.00368 SIGN Sign of value . If positive, the result is 1. If negative, –1[...]

Using mathemati cal functions 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). You will find the symbols for the symbolic functions = and | ( where ) in the CHARS menu ( CHARS ) as well as the MATH [...]

11-18 Using mathe matical functions QUOTE Encloses an expression that should not be evaluated numerically. QUOTE( exp re s s io n ) Examples QUOTE(SIN(45)) F1(X) stor es t he e xpre ssion S IN(4 5) r a ther than t he value of SIN( 45 ) . Another meth od is to enclo se the e xpr ession in single quotes. Fo r e xa m p l e, X^3+2*X F1(X) puts the e xp[...]

Using mathemati cal functions 11-19 ≥ Greater than or equal to. Returns 1 if true, 0 if false. va l ue 1 ≥ va l u e 2 AND Compares value1 and value2 . Returns 1 if they are both non-zero, otherwise returns 0. va l ue 1 AND va l u e 2 IFTE If expression is true, do the trueclause ; if not, do the falseclause. IFTE( e xpressi on , truec lause , f[...]

11-20 Using mathe matical functions SEC Secant: 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. In HOME When you perform calculations tha t contain normal variab[...]

Using mathemati cal functions 11-21 Symbolic calculations in the Function aplet You can perform symbolic operations i n the Function aplet’s Symbolic view. For example, to find the derivative of a function in the Function aplet’s Symbolic view, you define two functions and define the second function as a derivative of the first function. You th[...]

11-22 Using mathe matical functions 3 . Sho w 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 derivati ve of the first function. For example, to differentiate : 1. Access the F uncti[...]

Using mathemati cal functions 11-23 To find the indefinite integral using formal variables F or ex ample, to f ind t he ind ef inite i ntegral of use: 1. Enter the func tion . 0 S1 3 X 5 X 2 . Sho w the r esult for mat. 3 . Press to close the sho w w indow . 4. Copy the r esult and eva l u a te. Th us , substit uting X for S1, it can be seen th at:[...]

11-24 Using mathe matical 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. x 0 =[...]

Variables an d memory manage ment 12-1 12 V ar iables and memor y manag ement Introduction The hp 39g+ has approximately 232K of user memory. 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. The hp 39g+ has t[...]

12-2 Variables and memory managemen t Storing and recalling variables You can store numbers or expressi ons from a previous 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. Numeric precision in the display, however, de pends on the display mode (Standar[...]

Variables an d memory manage ment 12-3 5 . Enter a name f or the v ar iable . A 6. P re s s to st or e the r esult . 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 . A To use variables in calculations You can use v[...]

12-4 Variables and memory managemen t The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organi sed by category. For each variable category in the left column, there is a list of variables in the right colu mn. You select a variable category and then select a variable in the category. 1. Open the V A RS [...]

Variables an d memory manage ment 12-5 5 . Choos e whether t o place the var iable name or the v ari able v alue on the command line . – Pr ess to indicate that y ou want the v ari able ’s c ontents t o appear on the command line . – Pr ess to indicate that y ou want the v ari able ’s name to appear on the command line . 6 . Pres s to place[...]

12-6 Variables and memory managemen t 4. Enter data for L2 . 55 48 86 90 77 5. P re s s to access HO ME . 6 . Open the v ar iable men u and selec t L1. 7 . Cop y it to the c ommand line . Note: Because the option is hi ghlighted , the var iable ’s name , r ather than its contents , is copied to the command line . 8. Insert the + operato r and sel[...]

Variables an d memory manage ment 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. You cannot store mat rices in va riab les other than M0 to M 9. Ca te- gory [...]

12-8 Variables and memory managemen t Aplet variables Aplet variables store values that are unique t o a particular aplet. These include s ymbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections. See the Reference Information chapter for more inform[...]

Variables an d memory manage ment 12-9 6 . T o copy the v alue of the v ar iable in to the edit line , pres s and pr ess . 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. For example, if the available memory is low, you can use the Memor[...]

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Matrices 13-1 13 M atrices Introduction You can perform matrix calc ulation s in HOME and in programs. The matrix and each row of a matr ix appear in brackets, and the elements and rows are separated by commas. For example, the following matrix: is displayed in the history as: [[1,2,3],[4,5,6]] (If the Decimal Mark mode is set to Comma , then separ[...]

13-2 Matr ices Creating and storing matrices You can create, edit, delete, send, and receiv e matrices in the Matrix catalog. To open the Matrix catalog, press MATRIX . You can also create and store matrices—named or unnamed—-in HOME. For example, the command: POLYROOT([1,0,–1,0]) X M1 stores the root of the c omplex vector of length 3 into t[...]

Matrices 13-3 To create a ma trix in the Matrix Catalog 1. Press MA TRIX to open the Matr i x Catalog . The Matri x catalog lists the 10 av ailable matri x var iables, M0 to M9 . 2 . Highli ght the matr i x var iable name y ou want to use and pres s . 3 . Select the ty pe of matr ix to cr eate . – For a vector (one -d imensional array) , sele ct [...]

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 calculato rs just as you can send aplets, programs, lists, and notes. 1. Align the hp 3 9 g+ calc ulators ’ infr ared po rts. 2 . Open the Matri x catalogs on both[...]

Matrices 13-5 To display a matrix • In the Matri x catalog ( MATRIX ) , highlight the matri x name and pr ess . • In HOME , ent er the name of the matr ix v ar iable and pr ess . 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 . To create a ma trix in HOME 1. Enter th[...]

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. Matrix arithmetic You[...]

Matrices 13-7 3 . Add the matr ices that yo u cr e 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 scalar can be real or complex. For example, to divide the result of the previous[...]

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 matri x INVERSE command. Enter INVERSE ( ma trixn ame ) in HOME and press . To n[...]

Matrices 13-9 4. Create a ne w matri x. Sele ct Real matrix 5 . Enter the equati on coeff ic ients. 23 4 11 1 4 12 In this e x ample , the matri x you c reat ed is listed as M2 . 6 . Retur n to HOME and e nter the calc ulation to left-multipl y the constants v ector b y the in ve rse o f the coeff ic ien ts matr i x . M2 x –1 M1 The result is a v[...]

13-10 Matr ices • F unction s al wa ys pr oduce and displa y a re sult. T he y do not c hange any st or ed var iables , such as a matri x va ria b le. • F unctions ha v e ar guments that ar e enc losed in pare ntheses and separ ated by commas; f or e xample , CROSS ( vect or 1 , ve c to r 2 ) . The matr ix in put can be either a matr ix v ar ia[...]

Matrices 13-11 DET Determinant of a square matrix . DET ( matr ix ) DOT Dot Product of two arrays, matrix1 matrix2 . DOT ( matr ix1, matr i x2 ) EIGENVAL Displays the eigenvalue s in vector form for matrix . EIGENVAL ( matr ix ) EIGENVV Eigenvectors and Eige nvalues for a squa re matrix . Displays a list of two arra ys. The first contains the eigen[...]

13-12 Matr ices calculation for each element substitutes the current row number for I and the current column number for J. MAKEMAT ( ex p re s s i o n , rows , columns ) Example MAKEMAT(0,3,3) r eturns a 3×3 z er o matri x, [[0,0,0],[0,0,0],[0,0,0]] . QR QR Factorization. Factors an m × n matrix into three matrices: {[[ m × m orthogonal ]],[[ m [...]

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 ( matr ix ) SVL Singular Values. Returns a vector containing the singular values of matrix. SVL ( matr ix ) TRACE Finds the trace of a square matrix. The trace is e[...]

13-14 Matr ices 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. M2 is used in this example. The reduced[...]

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 o f real numbers such as {1,2,3} . (If the Decimal Mark mode is set to Comma , then the separators are periods.) Lists re[...]

14-2 Lists 3 . E nter th e val ues you want in t he li st, pressi ng after each one. V alue s can be r eal or comple x numbers (o r an expr ession) . If you enter a calc ulation , it is e valuated and the r esult is inserted in the list . 4. When done , pr ess LIST to se e the List catalog, or pr ess t o re turn to HO ME . List catalog keys The lis[...]

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 t he edit l ine . Start and end the list w ith br aces (the shifted and ke y s) and separ ate each element with a comma. 2. P r e s s to ev aluate and display the list . Immediatel y after typ ing[...]

14-4 Lists Displaying and editing lists To display a list • In the L ist catalog, hi ghlight the list name and pr ess . • In HOME , ente r the name of the list and pr ess . To display one element In H OME, enter listname ( element# ). For example, if L2 is {3,4,5,6}, then L2(2) returns 4 . To edit a list 1. Open the List catalog. LIST . 2. P r [...]

Lists 14-5 To insert an element in a list 1. Open the List catalog. LIST . 2. P r e s s or to highli ght the name of the list y ou wan t to edit (L1, etc .) and pre ss to displa y the list conten ts. New elements ar e inser ted abov e the highlighted positi on . In this example, an element, with the value of 9, is inserted between the first and sec[...]

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 CLEA R . Transmitting lists You can send lists to calculators or PCs just[...]

Lists 14-7 • If Dec i mal Mark in Mode s is set to Comma , use peri ods to separa te ar guments. F or e xample , CONCAT(L1.L2) . Common operators like +, –, ×, and / c an take lists as arguments. I f there ar e two ar guments and both ar e lists, then the lists must have the same length, since the calculation pairs the elements . If there are [...]

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 l e , be gin , end , incr ement ) The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression. Examp[...]

Lists 14-9 SIZE Calculates the number of elements in a list. SIZE( list ) Also works with matrices. Σ LIST Calculates the sum of all elements in list. Σ LIST( list ) Example Σ LIST({2,3,4}) ret u r n s 9 . SORT Sorts ele ments in a scending orde r. SORT( list ) Finding statistical values for list elements T o f i n d v a l u e s s u c h a s t h [...]

14-10 Lists 2 . In HOME , stor e L1 into C1. Y o u w ill then be able to see the list dat a in the Numer ic v ie w of the S tatisti cs apl et. L1 C1 3 . Start the Statis tic s aplet , and selec t 1-var ia ble mode (pr ess , if necessary , to display ). Sele ct Statistics Note: Y ou r list values ar e no w in column 1 (C1) . 4. In t h e Sy mb ol ic [...]

Notes and sketches 15-1 15 Notes and sk etc h es Introduction The hp 39g+ has text and picture editors for entering notes and sketc hes. • E ach aplet has its o wn independent Note v ie w and Sk etc h vi e w . Not es and sk etc hes that y ou c r eate in these vi e ws ar e assoc iated w ith t he aplet. When y ou sa v e the aplet , or send it to an[...]

15-2 Notes and sketches Note edit keys Key M e a n i n g Space key for text entry. Displays next page of a multi- page note. Alpha-lock for letter entry. Lower-case alpha-loc k for letter entry. Backspaces cursor and deletes character. Deletes current character. Starts a new line. CLEAR Erases the entire note. Menu for entering variable names, and [...]

Notes and sketches 15-3 Aplet sketch view You can attach pictures to an aplet in its Sketch view ( SKETC H ). Y our wor k is aut omaticall y sav ed w ith the aplet . Press an y other vi ew k e y or to e xit the Sk etch v ie w Sketch keys To dr aw a li ne 1. In an aplet, pr ess SKETCH fo r the Sketc h v ie w . 2 . In Sk etch v ie w , pres s and mo v[...]

15-4 Notes and sketches To draw a box 1. In Sk etc h v ie w , pr ess and mov e the cur sor to wher e you w ant any corner of the bo x to be. 2. P r e s s . 3 . Mov e the cu rsor to mar k the opposite corner fo r the bo x . Y ou can adj ust the si z e of the bo x b y mo ving the cu rs o r . 4. Pres s to f inish the bo x . To draw a circle 1. In Sket[...]

Notes and sketches 15-5 To label parts of a sketch 1. Pres s and type the te xt on the edit line . T o lock the Alpha shift on , pre ss (for upper case) or (for lo w er case). T o mak e the label a smaller c har act er si z e , turn o f f befo r e pres sing . ( is a toggle betw een small and lar ge font si z e) . The smaller c har acter si z e cann[...]

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 iew o f th e aplet ( SKETCH ). T he graphi c w ill be copied her e. 2 . Press , . 3 . Highlight Graphic , then pr ess and highligh t the name of the v ari able ( G1 , etc.) . 4. Pres s to r e[...]

Notes and sketches 15-7 4. W rite y our note . See “Note e dit k ey s ” on page 15- 2 fo r mor e infor mation on the entry and editing of notes. 5 . When you ar e finished, press or an aplet ke y to e xit Notepad . Y our wor k is automati cally s av ed. Notepad Catalog keys Key M e a n i n g Opens the selected note for editing. Begins a new not[...]

15-8 Notes and sketches To import a note You can impo rt a note from the Notepad i nto an aplet’s Note view, and vice versa. Supp ose you want to copy a note named “Assignments” fr om the Notepad into the Function Note view: 1. In the Func tion aplet , displa y the Note v iew ( NOTE ). 2 . Pres s , highlight Note pad in the left column, then [...]

Programming 16-1 16 Pr ogramming Introduction This chapter describes how to pro gram using the hp 39g+. In this chapter you’ll learn about: • using the Pr ogram catalog to c r eate and edit pr ogr ams • pr ogr amming commands • stor ing and retr ie v ing v ari ables in pr ograms • pr ogr amming var iables. HINT More informatio n on progra[...]

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 progr am, the task can be simple—or it can be di vided further into other programs that perform smaller tasks. Program catalog The Program catalog is wher e you create, edit[...]

Programming 16-3 Program catalog k eys 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. Receives the highlighted program from another hp 39g+ or from a disk drive. Runs the h[...]

16-4 Programming Creating and editing programs Create a new program 1. Pr ess PROGRM to open the Pr ogr am catalog . 2. P r e s s . The hp 3 9 g+ prompts yo u f or a n a m e. A pr ogr am name can contain spec ial char acters , such as a space . Ho we ver , if yo u use spec ial char acter s and then run the pr ogram b y typ ing it in HOME , y ou mus[...]

Programming 16-5 2 . On the left , us e or to hi ghlight a command category , then pres s to access the commands in the category . Select the command that y ou w ant . 3 . Pres s to paste the command into the pr ogr am editor . Edit a program 1. Pres s PROGRM to open the Pr ogram catalog. 2 . Use the ar r ow k ey s to highligh t the pr ogr am y ou [...]

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. Display s previous page of th e program. Displays next page of the program. Moves up or down one line. Moves right or left one character. Alpha-lock for letter entry. Press A...Z to lock lower case. Backspaces c[...]

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. If you start the program from HOME, the hp 39[...]

16-8 Programming Copy a program You can use the following procedure if you want to make a copy of y our work before editing—or if you want to use one program as a template for another. 1. Pr ess PROGRM to open the Pr ogr am catalog . 2. P r e s s . 3 . T ype a ne w file name , then ch oose . T he Progr am E ditor opens with a ne w progr am. 4. Pr[...]

Programming 16-9 Delete a program To delete a program: 1. Press PRO GRM to open the Pr ogram catalog . 2 . Highli ght a pr ogram to de lete , then pr ess . Delete all programs You can delete all programs at once. 1. In the Progr am catalog , pr ess CLEAR . 2. P r e s s . Delete the contents of a program You can clear t he contents of a program with[...]

16-10 Programming 4. D ev elop a progr am that uses the SE T VIEW S command to modify the aplet’s VIEW S menu . The menu opti ons pr o v ide links to ass oc iated pr ogr ams. Y ou can spec i fy an y other pr ograms that y ou want transfer r ed with the aplet. See “SETVI EW S” on page 16 - 14 f or infor mation on the command . 5 . Ensure that [...]

Programming 16-11 Save the aplet 1. Open the F uncti on aplet and sa ve it as “EXP ERIMENT ” . The ne w aple t appears in the A plet library . Select Function EXP ERIMENT 2 . Create a pr ogram called EXP .ME1 w ith contents as show n. T his pr ogr am conf igur es the plot r anges, then r uns a pr ogr am that allo ws y ou to s et the angle f orm[...]

16-12 Programming 6 . Open the Pr ogram cat alog and cr eate a pr ogr am named “EXP .S V” . Inc lude the follo wing code in the pr ogr am. E a c h entry line after the command SETVIEW S is a tri o th at consists of a VIEW S menu te xt line (a space indicate s none), a progr am name , and a number that def ines the vi ew to go to after the pr og[...]

Programming 16-13 ’ ’ ’ ’ ;’ ’ EXP.ANG’ ’ ;0; The pr o gr am EXP .ANG is a sma ll ro utine that is called by other pr ogr ams that the aplet u ses . This e ntry spec ifi es that the pr ogr am EXP.ANG is tr ansferr ed when the aplet is tr ansfer r ed , but the space in the fi rst q uotes en sur es that no entry 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. T hen a checkmar k would appear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view. CHECK n : SELECT Selects the named aplet and ma [...]

Programming 16-15 options u se , or the pr ogram that def ines the aplet’s VIEW S menu . • Y ou can inclu de a “Start ” optio n in the VIEW S menu to spec if y a pr ogr am that y ou w ant to r un auto maticall y when the aplet s tarts. This pr ogram typically sets up the aplet’ s initial configur ation . The S T AR T optio n on the menu i[...]

16-16 Programming ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected. All pr ograms that are identified in the aplet’s SETV IEWS command are transferred when the aplet is transmitted. ViewNumber V iewNumber is the number of a view to start after the program finishes runn ing. For example, if[...]

Programming 16-17 View numbers The Function aplet views are numbered as follows: UNCHECK Unchecks (unselects) the co rresponding function in the current aplet. For example, Uncheck 3 would unc heck F3 if the current aplet is Function. UNCHECK n : Branch commands Branch commands let a progr am make a decision based on the result of one or more tests[...]

16-18 Programming IF... THEN... ELSE... END Executes the true-claus e sequence of commands if the test- clause is true, or the false-clause se quence of commands if the test-clause is false. IF test-clause THEN true-clause ELSE false-clause END Example 1 X A : IF A==1 THEN MSGBOX "A EQUALS 1" : ELSE MSGBOX "A IS NOT EQUAL T O 1"[...]

Programming 16-19 RUN Runs the named program. If your program name contains special characters, such as a space, then you must enclose the fi le name in double quotes (" "). RUN " pr ogram name " : or RUN pr ogr amname : STOP Stops the current program. STOP : Drawing commands The drawing commands act on the display. The scale of[...]

16-20 Programming ERASE Clears the display ERASE: FREEZE Halts the program, freezing the current display. Execution resumes when any key is pressed. LINE Draws a line from (x1, y1) to ( x2, y2 ) . LINE x1; y1; x2 ; y2: PIXOFF Turns off the pixel at the specified coordinates (x,y) . PIXOFF x;y : PIXON Turns on the pixel at the specified coordinates [...]

Programming 16-21 → DISPLAY Displays graphic from graphicname in the display. → DISPLAY gr aphi cname : → GROB Creates a graphic from expres sion , using font_size , and stores the resulting graphic in graphicname . Font sizes are 1, 2, or 3. If the fontsize argument is 0, the hp 39g+ creates a graphic display li ke that created by the SHOW o[...]

16-22 Programming → PLOT Puts graph from graphicname into the Plot view display. → PLOT gr aphicname : REPLACE Replaces portion of graphic in graphicname1 with graphicname2 , s tarting at position . REPLACE also works for lists and matrices. REPLACE gr aphi cname1 ; ( position ) ; gr aphi cname2 : SUB Extracts a portion of the named graphic (or[...]

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 lo op-clause is not executed if the test is initially false. Its syntax is: WHILE test- claus e REPEAT loop-c[...]

16-24 Programming DELCOL Delete Column. Deletes the specified column from the specified matrix . DELCOL name ; c olumn_number : DELROW Delete Row. Deletes the spe cified row from the specified matrix. DELROW nam e ; row _ n u m b e r : EDITMAT Starts the Matrix Editor and displays the specified matrix. If used in programming, return s to the progra[...]

Programming 16-25 SUB Extracts a sub-object— a portion of a list, matrix, or graphic fro m 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 lists, or an ordered pair, ( X,Y ), fo r graphics. SUB name ; obj ect ; star t ; end : SWAPCOL Swaps Columns . Exchanges [...]

16-26 Programming CHOOSE Creates a choose box, which is a box co ntaining a list of options from which the user chooses one. Each option i s numbered, 1 through n . The result of the choose command is to store the number of the option chosen in a variable. The syntax is CHOOSE def ault_option_number ; title ; optio n 1 ; optio n 2 ; ... option n : [...]

Programming 16-27 Examples 5.152000 X DAT E( sets the date to Ma y 15, 2000) . 10.1500 X TIME (sets the time t o 10:15 am) . EDITMAT Matrix Editor. Opens the Matrix editor fo r the specified matrix. Returns to the program when user presses EDITMAT matr i xname : The EDITMAT command can also be used to create matrices. 1. Press CMDS 2. P r e s s M 1[...]

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 e xpressions and quoted strings of text. The expressions are evaluated and turned into strings of text. For example, "AREA IS:" 2+ 2 becomes [...]

Programming 16-29 Stat-One commands DO1VSTATS Calculat es STAT S using datasetname and stores the results in the corresp onding variables: N Σ , Tot Σ , Mean Σ , PVar Σ , SVar Σ , PSDev, SSDev, Mi n Σ , Q1, Median , Q3, and Max Σ . Datasetname can be H1 , H2, ..., or H5. Datasetname must include at least two data points. DO1VSTATS datasetnam[...]

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 keep the s ame valu es in HOME and in aplets. Aplet variables are those whose values depend on the current aplet. The aplet [...]

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 a n off. In a program, type 1 X Coord —to tur n coor din ate displa y on (defa ult). 0 X Coord —to tur n coor dinate display o ff . Extremum F[...]

16-32 Programming Hwidth Statistics Sets the width of histogram bars. From Plot Setup in 1VAR sta ts set a value for Hwidth or In a program, type n X Hwidth Indep All Aplets Defines the value of the inde pendent variable us ed 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 NR NG . or In a program, type X Nmin X Nmax wh e re Recenter All Ap lets Recenters at the crosshairs locations when zooming. From Plot-Zoom-Set Factors, check[...]

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 —f or simultaneous gr aphing. 0 X Simult —f or sequential gr aphing. Slope Function Contains the last value foun[...]

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 TR NG . or In a pr ogr am , type X Tmin X Tmax wh e re Tracing All Ap lets Turns the tracing mode on or off in P lot view. In a program, type 1 X Tracing —to [...]

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. From the Plot Setup input form, enter a value for Ytick . or In a program, typ[...]

Programming 16-37 Xzoom All Ap lets Sets the horizontal zoom factor. From Plot-ZOOM-Set Factors, enter the value for XZ OOM . or In a program, type n X XZOOM wh e re Yzoom All Ap lets Sets the vertical zoom factor. From Plot-ZOOM-Set Factors, enter the value for YZ OOM . or In a program, type n X YZOOM Symbolic-view variables Angle All Ap lets Sets[...]

16-38 Programming R1...R9, R0 Polar Can contain any expression. In dependent variable is θ . Example '2*SIN(2* θ )' X R1( θ ) U1...U9, U0 Sequence Can contain any expression. In dependent variable is N. Example RECURSE (U,U(N-1)*N,1,2) X U1(N) E1...E9, E0 Solve Can contain any equation or expression. Independent variable is selected by[...]

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 column s of data. Can contain lists. Enter da ta in th e Numeric view or In a program, type LIST X C n wh e re n = 0, 1, 2, 3 ... 9 Digits All Ap [...]

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 exce pt Statistics aplet Sets the column to be highlighted in Numeric view. In a program, type n X NumCol where n can be 0 [...]

Programming 16-41 NumStep Function Parametric Polar Sequence Sets the step size (increment value) for an independent varia ble in N umeri c view. From Num Setup, enter a value for NU MSTEP . or In a program, type n X NumStep wh e re NumType Function Parametric Polar Sequence Sets the table format. From Num Setup, choose Automatic or Build You r Own[...]

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 variables are availa ble in Sketch view. Page All Aplets Sets a page i n a sketch set. A sketch set can c ontain up to 10 graphics. The graphic[...]

Extending aplets 17-1 17 Extending aplets Aplets are the application environments where you explore different clas ses of mathematical operations. You can extend the capability of the hp 39g+ in the following ways: • Cr eate ne w aplets , based on e x isting aplets, w ith spec ifi c conf igur ations suc h as angle measure , gr aphical or tabular [...]

17-2 Ext ending aple ts 1. Open the Solv e aplet and save it under the n e w name . Solve | T R I A N G L E S 2 . En t er t h e fo u r fo rmu l as : θ O H θ A H θ OA AB C 3 . Deci de whether y ou wan t the aplet to oper ate in Degr ees , R adians , or Gr ads. MODES Degrees 4. Vie w the Aplet L ibrary . The “TR IANGLE S” aplet is listed in t [...]

Extending aplets 17-3 Using a customized aplet To use the “T riangles” aplet, simply s elect 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. 1. Select the a plet. [...]

17-4 Ext ending aple ts Annotating an aplet with notes The Note view ( NOTE ) attaches a note to the curre nt aplet. See Chapter 15, “Notes and ske tches”. Annotating an aplet with sketches The Sketch view ( SKET CH ) attaches a picture to the current aplet. See chapter 15, “Notes and sketches”. HINT Notes and s k etches that you attach to [...]

Extending aplets 17-5 To transmit an aplet 1. Connect the P C or aplet disk dr iv e to the calculat or b y cable or align the tw o calc ulators ’ infr ar ed ports by mat ching up the tr iangle marks o n the rims o f the calc ulator s. P lace the calculato rs no mor e than 2 inches (5 cm) apar t. 2 . Sending calc ulator: Ope n the L ibr ary , hig [...]

17-6 Ext ending aple ts To sort the aplet list In the aplet library, press . Select the sorting scheme and press . • Chronologically pr od uces a c hr onological order based on the dat e an aplet w as last used . (The last- used aplet ap pears first , a nd so on .) • Alphabetically pr oduces an a lphabetical or der b y aplet name . To delete an[...]

Reference in formation R-1 R Re fer ence inf ormation 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. It is reusable (like a program, but easier to use) and it records all yo[...]

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 manipulate d by the List editor and catalog. matrix A two-dimensional array of values separated [...]

Reference in formation R-3 Resetting the hp 39g+ If the calculator “locks up” and seems to be stuck, you must reset it. This is much like resetting a PC. It cancels certain operations, restores ce rtain conditio ns, and clears temporary memory locations. However, it does not clear stored data (variables, ap let databases, programs) unless you u[...]

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. 1. Press and h old t[...]

Reference in formation R-5 To install the main batteries a. Slide up the battery compartment cove r as illustrated. b. Insert 3 new AAA(LR03) batteries into the main compartment. Make sure each battery is inserted in the indicated direction. To install the backup battery a. Press down the holde r. Push the plate to the shown direction and lift it. [...]

R-6 Reference information Variables Home variables The home variables are: Categor y Av ailabl e name Complex Z1 ... Z9 , Z0 Graphic G1 ... G9 , G0 Library Function Parametric Polar Sequence Solve Statistics User-named List L1 ... L9 , L0 Matrix M1 ... M9 , M0 Modes Ans Date HAngle HDigits HFormat Ierr Time Notepad User-named Program Editline User-[...]

Reference in formation R-7 Function aplet variables The function aplet variables a re: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Plot-FCN Area Extremum Isect Root Slope Symbolic Angle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Nume ric Dig[...]

R-8 Reference information Parametric aplet variables The parametric aplet variables are: Categor y Av ailabl e name Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Numeric Di[...]

Reference in formation R-9 Polar aplet variables The polar aplet variables are: Category Av ailable names Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θ step Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Nume ric Digits Format NumCol NumFont NumIndep N[...]

R-10 Reference information Sequence aplet variables The sequence aplet variables are: Categor y Av ailabl e name Plot Axes Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Numeric Digits Format NumCol NumFont NumIndep Num[...]

Reference in formation R-11 Solve aplet variables The solve aplet variables are: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Nume ric Digits Format NumCol NumRow Note NoteText Sketc h Page P[...]

R-12 Reference information Statistics aplet variables The statistics aplet variables are: Categor y Av ailabl e name Plot Axes Connect Coord Grid Hmin Hmax Hwidth Indep InvCross Labels Recenter S1mark S2mark S3mark S4mark S5mark StatPlot Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle S1fit S2fit S3fit S4fit S5fit N[...]

Reference in formation R-13 MATH menu categories Math functions The math functions are: Category Av ailable name Calculus TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL π Hype rb. ACOSH ASINH ATANH COSH SINH TANH ALOG EXP EXPM1 LNP1 List CONCAT ∆ LIST MAKELIST π LIST POS REVERSE SIZE Σ LIST SORT Loop ITERATE RECURSE Σ ∂ ∫[...]

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. POLYCOEF POLYEVAL POLYFORM POLYROOT Prob. COMB ! PERM RANDOM UTPC UTPF UTPN UTPT Real CEILING DEG → RAD FLOOR FNROOT FRAC HMS → → HMS INT MANT MAX MIN MOD %[...]

Reference in formation R-15 Program constants The program constants are: Tests < ≤ = = ≠ > ≥ AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category Av ailable nam e (Continued) Category Av ailable name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlo t Cobweb Stairstep S1...5fit Linear LogFit ExpFit Power [...]

R-16 Reference information Program commands The program commands are: Categor y Command Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE PIXOFF PIXON TLINE Graphic DISPLAY → → DISPLAY → GROB GROBNOT GROBOR GROBXOR MAKEGROB PLOT → → PLOT REPLACE SUB ZEROGROB Loop FOR = TO STE[...]

Reference in formation 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. Delete one or more matrices, lists, notes, or programs[...]

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 a nother calculato r. Re- send the data. Too Few Arguments The command[...]

Limiting Warranty W-1 Li m i t i n g W a rran t y hp 39g+ Graphing Calculator; Warranty period: 12 months 1. HP warr ants to y ou , th e end-user c ustomer , that HP har dw are , accessor ies and su pplies w i ll be fr ee fr om def ects in mater ials and w ork manship after the date of pur chase , for the per iod spec ified abo ve . If HP r ecei ve[...]

W-2 Limiting Warranty 6 . HP MAKE S NO O THER EXPRE S S W ARRANTY OR CONDI T ION WHETHER WR ITTEN OR ORAL. T O THE EXTENT ALL O WED B Y L O CAL LA W , ANY IMP LIED W ARRANTY OR CONDI TION OF MERCHANT ABILITY , S A T ISF A CT OR Y Q U ALITY , OR FI TNE SS F OR A P A R T ICUL AR PURP OSE IS LIMI TED T O THE DUR A TION OF THE EXP RE S S W ARRANTY SET [...]

Limiting Warranty W-3 Service Europe Country : T elephone numbers Au str ia +4 3-1 -3 60 2 7 71203 Belgium + 3 2 - 2 - 712 6 2 19 D e n m a r k + 45 - 8 - 233 28 4 4 Ea s t e r n Eu ro p e countr ies +4 20-5- 414 2 2 5 2 3 Fi n l a n d + 35 - 89 6 4 0 0 09 F r ance +3 3-1 - 4 99 3 9006 German y +4 9-6 9-9 5 30 7103 Gr eece +4 20 -5-414 2 2 5 2 3 Ho[...]

W-4 Limiting Warranty P lease logon to http://www .hp .com for t he la test ser vice a n d s u p p o r t in f o r m at i o n . L.Ame ric a Country : T elephone nu mbers Ar gentina 0 -810 -5 5 5-5 5 20 Bra zil Sao P aulo 3 7 4 7 - 77 9 9; RO T C 0 -800 -15 77 51 M exi c o M x C i t y 5 258 - 9922 ; RO T C 01-800 - 4 7 2 -66 84 Ven e z u e l a 0 8 0 [...]

Limiting Warranty W-5 Regulatory infor mation This section contains information that shows how the hp 39g+ graphing calculator comp lies with regulations in certain regions. Any modificati ons to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the 39g+ in these regions. USA This calculator generates, use[...]

W-6 Limiting Warranty Disposal of Waste Equipment by Users in Private Household in the European Union This s ymbol o n the pr oduct or on its pack aging indicates that this produc t 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 wa ste . Instead, it is yo ur responsibi li ty to di spose of your waste equipmen t b y handin[...]

Index I-1 Index A absolute value 11-5 add 11-3 algebraic en try 1-19 alpha characters typing 1-6 alphabetical so rting 17-6 angle measure 1-10 in statistics 8-12 setting 1-12 animation 15-5 creating 15 -5 annunciators 1-3 Ans (last answer) 1-24 antilogarithm 11-4 , 11-9 aplet attaching notes 17- 4 clearing 17-3 copying 17-4 definition of R-1 deleti[...]

I-2 Index chronological sorting 17-6 circle dra wing 15-4 clearing aplet 17-3 character s 1-22 display 1-2 2 display history 1-2 5 edit line 1-22 lists 14-6 plot 2-7 cobweb graph 6-1 coeffi cients polynomial 11-10 columns changing position 16-25 combinations 11 -12 commands aplet 16-14 branch 16-17 definition of R-1 drawing 16-19 graphic 16-20 loop[...]

Index I-3 definition of 11-6 in Function aplet 11-2 2 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 1-2 date and time 16-26 element 13-5 elements 14-4 engineering 1-11 fixed 1-11 fraction 1-11 history 1-22 line 1-23 matrices 13-5 parts of 1-2 prin[...]

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 16-3 1 grid 16-31 in menu map R-7 indep 16-32 isect 16 -32 labels 16-33 Recent er 16-3 3 root 16-33 ycross 16-36 G glossary R-1 graph analyzing statistical data in 8-1[...]

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 2-19 independent variable defined for Tracing mode 16-32 inference confidence intervals 9-15 hypothesis tests 9-8 One-Proportion Z-Interval 9-17 One-[...]

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 BREA K 16-23 DO...UNTIL...END 16-22 FOR I= 16-23 WHILE...REPE[...]

Index I-7 variables 13-1 matrix functions 13-10 COLNORM 13-10 COND 13-10 CROSS 13-1 0 DET 13-11 DOT 13-1 1 EIGENVAL 13-11 EIGENVV 13-11 IDENMAT 13-11 INVERSE 13- 11 LQ 13-11 LSQ 13-11 LU 13-11 MAKEMAT 13-11 QR 13-12 RANK 13-1 2 ROWNORM 13-12 RREF 13-12 SCHUR 13-12 SIZE 13-1 2 SPECNORM 13-12 SPECRAD 13-12 SVD 13-13 SVL 13-13 TRACE 13-13 TRN 13-13 ma[...]

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 16-3 3 ycross 16-36 parentheses to close arguments 1-21 to specify order of operation 1-21 pause 16 -28 permutations 11-12 pictures attaching in Sket[...]

Index I-9 preced ence 1-22 predicted values statistical 8-20 print contents of display 16-2 5 name and contents of variable 16-25 object in history 16-25 variables 16-25 probability functions ! 11-12 COMB 11-12 RANDOM 11-12 UTPC 11-12 UTPF 11-13 UTPN 11- 13 UTPT 11-13 program commands 16-4 copying 16-8 creating 16 -4 debugging 16-7 deleting 16-9 de[...]

I-10 Index intera ctive 3-10 n th 11-6 variable 16 -33 root-finding displaying 7-7 intera ctive 3-9 operat ions 3-10 variables 3-10 S S1mark-S5mark variables 16-33 scaling automatic 2-14 decimal 2-10 , 2-14 integer 2-10 , 2-14 , 2-16 options 2-14 resetting 2-14 trigonometric 2-15 scatter plot 8-15 , 8-16 connected 8-17 , 8-18 SCHUR decomposition 13[...]

Index I-11 data structure 16-39 define one-variable sample 16-29 define two-va riable data set’s de- pendent column 16-29 define two-variable data set’s in- dependent column 16 -29 defining a fit 8-12 defining a regression model 8-12 deleting data 8-11 editing data 8-11 frequency 16-29 inserting data 8-11 plot type 8-18 plotting data 8-15 predi[...]

I-12 Index ACOT 11-19 ACSC 11-19 ASEC 11-1 9 COT 11-1 9 CSC 11-19 SEC 11-20 trng 2-6 truncating values to decimal places 11-16 tstep 2-6 , 16-35 Two-Pr oportion Z- Interva l 9-17 Two-Pr oportion Z- Test 9-11 Two-Sample T-Inte rval 9-19 Two-Sample T-tes t 9-14 Two-Sample Z-Interval 9-16 typing letters 1-6 U undefined name R-18 result R-18 un-zoom 2-[...]