HP 39gs Graphing Calculator Manuel d'utilisateur

hp 39gs and hp 40gs graphing calculators Mastering the hp 39gs & hp 40gs A guide for teachers, students and other users of the hp 39gs & hp

4 SSOOMMEEKKEEYYBBOOAARRDDEEXXAAMMPPLLEESSShown below are snapshots of some typical screens (called “views”) which you might see when you press the ke

Convenient screen keys provided If the definition is recursive but only involves Tn−1 rather than both Tn−1 and Tn−2 then you need not enter a value

The NUM SETUP view offers more useful features. Change to that view now and change the NumStep value to 10. If you then swap back to the NUM view yo

15 TTHHEEEEXXPPEERRTT::SSEEQQUUEENNCCEESS&&SSEERRIIEESSDefining a generalized GP and the sum to n terms for it. If we define our GP using memo

Population type problems are also easily dealt with in this way. For example, “A population of mice numbers 5600 and is growing at a rate of 12.5% p

Modeling loans Suppose that I need to see the progress of a loan of $10,000 at a compound interest of 5.5% p.a. calculated each quarter, starting Jan.

Equations vs. expressions Entering the equation 16 TTHHEESSOOLLVVEEAAPPLLEETTThis aplet will probably rival the Function aplet as your ‘most used’ too

Solving for a missing value ⋅ ⋅The INFO report Suppose you had the problem: ⋅“What acceleration is needed to increase the speed of a car from 16 67

Multiple solutions and the initial guess Graphing in Solve Our first example was fairly simple because there was only one solution so it did not much

Transferring approximate solutions Referring to functions from other aplets The PLOT view on the previous page shows two curves. The horizontal line

Example 4 “Let X be a random variable, representing the heights of basketball players. If X is 2⋅normally distributed, with µ= 184 5 and σ= 105 t

5 KKEEYYSS&&NNOOTTAATTIIOONNCCOONNVVEENNTTIIOONNSSThere are a number of types of keys/buttons that are used on the hp 39gs and hp 40gs. The ba

A detailed explanation of PLOT in Solve The PLOT view in the Solve aplet is a little more complex than most others, since the active variable (x, t, t

Now press and you will see the calculator find the nearest solution to your guess. Finish by pressing to verify that the solution is valid. See page

⋅ ⋅The meaning of messages On pages 106, the values used were V= 27 78 , U=16 67 and D=100 and we were solving for A. 2 2Thus: v = u + 2ad 2 2 ⋅

17 TTHHEEEEXXPPEERRTT::EEXXAAMMPPLLEESSFFOORRSSOOLLVVEEEasy problems (x −1)12 (3 − x)−= −3 9 4 Have you ever thought “There has to be an easier way!”

Uni-variate vs. Bi-variate data Clearing data 18 TTHHEESSTTAATTIISSTTIICCSSAAPPLLEETT--UUNNIIVVAARRIIAATTEEDDAATTAAOne of the major strengths of the h

Sorting dataThe STATS key Functions of columns inserts space for a new number by shifting all the numbers down one space. The key labeled does exact

Registering columns as ‘in use’Working with frequency tables Auto scale xiChange into the SYMB view and edit yours so that it looks like the one on t

Plot Setup options Box and whisker graphsIf you use the left/right arrows and look at the bottom of the screen you’ll see that the frequencies and ran

The effect of HRngGrouped data & HWidth The effect of HRng is rather different. It controls what range of data is displayed on the graph, regardl

Centering columns in the histogram The HWidth variable controls the width of the columns, with the initial starting value and end value set by HRng.

Pop-up menus & short-cuts The Screen keys A special type of key unique to the hp 39gs, hp 40gs and family is the row of blank keys directly under

19 TTHHEEEEXXPPEERRTT::SSIIMMUULLAATTIIOONNSS&&RRAANNDDOOMMNNUUMMBBEERRSSNew columns as functions of old You have already seen the use of one

Simulation of a normal die Similarly the expression INT(RANDOM*6+1) will simulate one roll of the die. This means that MAKELIST(INT(RANDOM*6+1),X,1,50

Example 4: Simulate 100 observations on a normal random variable N(µ=80, σ2=50). Ensure that MODES is set to radian measure and type: MAKELIST(80+ 5

Uni vs. Bi-variate data Clearing data 20 TTHHEESSTTAATTIISSTTIICCSSAAPPLLEETT--BBIIVVAARRIIAATTEEDDAATTAAAs mentioned in the Univariate section, one o

Sorting paired columns Entering data as ordered pairs Adjusting the symbols used to plot points Move the highlight into column C1 and enter the xi val

The cursorSpecifying the fit modelMultiple data sets If you now press PLOT you will see the result shown right. If you look at the screen you will se

Choosing from available fit models The Statistics aplet is the only one which has a SYMB SETUP view, and even then only in mode. This view is supplie

The User Defined model When you set the model to user defined it means that you are expected to supply the complete equation, including the values of

Calculator Tip llght. ghligillustrated below. If you have trouble seeing the small dots that the calcu ator uses in its scatter-graphs by defau t then

Showing the line of best fit Now change to PLOT SETUP view and set the axes as shown right. From the NUM view, press the key and you will obtain the

You can also use these memories in calculations. Type in the following, not forgetting the ALPHA key before the D…. (3+D)/5 ENTER The calculator wil

A caveat for bivariate data Predicting using PREDYIn the SYMB view (see right) the equation is given to so many decimal places that it doesn’t fit ont

Predicting using the PLOT view RelErr as a measure of non-linear fit Using the PLOT view is the probably the more visually appealing method of obtain

Alternatively, when data is non-linear in nature you can transform the data mathematically so that it is linear. Let's illustrate this briefly wi

21 TTHHEEEEXXPPEERRTT::MMAANNIIPPUULLAATTIINNGGCCOOLLUUMMNNSS&&EEQQNNSSNew columns as functions of old As with univariate statistics, you can

If we now switch to the HOME view, we can recall these values and use them in a calculation to find the upper and lower cut off points for acceptance

Obtaining coefficients from the fit model The function PREDY from MATH gives a predicted y value using the last line of best fit that was calculated.

Cubic -a*X^3+b*X^2+cX+d −1⎡⎤ ⎡ 0001⎤ ⎡ PREDY (0)⎤ ⎢⎥ ⎢ ⎥ ⎢ a b⎢⎥ ⎢ 1111⎥ ⎢ PREDY (1) ⎥⎥= ×⎢⎥ ⎢ 8 4 2 1⎥ ⎢ PREDY (2)⎥c ⎢⎥ ⎢ ⎥ ⎢ ⎥⎢⎥ ⎢ 27 9 3 1⎥

While the value of Sxy will not change if the roles of independent and dependent columns are reversed, the S 2value of ()on the bottom means that th

Now position the highlight on column C2 and press the key. In the SORT SETUP screen (shown right) enter C1 as the Dependent column. This will have

eg. 2 A population of bacteria is known to follow a growth pattern governed by the equation N = N ekt ; t ≥ 0 . It is observed that at t = 3 hour

6 EEVVEERRYYTTHHIINNGGRREEVVOOLLVVEESSAARROOUUNNDDAAPPLLEETTSS!!A built in set of aplets are provided in the APLET view on the hp 39gs and hp 40gs. T

(iii) Find t so that N = 2N0 . The value of N is the y intercept of the line of best fit. These values 0 from the curve of best fit are not directly

22 TTHHEEIINNFFEERREENNCCEEAAPPLLEETTThis aplet is a very flexible tool for users investigating inference problems. It provides critical values for h

Change now to the NUM SETUP view to enter the required values. Rather than entering them by hand, press the key. If you have more than one copy of t

Confidence interval: T-Int 1-µ In the previous example we found that the evidence of our sample indicated that the mean number of matches in the boxes

Hypothesis test: T-Test µ1 -µ2 A farmer compared the 15-day mean weight of two sets of chicks, one group receiving feed supplement A and the other sup

The PLOT. probability of obtaining a test student-t value of 3.38 is 0.0015 and this view also shows that the vertical line representing the value of

The hypotheses are: H0: The sample is drawn from a population whose mean is the same as the standardized population (µ= µ) .0 HA: The sample

23 TTHHEEEEXXPPEERRTT::CCHHII22TTEESSTTSS&&FFRREEQQUUEENNCCYYTTAABBLLEESSWe will start with a small digression to look at a simple inferential

In the MATH menu, Probability section (see page 208), there is a function called UTPC (Upper-Tailed Probability Chi-squared) which will give the criti

To create it, go to the Program Catalog view and press the key. Enter any name you want, such as ‘CCreate’. Now type in the code below. The progr

Some typical aplet viewsThe Sequence aplet (see page 99) Handles sequences such as Tn = 2Tn−1 + 3; T1 = 2 or T = 2n−1 . Allows you to explore nrec

24 TTHHEELLIINNEEAARRSSOOLLVVEERRAAPPLLEETTThis is a very easy aplet to use. It is designed to solve simultaneous linear equations in 2 or 3 unknowns

EExxaammppllee33Solve the system of equations: −+73xy z=5 ⎫ ⎪ −5x z=2 ⎬ y z= −1⎭ −+22 ⎪ Although it may not be obvious at first glance, this system o

25 TTHHEETTRRIIAANNGGLLEESSOOLLVVEEAAPPLLEET TThis aplet allows you to solve for missing sides and angles in a triangle, either right angled or not.

Since this is not a right triangle, the first step is to ensure that is not selected, as is shown right. Any of the three angles α,βor δcan be used t

EExxaammppllee33Solve the triangle shown right. This is an example of a triangle that has two possible solutions, generally referred to as “The Ambigu

26 TTHHEEFFIINNAANNCCEEAAPPLLEETTThis aplet is designed to allow users to solve time-value-of-money (TVM) and amortization style problems quickly and

PMT - This is the size of the periodic payment. The assumptions made are that all payments are the same size and that no payments will be skipped. P

Annuities An engineer retires with $650,000 available for investment. She invests the money in a portfolio which is expected to have an average return

Amortization The second page of this aplet allows amortization calculations in order to determine the amounts applied towards the principal and intere

Choosing the level GRAPH mode27 TTHHEEQQUUAADDEEXXPPLLOORREERRTTEEAACCHHIINNGGAAPPLLEETTRather than being a multi-purpose aplet, this is a teaching ap

The PLOT view is used to display the function as a graph… key. This gives access to a number of other useful tools allowing further analysis of the f

SYMB mode Test modeAs can be seen in the screen shots right, the bottom half of the screen shows the roots (if any), the value of the discriminant and

There are two levels of ‘questions’ denoted by the keys and on the screen. An question will be in the main screen (-5 to 5 on each axis), whereas a

SIN vs. COSSYMB vs. GRPH mode 28 TTHHEETTRRIIGGEEXXPPLLOORREERRTTEEAACCHHIINNGGAAPPLLEETTRather than being a multi-purpose aplet like most of the othe

The operation of the two modes is summarized below. The PLOT mode The underlying concept in PLOT mode is that the graph controls the equation. The use

The c coefficient is shown as a multiple of π in radian mode rather than as a decimal. The currently active coefficient is highlighted and can be ch

29 TTHHEEMMAATTHHMMEENNUUSSThe MATH menu is accessed via the key below the APLET key. Any time that you are typing a value into any formula or setup

AAcccceessssiinnggtthheeMMAATTHHmmeennuuccoommmmaannddssThe mechanics of accessing the MATH menu is very simple. We will illustrate the process using

On the pages which follow we will look at most of the functions in each group. Some of the functions are not likely to be used at school level and so

TThheePPHHYYSSmmeennuuccoommmmaannddssThe PHYS menu is divided up into three sections by learning area. These sections are: • Chemistry • Physics •

TThheeMMAATTHHmmeennuuccoommmmaannddssThe MATH menu is divided up into sections by mathematical topics. These topics are: Real - rounding, roots, som

A mini-USB cable (see page 237) and software were provided with your hp 39gs and hp 40gs which you can use to connect your PC to your calculator via t

TThhee‘‘RReeaall’’ggrroouuppooffffuunnccttiioonnssCEILING(<num>) This is a ‘rounding’ function but different in that it always rounds up to the

FNROOT(<expression>,<variable>,<guess>) This function is like a mini version of the Solve aplet. If you feed it an algebraic expres

HMS (<dd.mmss>) This function works with time and angles. It converts degrees, minutes and seconds to degrees, and also hours, minutes and sec

⋅ ⋅ ⋅ ⋅ INT(<num>) This function is related to the FLOOR and CEILING functions. Unlike those two, which consistently move down or up respective

MIN(num1,num2) As with MAX, this function is used mainly by programmers. It returns the smaller of the two numbers entered. Eg. MIN(3,5) = 3 See als

%CHANGE(<num1>,<num2>) This function calculates the percentage change moving from X to Y using the formula 100(Y-X)/X. It can be used to

ROUND(<num>,<dec.pts>) This function rounds off a supplied number to the specified number of decimal places (d.p.). Eg. Round 66.65 to 1

⋅ ⋅ ⋅ ⋅ TRUNCATE(<num>) This function operates similarly to the ROUND function, but simply drops the extra digits instead of rounding up or dow

TThhee‘‘SSttaatt--TTwwoo’’ggrroouuppooffffuunnccttiioonnssPREDY(<x-value>) This function predicts the y value for a pair of columns set up as b

TThhee‘‘SSyymmbboolliicc’’ggrroouuppooffffuunnccttiioonnssThe = ‘function’ Although this is listed in the MATH menu as if it were a function, it is no

7 TTHHEEHHOOMMEEVVIIEEWWIn addition to the aplets, there is also the HOME view, which can best be thought of as a scratch pad for all the others. Thi

LINEAR?(<expression>,<var.name>) This is another of those functions which is probably aimed more at the programmer than at the normal user

3 +If you would like a solution such as 5 rather than 2.6180 then you would have to COPY the result, edit 2 the line to remove all but the decimal ro

TThhee‘‘TTeessttss’’ggrroouuppooffffuunnccttiioonnssThese are all functions which are of interest only to programmers, and consequently we will not co

Some further functions are available in the Hyperbolic group of functions. They are duplicates of functions available on the face of the calculator b

LNP1(<num>) As in the previous function, this is supplied to supplement the LN function and gives a more accurate value when x is near zero. Aga

TAYLOR(<expression>,<var_name>,<num>) Briefly, a Taylor polynomial allows you to approximate a complicated function via a simpler po

TThhee‘‘CCoommpplleexx’’ggrroouuppooffffuunnccttiioonnssComplex numbers on the hp 39gs & hp 40gs can be entered in either of two ways. Firstly, i

In addition to the trig functions, there are other functions that take complex arguments. ABS(<real>) or ABS(<complex>) The absolute funct

CONJ(<complex>) This function returns the complex conjugate. 23Eg. If z =+i , then find the complex conjugate z . 23Answer (see right): z =

TThhee‘‘CCoonnssttaanntt’’ggrroouuppooffffuunnccttiioonnssThese ‘functions’ consist of a set of commonly occurring constants. Two of them, MAXREAL and

The screen keys Aplet related keys The arrow keys EExxpplloorriinnggtthheekkeeyybbooaarrddThe first step in efficient use of the calculator is to fami

TThhee‘‘LLiisstt’’ggrroouuppooffffuunnccttiioonnssCONCAT(<list1>, <list2>) This function concatenates two lists - appending one on to the

Eg. 1 MAKELIST( X2,X,1,10,2) L1 produces { 1, 9, 25, 49, 81 } as X goes from 1 to 3 to 5 to … and also stores the result into L1. Eg. 2 MAKELIST(

SIZE(<list>) or SIZE(<matrix>) This function returns the size of the list or matrix specified. Since normal users would probably know a

TThhee‘‘LLoooopp’’ggrroouuppooffffuunnccttiioonnssThis is a group of functions that may be of use for students studying discrete functions and sequenc

RECURSE This functions is provided for programmers to let them define functions in the Sequence aplet. For example, typing RECURSE(U,U(N-1)*N,1,2)

TThhee‘‘MMaattrriixx’’ggrroouuppooffffuunnccttiioonnssThis group of functions is provided to deal with matrices. The scope of functions & abilitie

DET(<matrix>) This function finds the determinant of a square matrix. See page 213 for an example of its use in finding an inverse matrix. ⎡23⎤

INVERSE(<matrix>) This function produces the inverse matrix of an n x n square matrix, where possible. A fully worked example of the use of an

LSQ(<matrix1>,<matrix2>) The least squares function displays the minimum norm least squares matrix (or vector). LU(<matrix>) This L

ROWNORM(<matrix>) Finds the row norm of a matrix: the maximum, over all rows contained in the matrix, of the absolute values of the sum of the

Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO C

The SYMB, PLOT and NUM keys The APLET key is used to choose between the various different aplets available. Everything in the calculator revolves ar

For example, suppose we use the system of equations below, in which the third equation is a linear combination of the first two but the constant is no

SVD(<matrix>) This function performs a Singular Value Decomposition on an m × n matrix. The result is two matrices and a vector: {[[m × m squar

TThhee‘‘PPoollyynnoommiiaall’’ggrroouuppooffffuunnccttiioonnssThis group of functions is provided to manipulate polynomials. We will use the function

POLYFORM(<expression>,<var_name>) This is a very powerful and useful polynomial function. It allows algebraic manipulation and expansion

POLYROOT([coeff1,coeff2,…]) This function returns the roots of the polynomial whose coefficients are specified. The coefficients must be input as a v

TThhee‘‘PPrroobbaabbiilliittyy’’ggrroouuppooffffuunnccttiioonnssThis group of functions is provided to manipulate and evaluate probabilities and proba

PERM(<n>,<r>) This function gives the value of nP using rnn!the formula P= .r −(nr)! Eg. How many ways can 3 Math, 4 English, and 6 G

UTPN(<mean>,<variance>,<value>) This function, the ‘Upper-Tail Probability (Normal)’, gives the probability that a normal random var

The second value can be found by using the symmetry properties of the Normal Distribution, but it is probably just as fast to go back to the SYMB view

The MATRIX Catalog 30 WWOORRKKIINNGGWWIITTHHMMAATTRRIICCEESSThe hp 39gs & hp 40gs deal very well with matrices. They offer many powerful tools a

Intro to the VIEWS menu The VIEWS key pops up a menu from which you can choose various options. Part of the VIEWS menu for the Function aplet is show

Matrix calculations in the HOME viewIf you look at the list of screen keys on the bottom of the view, you will see one labeled . This determines whic

Solving a system of equations Another method is to store the result into a third matrix and then to view it through the Edit screen of the MATRIX Cat

Step 2. Enter the 3x3 matrix of coefficients in M1. Step 3. Enter the 3x1 matrix of into M2. Note the change to in order to make entering numbers

Finding an inverse matrix⎡2 1 4 ⎤ 1Eg. 2 Find the inverse matrix A− for the matrix A=⎢⎢1 1 3 ⎥⎥ ⎢−24 −1⎥⎦⎣ The first step is to store the matrix A in

The dot productEg. 4 Find the angle between the vectors a = (3, 4) and b = (4,1) . Using the formula that a b•=a ..cos θb • where a bis the dot pro

The list variables Operations on lists Statistical columns as lists 31 WWOORRKKIINNGGWWIITTHHLLIISSTTSSA list in the hp 39gs or hp 40gs is the equival

List functions Editing a list Operations on elementsThere are also a number of special functions available for list variables which are contained in t

Aplet notes vs. independent notes 32 WWOORRKKIINNGGWWIITTHHNNOOTTEESS&&TTHHEENNOOTTEEPPAADDThe hp 39gs & hp 40gs provide access to Notes w

If you the menu and press NOTE on this particular aplet then you would see the attached Note shown right. This is quite common with downloaded aple

Transferring notes using IR Editing software IInnddeeppeennddeennttNNootteessaannddtthheeNNootteeppaaddCCaattaallooggMost users are far more concerned

The VARS key The VARS key is used, mainly by programmers, as a compact way to access all the different variables stored by the calculator including ap

Locking ALPHA mode CCrreeaattiinnggaaNNootteeLet’s create a small Note containing some commonly used formulas. Press SHIFT NOTEPAD (not SHIFT NOTE )

The CHARS viewCorrupting notes Generally most characters you will need are on the keyboard, but additional special characters can be obtained through

Adding text to a sketch 33 WWOORRKKIINNGGWWIITTHHSSKKEETTCCHHEESSIf you have not already done so, read the previous chapter. As is explained there, e

DOT+LINE BOX There are two font sizes available via the key, with the default size being large. If you press the key then it will change to . Althou

CIRCLECut and paste images Storing to a GROBUsing the VAR key to paste The circle command is similar to the box command. You should position the curs

Simple Animations Capturing the PLOT screen You will now find yourself back in the graphics screen with a rectangle representing the size of the GROB

34 CCOOPPYYIINNGG&&CCRREEAATTIINNGGAAPPLLEETTSSOONNTTHHEECCAALLCCUULLAATTOORRThis chapter assumes a reasonable degree of familiarity with the

DDiiffffeerreennttmmooddeellssuusseeddiiffffeerreennttmmeetthhooddssttooccoommmmuunniiccaatteeAs has been discussed on page 7, the hp 39gs and hp 40gs

SSeennddiinngg//RReecceeiivviinnggvviiaatthheeiinnffrraa--rreeddlliinnkkoorrccaabbllee..Any aplet, note, program, matrix or list can be copied from on

The process is essentially: • Press the key on the sending calculator and the key on the receiving calculator. • Choose the option for your part

The SETUP views The ALPHA key gives access to the alphabetical characters, shown below and right of most keys. Pressing SHIFT ALPHA gives lower case.

Copying and adding to the Function aplet CCrreeaattiinnggaaccooppyyooffaaSSttaannddaarrddaapplleett..Imagine either of these two scenarios…. • you ar

Copying and adding to the Stats aplet Our student’s newly created copy of the Function aplet is now totally independent of its parent aplet. The stud

SSoommeeeexxaammpplleessooffssaavveeddaapplleettssThe Triangles aplet the Solve aplet and it under the new name of “Triangles”. Now In the APLET vie

Equations E1 and E2 These two equations can be used for calculations involving individual and cumulative Binomial probabilities. eg. Find the probabil

Equation E6 (≤≤) for an exponential distribution. To calculate Px a )use P(0 ≤≤). To calculate Px a ) just find Px a ) and then use the HOME view

Change to the HOME view and perform the calculation shown right and finally press PLOT. The result is a triangle with corners at (1,1), (2,1) and (1,3

The repetition of the first point is to ensure that the line forming the triangle is closed by connecting back to its starting point. The function fo

35 SSTTOORRIINNGGAAPPLLEETTSS&&NNOOTTEESSTTOOTTHHEEPPCCOOvveerrvviieewwMany users create elaborate collections of notes and aplets over time,

SSooffttwwaarreeiissrreeqquuiirreeddttoolliinnkkttooaaPPCCThe connectivity software for the hp 39gs and hp 40gs was being rewritten at the time when t

Both models use the same cable As has been discussed elsewhere the hp 39gs and hp 40gs were aimed at different markets. Both of them require communic

The MODES view Numeric formats The MODES view (see right) controls the numeric format used in displaying numbers and angles in aplets. At the bottom

Before beginning you should install the Connectivity software. This can be found on the CD that came with your calculator but it is best to download

The next stage is to use the software to transmit the aplet, list, matrix or note to the PC. The instructions which follow apply to the transmission

Normally the result of this will be a series of small pop up boxes on the PC showing the progress of the file transfer. Since most objects on the cal

Attached programs If your aplet is one that has been given to you by someone else such as your teacher, rather than simply a copy of one of the standa

RReecceeiivviinnggffrroommPPCCttooccaallccuullaattoorrThe process of retrieving objects that have been stored to the PC is almost identical to that of

36 AAPPLLEETTSSFFRROOMMTTHHEEIINNTTEERRNNEETTThe calculator comes with a number of aplets built into the chip. In addition to these there are hundred

The HP39DIR files You may notice separate download icons for the 38G and for the 39G, 40G and 39g+ with no mention of the new hp 39gs and hp 40gs. Th

Organizing your collection Shown below and right is the contents of one directory in part of my collection. If you’re only going to download a few apl

The process of transferring the newly downloaded aplet from the PC to the calculator is exactly the same as it is for an aplet which you have saved to

UUssiinnggddoowwnnllooaaddeeddaapplleettssNormally if you press the VIEWS key on your hp 39gs or hp 40gs then you will see a list of options which var

The screens right show the same two numbers displayed as in turn as; Fixed 4, Scientific 4 and Engineering 4. Calculator Tip If you have Labels turned

DDeelleettiinnggddoowwnnllooaaddeeddaapplleettssffrroommtthheeccaallccuullaattoorrAs was mentioned earlier, most of the aplets you download will have

CCaappttuurriinnggssccrreeeennssuussiinnggtthheeCCoonnnneeccttiivviittyyKKiittOne of the more useful abilities of the Connectivity Software is its abi

37 EEDDIITTIINNGGNNOOTTEESSUUSSIINNGGTTHHEECCOONNNNEECCTTIIVVIITTYYSSOOFFTTWWAARREEIn addition to allowing you to save and retrieve objects from the c

contained in the folder you have already selected. Assuming that you actually have notes in the folder then you will see something similar to the view

The names used to record the Notes on the PC are not terribly imaginative, as can be seen to the right. You must not change these names! They are re

38 PPRROOGGRRAAMMMMIINNGGTTHHEEHHPP3399GGSS&&HHPP4400GGSSTThheeddeessiiggnnpprroocceessssAn overview Although you can choose to simply create

Choosing the parent aplet The first stage in the creation process is to decide which of the standard aplets you wish to make the “parent” of your new

Most of the options in your VIEWS menu will be triggers for ‘helper’ programs you will write, and when the user chooses an option and presses ENTER, t

Another example of an existing aplet is shown right. It is called “Tangent Lines” and it draws a tangent line onto a graph and then lets the user mov

TThheeSSEETTVVIIEEWWSSccoommmmaannddThe VIEWS menu is created by the SETVIEWS command. It follows a repetitive pattern of listing a menu option, foll

The ANS keyThe negative key The CHARS key If you are not confident about using brackets, then the ANS key can be quite useful. 372 −×For example, you

Special entries in the SETVIEWS command In addition to the lines which form the menu for your aplet, there are some special entries which are treated

Shown below is a SETVIEWS program which illustrates this for an aplet with Function as its parent… producing a menu of… The behaviour will be: • Choo

EExxaammpplleeaapplleett##11––DDiissppllaayyiinnggiinnffooThis example uses the SETVIEWS command to create a simple (and totally useless) aplet, which

We’ll now create the associated ‘helper’ programs (shown below). Their names/titles are supplied above the code for each one. A short explanation is

Having created all of the programs that make up the aplet ‘Message’, we can now run the program .MSG.SV, severing the aplet’s link to its current VIEW

The next option in the menu is ‘Input value’. Choosing this option will create an input screen. The statement controlling this was: INPUT N; "M

The final option is ‘Show function’. The program this runs is a little more complex than the ones shown so far and illustrates a useful technique. Th

Finally the LINE and BOX commands commands are used to draw an oblique line across the screen and a box near the center. LINE Xmin; Ymin; Xmax; Ymax

EExxaammpplleeaapplleett##22––TThheeTTrraannssffoorrmmeerrAApplleettIf you haven’t already, read pages 234 which explain how to create a copy of the P

.TRANSF.SHAPE .TRANSF.MAT (continued…) Since the default contents of any variable is zero and there is no zero’th option on a list this means a progr

The DEL and CLEAR keys Another important key is the DEL key at the top right of the keyboard. This serves as a backspace key when typing in formulas

DDeessiiggnniinnggaapplleettssoonnaaPPCCPlease note The software used on the PC to edit and create Notes, programs and aplets was in the process of be

the program into Type the code for the code window. At the time this book was written there was some debate going on over whether the code should be

EExxaammpplleeaapplleett##33––TTrraannssffoorrmmeerrrreevviissiitteeddRun the Connectivity Kit and use the File menu to create a new folder called “Tr

As you enter each triplet, the boxes will blank ready for the next menu item to be added. You can construct the entire menu at one time OR you can ed

EExxaammpplleeaapplleett##44––TThheeLLiinneeaarrEExxpplloorreerraapplleettIf you would like more practice in using the programming utility then you ma

If you have done this correctly then your VIEWS menu have three entries shown right when it is transferred to the calculator. The text for the ‘helper

It will probably be easier to understand how the aplet works if you see it in action first so you may wish to download the aplet from The HP HOME View

The second and third lines insert a function into F1(X). This can only be done, of course, if the parent aplet is Function. If you do this when the

Still referring to the code on the previous page, you will see that it refers to PageNum. The sketches in the calculator’s SKETCH view are numbered 1,

The DISPXY command is a hugely useful command to programmers. It appears in the Prompt section of the MATH menu. It allows you to place a string of

AAnngglleeaannddNNuummeerriiccsseettttiinnggssIt is critical to your efficient use of the hp 39gs and hp 40gs that you understand how the angle and nu

The final check in the line UNTIL K==105.1 END: is to see if the user has pressed the ENTER key. If so then the loop will terminate and the screen wi

39 AALLTTEERRNNAATTIIVVEESSTTOOHHPPBBAASSIICCPPRROOGGRRAAMMMMIINNGGThe hp 39gs and hp 40gs are supplied with a simple and easy to use programming lang

The HPG-CC Programming language The hp 39g+ was the first of this family of calculators which didn't use the Saturn 5 as its ROM chip. Up to tha

The HPG-CC language was originally developed for use on the hp 49g+, which is a more sophisticated graphical calculator aimed at university and profes

40 FFLLAASSHHRROOMMUnlike all their predecessors, the hp 39gs & hp 40gs contain flash ROM. A ROM chip contains “Read Only Memory” and is used to

Generally any user memory will be lost as part of the updating process. Even if it is not, the instructions that come with the update will almost cer

41 PPRROOGGRRAAMMMMIINNGGCCOOMMMMAANNDDSSAs was explained in a previous chapter, the hp 39gs and hp 40gs are supplied with a simple and easy to use pr

TThheeBBrraanncchhccoommmmaannddssIF <test> THEN <true clause> [ELSE <false clause>] END Note the need for a double = sign when comp

RUN <program name> This command runs the program named, with execution resuming in the calling program afterwards. If a particular piece of code

TThheeDDrraawwiinnggccoommmmaannddssThis command draws an arc on the screen. It uses the current values in the PLOT SETUP view as the screen coordina

In the PLOTHOME view, view shown, the first positive root has been On the hp 39gs and hp 40g, if we now change to the ation shown right, we expect t

TLINE <x1>;<y1>;<x2>;<y2> This command is the same as LINE except that the line drawn reverses the current set/unset value of

TThheeGGrraapphhiiccssccoommmmaannddssSee the chapter “Programming the hp 39gs & hp 40gs” beginning on page 255 for examples illustrating some of

BREAK This command will exit from the current loop, resuming execution after the end of it. Calculator Tip There is no GOTO <label> command in t

TThheePPrriinnttccoommmmaannddssThese commands were supplied for use with the battery operated HP infra-red thermal printer that is designed for use w

TThheePPrroommppttccoommmmaannddssBEEP <frequency>;<duration> This will use the piezo crystal in the calculator to create a sound of the s

DISP <line number>;<expression> This command breaks the display up into 7 lines and allows output to them. Using the DISP command on a

DISPTIME This command pops up a box displaying the calculator’s internal time and date. These can be set by storing values to the variables Time and

WAIT <duration> This command pauses execution for the specified number of seconds. Execution resumes at the next statement after the WAIT comma

42 AAPPPPEENNDDIIXXAA::SSOOMMEEWWOORRKKEEDDEEXXAAMMPPLLEESSThe examples which follow are intended to illustrate the ways in which the calculator can b

Method 3 - Using the POLYROOT function The advantage of this is that it can be done in the HOME view and is quick and easy. It also has the advantage

Table of Contents Introduction ...

The MEMORY MANAGER view Settings made in the MODES view also apply to the appearance of equations and results displayed using the SHOW command, cover

FFiinnddiinnggccrriittiiccaallppooiinnttssaannddggrraapphhiinnggaappoollyynnoommiiaallFor the function fx 2+ + 6 …()= x3− 4x x (i) find the intercept

Step4. Because I know that part (iv) of the question requires me to re-use these extremum values in an integration (which I would like to be as accu

SSoollvviinnggssiimmuullttaanneeoouusseeqquuaattiioonnss..Solve the systems of equations below: 2xy= 4−−32x y = −7⎫ 3x y z(i) ⎬ (ii) −+2 − = −10.5

Step 3. Change into the HOME view and enter the calculation M1-1*M2. The result is the (x,y) coordinate of the solution displayed as a matrix. A si

EExxppaannddiinnggppoollyynnoommiiaallssExpand the expressions below. 4 (i) ( 2x + 3)5 (ii) (3a − 2b)(i) Use POLYFORM((2X+3)^4,X) to expand the poly

EExxppoonneennttiiaallggrroowwtthhA population of bacteria is known to follow a growth pattern governed by the equation NN kt ;t ≥ 0 . It is observe

(ii) Predict N for t = 15 hours. In the PLOT view, press up arrow to move the cursor onto the curve of best fit. Now press and enter the value 15.

SSoolluuttiioonnooffmmaattrriixxeeqquuaattiioonnssSolve for the value of X in A(I − 2X ) = B −⎛ 23⎞ ⎛ 3 2⎞where A =⎜ B =⎜ ⎟ ⎝− 15⎠⎟ , ⎝ 1 4⎠ The al

FFiinnddiinnggccoommpplleexxrroooottss()= z3+ iz − 4z i.i. Find all roots of the complex polynomial fz 2 − 4 ii. Find the complex roots of z5= 32 .

CCoommpplleexxRRoooottssoonntthheehhpp4400ggss() = z + iz2 − 4z i.i. Find all roots of the complex polynomial fz 3 − 4 ii. Find the complex roots o

Downloaded aplets & memory As you can see in the screen snapshot on the previous page, my calculator has a number of extra aplets. Two of them, S

AAnnaallyyzziinnggvveeccttoorrmmoottiioonnaannddccoolllliissiioonnssShip A is currently at position vector 21i+ 21jkm and is currently traveling at a

I want to graph this function for the first six seconds but I am not sure what y scale to use so I will set XRng to be 0 to 6 in the PLOT SETUP view a

2 IInnffeerreenncceetteessttiinngguussiinnggtthheeCChhii22tteesstt Grade awarded A teacher wishes to decide, at the 5% level of significance, Year A

Changing into the Solve aplet we can enter a formula which will allow us to calculate values from the Chi2 distribution using the UTPC function. With

43 AAPPPPEENNDDIIXXBB::TTEEAACCHHIINNGGOORRLLEEAARRNNIINNGGCCAALLCCUULLUUSSThere are many ways that the teaching or learning of functions and calculus

DDoommaaiinnssaannddCCoommppoossiitteeFFuunnccttiioonnssThere are a number of ways that the calculator can help with this. Examples are given below b

ii. When discussing the concept of a domain, the NUM view can be very useful in developing this (see right). In the SYMB view, enter the functions sh

GGrraaddiieennttaattaaPPooiinnttThis is best introduced using an aplet called “Chords” downloaded from The HP HOME View web site (at http://www.hphome

GGrraaddiieennttFFuunnccttiioonnOnce the concept of gradient at a point has been established the next step is to develop the idea of a gradient functi

TThheeCChhaaiinnRRuulleeIf desirable, an aplet is available from The HP HOME View web site (at http://www.hphomeview.com), called “Chain Rule”, which

The GRAPHICS MANAGER The LIBRARY MANAGERThere are two views, shown right, for which the only access is via the MEMORY MANAGER screen. The first of th

AArreeaaUUnnddeerrCCuurrvveessThis topic is most easily handled using an aplet from The HP HOME View web site (at http://www.hphomeview.com). This ap

IInneeqquuaalliittiieessThe topic of inequalities is one that is often included in calculus courses, particularly during the study of ≥ 2 , ) :domains

PPiieecceewwiisseeDDeeffiinneeddFFuunnccttiioonnssPiecewise defined functions can easily be graphed on the calculator by breaking them up into their c

Students should also be encouraged to press the button after finding a solution since a case like this will give ‘Extremum’ whereas a correct solutio

44 AAPPPPEENNDDIIXXCC::TTHHEECCAASSOONNTTHHEEHHPP4400GGSSIInnttrroodduuccttiioonnThis appendix is intended to give a useful introduction and over view

The chances are that one will have a ‘+’ symbol to the left of it, while the other has a ‘-‘. This is telling you that the ‘+’ value is greater than r

What is the difference between the hp 39g, hp 40g, hp 39g+ and the hp 39gs & hp 40gs There were two competing sets of requirements at the time tha

UUssiinnggtthheeCCAASSThe first step is to activate the CAS. This is done from the HOME view by pressing screen key 6 (SK6), labeled . When you do, y

Defining new variables In addition to the pre-defined variables you can also define your own using the STORE command. These new variables can have na

ii. Assume that we want to show working by evaluating the binomial expression separately. Press , , , , to highlight the right hand bracket and

FFrraaccttiioonnssoonntthheehhpp3399ggssaannddhhpp4400ggssEarlier we examined the use of the MODES view, and the meaning of Number Format. We discuss

viii. Pressing this time will result in the screen shown below right which displays the two complex roots. ix. Press , , CLEAR to clear the highl

Pressing down arrow at that point moved down the tree. The default is to move to the left-most node D. This meant that the 2 was highlighted and so wh

5 After typing the 5, press up arrow once to highlight that node S. If you now press left arrow you will find that the highlight will jump horizontall

Special characters As in the HOME view, special characters such as inequalities are available from the CHARS view, although the appearance of the CHAR

Special editing commands – Undo, multi-select & swap Unlike most calculators the CAS editing screen has an undo function. If you have performed s

iv. SHIFT Pressing SHIFT swaps the currently highlighted/selected branch for the one on the immediate left. and then extended the selection using

Changing Font Although the default font is very easy to read, it is quite large and often makes parts of the expression or result extend off the scree

If you want to delete the entire expression then the simplest method is to press HOME, exit the CAS and then re-enter it with a blank screen. Alterna

The PUSH and POP commands Occasionally it is desirable to transfer results from the normal HOME view to the CAS screen or vice versa. This is done u

If you choose the Function aplet then you will be asked to nominate a destination. The current contents of each function is shown to allow you to cho

The second point to remember involves the method the hp 39gs and hp 40gs use when converting decimals to fractions, which is basically to generate (in

Notice the lack of a ‘+c’ indefinite constant in the integration result. Here, this is because we are using the definite integral (see page 73 and the

EExxaammpplleessuussiinnggtthheeCCAASSIn these examples we will begin with exercises which demonstrate the basic abilities of the CAS to simplify expr

Example 2: Simplifying surds Simplify the surd expression: 218 − 72 + 75 i. Begin by entering the expression: 2 SHIFT 18 SHIFT SHIFT 72 SHI

There are two ways that functions can be used in the CAS. The first is to use them as the expression is entered. In this method the order is to choose

x 2 iii) Find lim x x→∞ 2 + 5 Limits to infinity are also permitted using the lim function, with infinity entered using the shortcut SHIFT 0. scro

Example 4: Factorizing expressions If you highlight an expression such as (2x+3)4 and press ENTER then the CAS will expand the bracket. Since the re

Example 5: Solving equations Solve the equation x413−= , giving i) real solutions and ii) complex solutions. From within the CAS, press SHIFT M

The LINSOLVE function can also be used to solve problems with symbolic coefficients such as the one below. Solve the system of equations: The comman

Example 7: Solving a simultaneous integration A continuous random variable X, has a probability distribution function given by: ⎧+abx +x2 for 1 ≤x

We can now use the LINSOLVE function to find A and B. While the second linear equation is still highlighted, fetch the LINSOLVE command from the men

Pitfalls in Fraction mode The Fraction setting is thus far more powerful than most calculators but can require that you understand what is happening.

Example 8: Defining a user function The DEF function allows you to define your own functions, which are then available for use. In the example below

We can now test to see if this is a prime number by using the ISPRIME? function from the MATH menu. This is found in the Integer section of the CAS fu

Example 9: Investigation of a complex function ()= 1 z2 + z in parametric form and graph it. ShowRewrite the function fz 2 π⎛⎞that it is symmetrica

iv. And, having linearized it, we store it as a variable M in case we need to refer to it again. ALPHA M ENTER When the STORE command is executed t

vi. Clear the current contents of the screen using SHIFT ALPHA CLEAR. Then perform the same definition assignment for Y1(t) as the imaginary part

viii. We can see symmetry visually if the function is graphed and the aplet best suited to this is the Parametric aplet. When a function is sent to

One additional step is required. For some reason the Parametric aplet doesn’t seem to properly accept the functions. If you press PLOT now you will

Example 10: First order linear differential equation In order to illustrate the use of the CAS help pages discussed on page 361 we will the example p

TThheeCCAASSmmeennuussThere are a variety of different places that functions are stored, often overlapping for greater convenience. The Screen menus O

The MATH menu Pressing the MATH button in the CAS has a different effect than in the HOME screen. In the HOME screen the result is as shown right. A

The reason for this ‘error’ is that the 1/3 and 4/5 were converted to decimals and added to give 1.133333…. This was converted back to a fraction u

The CMDS menu All of the functions listed in the table on the previous page are also available via the SHIFT CMDS menu where they are in alphabetical

OOnn--lliinneehheellppOne of the most helpful features of the hp 40gs CAS is the on-line help provided by the SYNTAX button (SHIFT 2). Pressing SYNTA

CCoonnffiigguurriinnggtthheeCCAASSIn most of the examples which precede this section it was assumed that the CAS was in its default settings. Two ver

Below the title bar you can see the first section of a series of alternatives which let you manipulate the configuration. Most alternatives are toggle

Num. Factor mode When the Num. Factor setting is selected, approximate roots are used when factoring. For example, is irreducible over the integers bu

Increasing-powers mode When Increasing-powers mode is selected, polynomials will be listed so that the terms will have increasing powers of the indepe

TTiippss&&TTrriicckkss--CCAASS• In CAS, angles are always expressed in radians and no other setting is possible. When you are the calculator

COPYing calculations Clearing the History TThheeHHOOMMEEHHiissttoorryyThe HOME page maintains a record of all your calculations called the History. Y

SHOWing results key you will see another screen key labeled . This key will display an expression the way you would write it on the page rather tha

SSttoorriinnggaannddRReettrriieevviinnggMMeemmoorriieessEach of the alphabetic characters shown in orange below the keys can function as a memory. So

The Statistics Aplet - Univariate Data...114 The Expert: Simulations &

RReeffeerrrriinnggttooootthheerraapplleettssffrroommtthheeHHOOMMEEvviieeww..Once functions or sequences have been defined in other aplets, they can be

AAbbrriieeffiinnttrroodduuccttiioonnttootthheeMMAATTHHMMeennuuThe MATH menu holds all the functions that are not used often enough to be worth a key o

RReesseettttiinnggtthheeccaallccuullaattoorrIt is probably inevitable as the line between calculators and computers becomes blurred that calculators w

Hard reboot (with loss of memory) To completely reset the calculator’s memory back to factory settings press ON+SK1+SK6. (SK1=”screen key 1”) When do

• Take the batteries out, including the round backup battery. Press and hold the ON button for 2 minutes to remove any possible remaining power from

SSuummmmaarryy• The up/down arrow key moves the history highlight through the record of previous calculations. When the highlight is visible, the key

Choose the aplet 8 TTHHEEFFUUNNCCTTIIOONNAAPPLLEETTThe Function aplet is probably the one that you will use most of all. It allows you to: • graph e

The SYMB view key. When you do, your screen should change so that it appears like the one on the right. This is the SYMB view. Notice that the scre

The NUM view The PLOT view If you now press the NUM key, you will see the screen on the right. It shows the calculated function values for F1(X), sta

AAuuttooSSccaalleeAuto Scale attempts to fit the best possible vertical scale to the horizontal scale you have chosen. It is not always successful but

Working with Notes & the Notepad...217 Independent Notes and the Notep

Detail vs. Faster TThheePPLLOOTTSSEETTUUPPvviieewwIn the information that follows it will be assumed that you have performed the tasks on the previous

SimultaneousConnect AxesLabels Grid The first option Simult controls whether each graph is drawn separately (one after the other) or whether they are

The MENU toggle TThheeddeeffaauullttaaxxiisssseettttiinnggssThe default scale is displayed in the PLOT SETUP view shown right. It may seem a strange

TThheeMMeennuuBBaarrffuunnccttiioonnssIn the examples and explanations which follow, the functions and settings used are: Trace is quite a useful tool

Goto This function allows you to move directly to a point on the graph without having to trace along the graph. It is very powerful and useful. Suppos

The Zoom Sub-menu The next menu key we’ll examine is . Pressing the key under pops up a new menu, shown right. The list which follows covers the p

As you move the cursor to a position at the diagonally opposite corner of a rectangle, the selection box will appear on the screen. expands the box t

TThheeFFCCNNmmeennuuNote: Before continuing, set the axes back to the way we set them at the top of page 53. Looking at the menu functions again, you

Intersection menu is Intersection. If you choose this option, then you will be presented with a choice similar to the one in the screen shown right.

Definite integrals Signed area… menu is the Signed Area tool. Before we begin to use it, make sure that Another very useful tool provided in the is

Appendix A: Some Worked Examples...298 Finding the intercepts of a quadratic

Tracing the integral in PLOT key, an alternative method is to use the tracing facility. The advantage of this is that the ‘area’ is shown visually a

Areas between and under curves If we are wanting to find true areas rather than the ‘signed areas’ given by a simple definite integral then we must ta

9 TTHHEEEEXXPPEERRTT::WWOORRKKIINNGGWWIITTHHFFUUNNCCTTIIOONNSSEEFFFFEECCTTIIVVEELLYYFinding a suitable set of axes This is probably the most frustrati

Change into the NUM view and scroll through the window from zero to 100. As you do so, take note of the values that the function takes. From the dis

The advantage of doing it this way is that if you zoom in or out by a factor of 2 or 4 or 5, the cursor jumps will stay at (relatively) nice values al

On the other hand there is a way to further simplify the expression. the result and enclose it with the POLYFORM function as shown right, adding a

Differentiating There are different approaches that can be taken to differentiating, most of which are best done in the SYMB view of the Function aple

Algebraic differentiation is most easily handled in the SYMB view of Function. The best method is to define your function as F1(X) and its derivative

The simplest way to deal with this is to use scales which are multiples of 13 xthe default scales. For example by using −≤≤13 and 6.2 y 6.4 − ≤≤

However, for the scale of -6 to 6 the pixels are no longer 'nice' values of 0.1. If you try to trace the circle you'll see that the pi

The hp 39gs vs. the hp 40gs 2 IINNTTRROODDUUCCTTIIOONNThis book is intended to help you to master your hp 39gs or hp 40gs calculator but will also be

NumStart & NumStep Retaining calculated values When you find an extremum or an intersection, the point is remembered until you move the cursor eve

Automatic vs. Build Your Own ZOOMLooking at the NUM SETUP view you will see an entry called NumType with the default value of Automatic. The alternat

Integration: The definite integral using the ∫ function The situation for integration is very similar to that of differentiation. As with differentia

Integration: The algebraic indefinite integral Algebraic integration is also possible (for simple functions), in the following fashions: • If done in

A caveat when integrating symbolically… This substitution process has one implication which you need to be wary of and so it is worth examining the pr

Integration: The definite integral using PLOT variables As was discussed earlier, when you find roots, intersections, extrema or signed areas in the P

()= x2− 2 andSuppose we want to find the area between fx () 0.5x −1 from x = -2 to the first positive intersection of the two gx = graphs. From the h

Piecewise defined functions It is possible to graph piecewise defined functions using the Function aplet, although it involves literally splitting the

‘Nice’ scales As discussed earlier, the reason for the seemingly strange default scale of -6.5 to 6.5 is to ensure that each dot on the screen is exac

Nice scales in the PLOT-TABLE viewA time when ‘nice’ scales are more important is when you use the Plot-Table option in the VIEWS menu. If you use th

Many of the markets targeted by the hp 40gs do not allow infra-red communication in assessments and so, on the hp 40gs, this ability is permanently di

Problems when evaluating limits In evaluating limits to infinity using substitution, problems can be encountered if values are used which are too larg

A related effect happens when investigating the behavior of the commonly used ⎛ 1 ⎞n calculus limit of lim ⎜1 + . One of the common tasks given to s

Eventually the calculator reaches a value on the x axis which is large enough that it rounds off to a smaller number than 1.00000000003, which is 1.00

Gradient at a point as the limit of the slope of a chord PLOT view or via the δ differentiation operator. For students first being introduced to calc

Finding and accessing polynomial roots The POLYROOT function can be used to find roots very quickly, but the results are often difficult to see in the

10 TTHHEEVVIIEEWWSSMMEENNUUIn addition to the views of PLOT, SYMB and NUM (together with their SETUP views), there is another key which we have so fa

Plot-Detail Choosing Plot-Detail from the menu splits the screen into two halves and re-plots the graph in each half. The right hand side can now be

Plot-Table The next item on the VIEWS menu is Plot-Table. This option plots the graph on the right, with the Numeric view on the right half screen.

Nice table values What makes this view even more useful is that the table keeps its ‘nice’ scale even while the usual tools are being used. As you c

Auto Scale Auto Scale is an good way to ensure that you get a reasonable picture of the graph if you are not sure in advance of the scale. After usin

3 GGEETTTTIINNGGSSTTAARRTTEEDDLet’s begin by looking at the fundamentals - the layout of the keyboard and the positions of the important keys used fre

65 The Integer option is similar to decimal, except that it sets the axes so that each pixel is 1 rather than 0.1 thus giving an X scale of −≤ X ≤ 6

DDoowwnnllooaaddeeddAApplleettssffrroommtthheeIInntteerrnneettThe most powerful feature of the hp 39gs & hp 40gs is that you can download aplets a

Choose XRng, YRng & TRng 11 TTHHEEPPAARRAAMMEETTRRIICCAAPPLLEETTAn example of a graph from this aplet is: xt t() =5cos()⎪⎬⎫ 0 ≤≤2π()⎪⎭t which giv

TStep controls smoothness The effect of TRng will be visible.The X and Y ranges control the lengths of the axes. They determine how much of the funct

Calculator Tip  TStep Using  MODES lDecreasing beyond a certain point will slow down the graphing process without smoothing the graph any further.

12 TTHHE EEEXXPPEERRTT::VVEECCTTOORRFFUUNNCCTTIIOONNSSFFuunnaannddggaammeessApart from the normal mathematical and engineering applications of paramet

VVeeccttoorrssThe Parametric aplet can be used to visually display vector motion in one and two dimensions. Example 1 A particle P is moving in a stra

Example 2 Two ships are traveling according to the vector motions given below, where time is in hours and distance in kilometers. Illustrate their mot

Choose XRng, YRng & θRng θStep and smoothness Changing the default for θStep Circular circles 13 TTHHEEPPOOLLAARRAAPPLLEETTThis aplet is used to g

Recursive or non-recursive First, second & general terms 14 TTHHEESSEEQQUUEENNCCEEAAPPLLEETTThis aplet is used to deal with sequences, and indirec