HP 40gs Manual do Utilizador

HP 40gs graphing calculatoruser's guideEdition1Part Number F2225AA-90001hp40g+.book Page i Friday, December 9, 2005 1:03 AM

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Triangle Solve aplet 9-19Triangle Solve apletAbout the Triangle Solver apletThe Triangle Solver aplet allows you to determine the length of a side of

9-2 Triangle Solve apletOpen the Triangle Solver aplet1. Open the Triangle Solver aplet. Select Triangle SolverThe Triangle Solver aplet opens.Note: i

Triangle Solve aplet 9-3lengths as B and C, we would need to specify the angle as α. The illustration on the display will help you determine where to

Not enough dataIf you are using the general input form, you need to specify at least three values for the Triangle Solver to be able to calculate the

Statistics aplet 10-110Statistics apletAbout the Statistics apletThe Statistics aplet can store up to ten data sets at one time. It can perform one-va

10-2 Statistics apletOpen the Statistics aplet1. Open the Statistics aplet and clear existing data by pressing . Select Statistics The Statistics apl

Statistics aplet 10-3Choose fit and data columns4. Select a fit in the Symbolic setup view. SETUP-SYMB Select LinearYou can create up to five explorat

10-4 Statistics apletSetup plot 8. Change the plotting range to ensure all the data points are plotted (and select a different point mark, if you wish

Statistics aplet 10-5Predict values 13.To find the predicted sales figure if advertising were to go up to 6 minutes: S (to highlight Stat-Two) (to

P-1PrefaceThe HP 40gs is a feature-rich graphing calculator. It is also a powerful mathematics learning tool, with a built-in computer algebra system

10-6 Statistics apletEntering and editing statistical dataThe Numeric view ( ) is used to enter data into the Statistics aplet. Each column represents

Statistics aplet 10-7Example You are measuring the height of students in a classroom to find the mean height. The first five students have the followi

10-8 Statistics aplet3. Find the mean of the sample. Ensure the / menu key label reads . Press to see the statistics calculated from the sample dat

Statistics aplet 10-9To continue our example, suppose that the heights of the rest of the students in the class are measured, but each one is rounded

10-10 Statistics aplet5. Move the highlight bar into the right column of the H1 definition and replace the frequency value of 1 with the name C2. 26.

Statistics aplet 10-11Edit a data set In the Numeric view of the Statistics aplet, highlight the data value to change. Type a new value and press , or

10-12 Statistics apletDefining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or “

Statistics aplet 10-13To define your own fit1. In Numeric view, make sure is set.2. Display the Symbolic view. 3. Highlight the Fit expression (Fit1

10-14 Statistics apletComputed statisticsOne-variableWhen the data set contains an odd number of values, the data set’s median value is not used when

Statistics aplet 10-15Two-variablePlotting You can plot:• histograms ( )• box-and-whisker plots ( )• scatter plots ( ).Once you have entered your data

P-2NoticeThis manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibited by

10-16 Statistics apletTo plot statistical data1. In Symbolic view ( ), select ( ) the data sets you want to plot. 2. For one-variable data ( ), select

Statistics aplet 10-17Scatter Plot Two-variable statistics. The numbers below the plot indicate that the cursor is at the first data point for S2, at

10-18 Statistics apletRelative Error The relative error is a measure of the error between predicted values and actual values based on the specified Fi

Statistics aplet 10-19For instance, the data set (1,1), (3,9), (4,16), (2,4) would be plotted and traced in the order (1,1), (2,4), (3,9), (4,16).Trou

10-20 Statistics apletCalculating predicted valuesThe functions PREDX and PREDY estimate (predict) values for X or Y given a hypothetical value for th

Statistics aplet 10-21• Enter PREDY(x-value) to find the predicted value of the dependent variable given a hypothetical independent variable.You can t

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Inference aplet 11-111Inference apletAbout the Inference apletThe Inference capabilities include calculation of confidence intervals and hypothesis te

11-2 Inference apletInference aplet’s SYMB view keysThe table below summarizes the options available in Symbolic view.If you choose one of the hypothe

Inference aplet 11-3Select the inferential method2. Select the Hypothesis Test inferential method.Select HYPOTH TEST3. Define the type of test. Z–Tes

Getting started 1-11Getting startedOn/off, cancel operationsTo turn on Press to turn on the calculator.To cancel When the calculator is on, the ke

11-4 Inference apletBy default, each field already contains a value. These values constitute the example database and are explained in the feature o

Inference aplet 11-5A calculator produces the following 6 random numbers:0.529, 0.295, 0.952, 0.259, 0.925, and 0.592Open the Statistics aplet1. Open

11-6 Inference apletOpen Inference aplet6. Open the Inference aplet and clear current settings. Select Inference Select inference method and type7. Se

Inference aplet 11-7Import the data 10.Import the data from the Statistics aplet. Note: The data from C1 is displayed by default.Note: Press to see

11-8 Inference apletHypothesis testsYou use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or tw

Inference aplet 11-9Results The results are:Two-Sample Z-TestMenu name Z-Test: μ1–μ2On the basis of two samples, each from a separate population, this

11-10 Inference apletResults The results are:One-Proportion Z-TestMenu name Z-Test: 1πOn the basis of statistics from a single sample, this test measu

Inference aplet 11-11Inputs The inputs are:Results The results are:Two-Proportion Z-TestMenu name Z-Test: π1 – π2On the basis of statistics from two s

11-12 Inference apletInputs The inputs are:Results The results are:One-Sample T-TestMenu name T-Test: 1 μThe One-sample T-Test is used when the popula

Inference aplet 11-13Inputs The inputs are:Results The results are:Field name DefinitionSample mean.Sx Sample standard deviation.n Sample size.μ0 Hypo

1-2 Getting startedThe displayTo adjust the contrastSimultaneously press and (or ) to increase (or decrease) the contrast.To clear the display •

11-14 Inference apletTwo-Sample T-TestMenu name T-Test: μ1 – μ2The Two-sample T-Test is used when the population standard deviation is not known. On t

Inference aplet 11-15Results The results are:Confidence intervalsThe confidence interval calculations that the HP 40gs can perform are based on the No

11-16 Inference apletResults The results are:Two-Sample Z-IntervalMenu name Z-INT: μ1– μ2This option uses the Normal Z-distribution to calculate a con

Inference aplet 11-17One-Proportion Z-IntervalMenu name Z-INT: 1 πThis option uses the Normal Z-distribution to calculate a confidence interval for th

11-18 Inference apletResults The results are:One-Sample T-IntervalMenu name T-INT: 1 μThis option uses the Student’s t-distribution to calculate a con

Inference aplet 11-19Results The results are:Two-Sample T-IntervalMenu name T-INT: μ1 – μ2This option uses the Student’s t-distribution to calculate a

11-20 Inference apletResults The results are:Result Description Critical T Critical value for T. μ MinLower bound for μ1 – μ2. μ MaxUpper bound for μ1

Using the Finance Solver 12-112Using the Finance SolverThe Finance Solver, or Finance aplet, is available by using the APLET key in your calculator.

12-2 Using the Finance Solvercombined amount earns interest at a certain rate. Financial calculations involving compound interest include savings acco

Using the Finance Solver 12-3flow diagram shows lease payments at the beginning of each period.The following cash flow diagram shows deposits into an

Getting started 1-3Annunciators. Annunciators are symbols that appear above the title bar and give you important status information.The keyboardAnnunc

12-4 Using the Finance SolverPerforming TVM calculations1. Launch the Financial Solver as indicated at the beginning of this section.2. Use the arrow

Using the Finance Solver 12-5Example 1 - Loan calculationsSuppose you finance the purchase of a car with a 5-year loan at 5.5% annual interest, compou

12-6 Using the Finance SolverExample 2 - Mortgage with balloon paymentSuppose you have taken out a 30-year, $150,000 house mortgage at 6.5% annual int

Using the Finance Solver 12-7Calculating AmortizationsAmortization calculations, which also use the TVM variables, determine the amounts applied towar

12-8 Using the Finance Solver3. Press the soft menu key to amortize the new batch of payments. Repeat steps 1 through 3 as often as needed.Example

Using mathematical functions 13-113Using mathematical functionsMath functionsThe HP 40gs contains many math functions. The functions are grouped in ca

13-2 Using mathematical functionsTo select a function 1. Press to display the MATH menu. The categories appear in alphabetical order. 2. Press or

Using mathematical functions 13-3Functions common to keyboard and menusThese functions are common to the keyboard and MATH menu. Keyboard functions Th

13-4 Using mathematical functions,,, Add, Subtract, Multiply, Divide. Also accepts complex numbers, lists and matrices.value1+ value2, etc.exNatural e

Using mathematical functions 13-5ExampleASIN(1) returns 90 (Degrees mode).ACOS Arc cosine: cos–1x. Output range is from 0° to 180°, 0 to π, or 0 to 20

1-4 Getting startedMenu keys• On the calculator keyboard, the top row of keys are called menu keys. Their meanings depend on the context—that’s why th

13-6 Using mathematical functionsExample2^8 returns 256 ABS Absolute value. For a complex number, this is .ABS(value)ABS((x,y))ExampleABS(–1) returns

Using mathematical functions 13-7Example(0,s1,2*X+3,X) finds the indefinite result 3*s1+2*(s1^2/2)See “To find the indefinite integral using forma

13-8 Using mathematical functionsExampleIM((3,4)) returns 4RE Real part x, of a complex number, (x, y).RE((x, y))ExampleRE((3,4)) returns 3ConstantsTh

Using mathematical functions 13-9→C Convert from Fahrenheit to Celcius.Example→C(212) returns 100→F Convert from Celcius to Fahrenheit.Example→F(0) re

13-10 Using mathematical functionsCOSH Hyperbolic cosine COSH(value)SINH Hyperbolic sine.SINH(value)TANH Hyperbolic tangent.TANH(value)ALOG Antilogari

Using mathematical functions 13-11RECURSE Provides a method of defining a sequence without using the Symbolic view of the Sequence aplet. If used with

13-12 Using mathematical functionsExampleFor x4+2x3–25x2–26x+120: POLYEVAL([1,2,-25,-26,120],8) returns 3432.POLYFORM Polynomial form. Creates a polyn

Using mathematical functions 13-13Factorial of a positive integer. For non-integers, ! = Γ(x + 1). This calculates the gamma function.value!PERM Numb

13-14 Using mathematical functionsUTPT Upper-Tail Student’s t-Probability given degrees of freedom, evaluated at value. Returns the probability that t

Using mathematical functions 13-15HMS→ Hours-minutes-seconds to decimal. Converts a number or expression in H.MMSSs format (time or angle that can inc

Getting started 1-5Entry/Edit keysThe entry and edit keys are:Key Meaning (CANCEL)Cancels the current operation if the calculator is on by pressing .

13-16 Using mathematical functionsExample 9 MOD 4 returns 1% x percent of y; that is, x/100*y.%(x, y)Example%(20,50) returns 10%CHANGE Percent change

Using mathematical functions 13-17ExamplesSIGN (–2) returns –1SIGN((3,4)) returns (.6,.8)TRUNCATE Truncates value to decimal places. Accepts complex n

13-18 Using mathematical functionsExamplesISOLATE(2*X+8,X) returns -4ISOLATE(A+B*X/C,X) returns -(A*C/B)LINEAR? Tests whether expression is linear for

Using mathematical functions 13-19Test functionsThe test functions are logical operators that always return either a 1 (true) or a 0 (false).< Less

13-20 Using mathematical functionsXOR Exclusive OR. Returns 1 if either value1 or value2—but not both of them—is non-zero, otherwise returns 0.value1

Using mathematical functions 13-21names. The HP 40gs has six formal names available for use in symbolic calculations. These are S1 to S5. When you per

13-22 Using mathematical functionsdifferentiation function substitutes the value that X holds, and returns a numeric result.For example, consider the

Using mathematical functions 13-23 F1 3. Select F2(X) and evaluate it.4. Press to display the result. Note: Use the arrow keys to view the entire

13-24 Using mathematical functions4. Copy the result and evaluate. Thus, substituting X for S1, it can be seen that: This result is derived from subst

Using mathematical functions 13-25Program constantsThe program constants are numbers that have been assigned to various calculator settings to enable

1-6 Getting startedShifted keystrokesThere are two shift keys that you use to access the operations and characters printed above the keys: and . CHAR

13-26 Using mathematical functions3. Use the arrow keys to navigate through the options.4. To see the symbol and value of a selected constant, press

Using mathematical functions 13-273. Select light s...from the Physics menu.4. Press . The menu closes and the value of the selected constant is copi

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Computer Algebra System (CAS) 14-114Computer Algebra System (CAS)What is a CAS?A computer algebra system (hereafter CAS) enables you to perform symbol

14-2 Computer Algebra System (CAS)using vectors and matrices. (Vectors and matrices cannot be entered using the Equation Writer).To open the Equation

Computer Algebra System (CAS) 14-33. Press and to select just the 20 in the term. 4. Press the menu key and choose FACTOR. Then press .Note th

14-4 Computer Algebra System (CAS)10.Press three times to select the entire expression and then press to simplify it to the form required.CAS varia

Computer Algebra System (CAS) 14-5CAS modesThe modes that determine how CAS operates can be set on CAS MODES screen. To display CAS MODES screen, pres

14-6 Computer Algebra System (CAS)calculated as closed-form algebraic expressions, whenever possible. [Default: unselected.]Num. Factor mode When the

Computer Algebra System (CAS) 14-7Using CAS functions in HOMEYou can use many computer algebra functions directly in the HOME screen, as long as you t

Getting started 1-7HELPWITH The HP 40gs built-in help is available in HOME only. It provides syntax help for built-in math functions. Access the HELPW

14-8 Computer Algebra System (CAS)Symbolic matrices are stored as a list of lists and therefore must be stored in L0, L1…L9 (whereas numeric matrices

Computer Algebra System (CAS) 14-9HELP and press . The menu of help topics appears. Each help topic includes the required syntax, along with real sam

14-10 Computer Algebra System (CAS)For example, suppose you have stored the expression x2 in G, and have defined the function F(x) as x2. Suppose now

Computer Algebra System (CAS) 14-11Typing: DEF(U(N) = 2N+1)produces the result:U(N) = 2N+1Typing: U(3)then returns:7ExampleCalculate the first six Fer

14-12 Computer Algebra System (CAS)which gives4294967297You can factor F(5) with FACTOR, which you’ll find in the ALGB menu on the menu bar.Typing:FAC

Computer Algebra System (CAS) 14-13In real mode, the result is:In complex mode (using CFG), the result is:PARTFRAC Partial fraction expansionPARTFRAC

14-14 Computer Algebra System (CAS)Example 2Typing:SUBST(QUOTE(CONJ(Z)),Z=1+i)gives:CONJ(1+i)STORE Store an object in a variableSTORE stores an object

Computer Algebra System (CAS) 14-15SUBST Substitute a value for a variableSUBST has two parameters: an expression dependent on a parameter, and an equ

14-16 Computer Algebra System (CAS)DIFF menuDERIV Derivative and partial derivativeDERIV has two arguments: an expression (or a function) and a variab

Computer Algebra System (CAS) 14-17DERVX(F)Or, if you have defined F(X) using DEF, that is, if you have typed:then type:DERVX(F(X))Simplify the result

NoticeREGISTER YOUR PRODUCT AT: www.register.hp.comTHIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHA

1-8 Getting started• Pressing displays the list of Program Constants. You can use these in programs that you develop.• Pressing displays a menu of

14-18 Computer Algebra System (CAS)and with period T (T being equal to the contents of the variable PERIOD).If f(x) is a discrete series, then:Example

Computer Algebra System (CAS) 14-19IBP returns the AND of and of that is, the terms that are calculated when performing a partial integration.It rem

14-20 Computer Algebra System (CAS)Example Given:calculate a primitive of f.Type:Or, if you have stored f(x) in F, that is, if you have already typed:

Computer Algebra System (CAS) 14-21gives a primitive:NoteYou can also type which gives the primitive which is zero for x = 1ExampleCalculate:Typing:

14-22 Computer Algebra System (CAS)QUOTE(expression), to avoid rewriting the expression in normal form (i.e., not to have a rational simplification of

Computer Algebra System (CAS) 14-23Typing:gives:2NOTE: To find the limit as x approaches a+(resp a–), the second argument is written:X=A+0(resp X=A-0)

14-24 Computer Algebra System (CAS)PREVAL is used for calculating an integral defined from a primitive: it evaluates this primitive between the two li

Computer Algebra System (CAS) 14-25Typing:gives:• Example — Expansion in the vicinity of x=+∞ or x=–∞Example 1Give a 5th-order expansion of arctan(x)

14-26 Computer Algebra System (CAS)You must be in Rigorous (not Sloppy) mode to apply SERIES with unidirectional expansion. (See “CAS modes” on page 1

Computer Algebra System (CAS) 14-27TABVAR Variation tableTABVAR has as a parameter an expression with a rational derivative.TABVAR returns the variati

Getting started 1-9To search a menu • Press or to scroll through the list. If you press or , you’ll go all the way to the end or the beginni

14-28 Computer Algebra System (CAS)Typing:gives:Note‘th-order’ means that the numerator and the denominator are expanded to the 4th relative order (he

Computer Algebra System (CAS) 14-29Typing:DISTRIB((X+1)·(X+2)·(X+3))gives:EPSX0 Disregard small valuesEPSX0 has as a parameter an expression in X, and

14-30 Computer Algebra System (CAS)Typing:EXP2POW(EXP(N · LN(X)))gives:FDISTRIB DistributivityFDISTRIB has an expression as argument.FDISTRIB enables

Computer Algebra System (CAS) 14-31Example 3Typing:LIN(SIN(X))gives:LNCOLLECT Regroup the logarithmsLNCOLLECT has as an argument an expression contain

14-32 Computer Algebra System (CAS)Typing:SINCOS(EXP(i·X))gives after turning on complex mode, if necessary:cos(x) + i · sin(x)SIMPLIFY SimplifySIMPLI

Computer Algebra System (CAS) 14-33Typing:XQ(1.414213562)gives:√2SOLV menuThe SOLV menu contains functions that enable you to solve equations, linear

14-34 Computer Algebra System (CAS)To produce the solutions for y(0) = 1, type:which gives:Example 2Solve:y” + y = cos(x)y(0) = 1 y’(0) = 1It is possi

Computer Algebra System (CAS) 14-35LDEC Linear differential equations having constant coefficientsLDEC enables you to directly solve linear differenti

14-36 Computer Algebra System (CAS)L1=2L1+L2ENTERReduction Resultthen press ENTER. The following is then written to the Equation Writer:(x = −2) AND (

Computer Algebra System (CAS) 14-37then press ENTER. The following is then written to the Equation Writer:SOLVE Solve equationsSOLVE has as two parame

1-10 Getting startedMode settingsYou use the Modes input form to set the modes for HOME.HINTAlthough the numeric setting in Modes affects only HOME, t

14-38 Computer Algebra System (CAS)SOLVEVX Solve equationsSOLVEVX has as a parameter either:(1) an equality between two expressions in the variable co

Computer Algebra System (CAS) 14-39Typing:ACOS2S(ACOS(X) + ASIN(X))gives, when simplified:ASIN2C Transform the arcsin into arccosASIN2C has as a trigo

14-40 Computer Algebra System (CAS)Typing:ATAN2S(ATAN(X))gives:HALFTAN Transform in terms of tan(x/2)HALFTAN has a trigonometric expression as an argu

Computer Algebra System (CAS) 14-41TAN2CS2 transforms this expression by replacing tan(x) with .Typing:TAN2CS2(TAN(X))gives:TAN2SC Replace tan(x) with

14-42 Computer Algebra System (CAS)TCOLLECT linearizes this expression in terms of sin(n x) and cos(n x), then (in Real mode) reconstructs the sine an

Computer Algebra System (CAS) 14-43gives:4·cos(x)3–3·cos(x)TLIN Linearize a trigonometric expressionTLIN has as an argument a trigonometric expression

14-44 Computer Algebra System (CAS)Typing:TRIG(SIN(X)2 + COS(X)2 + 1)gives:2TRIGCOS Simplify using the cosinesTRIGCOS has as an argument a trigonometr

Computer Algebra System (CAS) 14-45CAS Functions on the MATH menuWhen you are in the Equation Writer and press , a menu of additional CAS functions av

14-46 Computer Algebra System (CAS)returns:Y = X –1 + 2Pressing simplifies this to:Y = X + 1IM See “IM” on page 13-7.– Specifies the negation of the

Computer Algebra System (CAS) 14-47DIVISGives the divisors of an integer.ExampleTyping:DIVIS(12)gives:12 OR 6 OR 3 OR 4 OR 2 OR 1Note: DIVIS(0) return

Getting started 1-11Setting a modeThis example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current

14-48 Computer Algebra System (CAS)In step-by-step mode, there are a number of intermediate results:18 mod 15 = 315 mod 3 = 0Result: 3Pressing or

Computer Algebra System (CAS) 14-49[48,1,0][30,0,1]*–1[18,1,–1]*–1[12,–1,2]*–1[6,2,–3]*–2Result: [6,2,–3]Pressing or then causes 2 AND –3 = 6 to b

14-50 Computer Algebra System (CAS)IREMAINDER works with integers and with Gaussian integers. This is what distinguishes it from MOD.Example 2Typing:I

Computer Algebra System (CAS) 14-51NEXTPRIME NEXTPRIME(n) returns the smallest prime or pseudo-prime greater than n.ExampleTyping:NEXTPRIME(75)gives:7

14-52 Computer Algebra System (CAS)DIVMOD Division in Z/pZ or Z/pZ[X].Example 1In Z/pZ, the arguments are two integers: A and B. When B has an inverse

Computer Algebra System (CAS) 14-53FACTORMOD Factors a polynomial in Z/pZ[X], providing that p ≤ 97, p is prime and the order of the multiple factors

14-54 Computer Algebra System (CAS)MULTMOD Performs a multiplication in Z/pZ or in Z/pZ[X].Example 1Typing:MULTMOD(11, 8)gives:–3Example 2Typing:MULTM

Computer Algebra System (CAS) 14-55SUBTMOD Performs a subtraction in Z/pZ or Z/pZ[X].Example 1Typing:SUBTMOD(29, 8)gives:–5Example 2Typing:SUBTMOD(11X

14-56 Computer Algebra System (CAS)FACTOR Factors a polynomial.Example 1Typing:FACTOR(X2 – 2)gives:Example 2Typing:FACTOR(X2 + 2·X + 1)gives:GCD Retur

Computer Algebra System (CAS) 14-57LCM Returns the LCM (Least Common Multiple) of two polynomials.ExampleTyping:LCM(X2 + 2·X + 1, X2 – 1)gives:LEGENDR

1-12 Getting startedThe cursor (highlight) is in the first field, Angle Measure.2. Press to display a list of choices. 3. Press to select Degrees,

14-58 Computer Algebra System (CAS)PROPFRAC PROPFRAC rewrites a rational fraction so as to bring out its whole number part.PROPFRAC(A(X)/ B(X)) writes

Computer Algebra System (CAS) 14-59Note that in step-by-step mode, synthetic division is shown, with each polynomial represented as the list of its co

14-60 Computer Algebra System (CAS)Example 1Typing:TCHEBYCHEFF(4)gives:Example 2Typing:TCHEBYCHEFF(–4)gives:Real menuCEILING See “CEILING” on page 13-

Computer Algebra System (CAS) 14-61Tests menuASSUME Use this function to make a hypothesis about a specified argument or variable.ExampleTyping:ASSUME

14-62 Computer Algebra System (CAS)CAS Functions on the CMDS menuWhen you are in the Equation Writer and press , a menu of the full set of CAS funct

Computer Algebra System (CAS) 14-63ExampleFind the solutions P(X) of:P(X) = X (mod X2 + 1)P(X) = X – 1 (mod X2 – 1)Typing:CHINREM((X) AND (X2 + 1), (X

14-64 Computer Algebra System (CAS)Example 1Typing:EXP2HYP(EXP(A))gives:sinh(a) + cosh(a)Example 2Typing:EXP2HYP(EXP(–A) + EXP(A))gives:2 · cosh(a)GAM

Computer Algebra System (CAS) 14-65ExampleTyping:IABCUV(48, 30, 18)gives:6 AND –9IBERNOULLI Returns the nth Bernoulli’s number B(n) where:ExampleTypin

14-66 Computer Algebra System (CAS)ILAP is the inverse Laplace transform of a given expression. Again, the expression is the value of a function of th

Computer Algebra System (CAS) 14-67Typing:gives:LAP See ILAP above.PA2B2 Decomposes a prime integer p congruent to 1 modulo 4, as follows:p = a2 + b2.

Getting started 1-13symbolic views of the aplets in the following table. See “Aplet view configuration” on page 1-18 for further information.In additi

14-68 Computer Algebra System (CAS)gives:Psi Returns the value of the Digamma function at a.The Digamma function is defined as the derivative of ln(Γ(

Computer Algebra System (CAS) 14-69ExampleTyping:SIGMA(X · X!, X)gives:X!because (X + 1)! – X! = X · X!.SIGMAVX Returns the discrete antiderivative of

14-70 Computer Algebra System (CAS)TSIMP Simplifies a given expression by rewriting it as a function of complex exponentials, and then reducing the nu

Equation Writer 15-115Equation WriterUsing CAS in the Equation Writer The Equation Writer enables you to type expressions that you want to simplify, f

15-2 Equation WriterALGB menu The menu contains functions that enable you to perform algebra, such as factoring, expansion, simplification, substitu

Equation Writer 15-3REWRI menu The menu contains functions that enable you to rewrite an expression in another form. SOLV menu The menu contains f

15-4 Equation Writer• The fourth symbol, S, in the above example, indicates that you are in step-by-step mode. If you were not in step-by-step mode, t

Equation Writer 15-5Entering expressions and subexpressionsYou type expressions in the Equation Writer is much the same way as you type them in the HO

15-6 Equation Writerthis case, you have to press to select elements in the expression. The following illustration shows how an expression can be vie

Equation Writer 15-7• Press again and again to progressively select more of the top-most branch, and then lower branches (5x, 5x + 3, and then the e

1-14 Getting startedcharge and transferred to the HP 40gs using the provided Connectivity Kit. Quad Explorer apletThe Quad Explorer aplet is used to i

15-8 Equation Writer(– X) apply to it. As a result, the entered expression is interpreted, and displayed, as (2 + X)(3 – X). Select the entire express

Equation Writer 15-9Select the fifth branch by pressing . At this point, the desired expression is in the Equation Writer, as shown at the right. Sup

15-10 Equation WriterPressing produces the result of the partial calculation. Summing upPressing enables you to select the current element and it

Equation Writer 15-11How to modify an expression If you’re typing an expression, the key enables you to erase what you’ve typed. If you’re selecting

15-12 Equation WriterAccessing CAS functionsWhile you are in the Equation Writer, you can access all CAS functions, and you can access them in various

Equation Writer 15-13select the entire expression and press , you obtain: However, if you type:select the entire expression and press , you obtain 1

15-14 Equation WriterFirst option: function first, then argumentsIn the Equation Writer, press , select FACTOR and then press or . FACTOR() is disp

Equation Writer 15-15Press to obtain the an intermediate result (42 – 4) and again to evaluate the intermediate result. The final answer is 12. Se

15-16 Equation WriterPress to obtain an intermediate result, (4– 2)(4 + 2), and again to evaluate the intermediate result. The final answer, as be

Equation Writer 15-17• MODULO contains the value of p for performing symbolic calculations in Z/pZ or in Z/pZ[X]. You can change the value of p either

Getting started 1-15Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of as the values of a, b, c and d

15-18 Equation WriterDiff&Int (), Rewrite (), Solve () and Trig (). • The Complex menu, providing functions specific to manipulating with complex

Equation Writer 15-19Press to clear the value of the highlighted variable.Press to change the name of the highlighted variable.Press to define a new v

15-20 Equation WriterNOTEThis operation supposes that the current variable is also the variable of the function or curve you want to graph. When the e

Equation Writer 15-21Short-cut keys In the Equation Writer, the following are short-cut keys to the symbols indicated: 0 for ∞ 1 for i 3 for π 5 for

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Step-by-Step Examples 16-116Step-by-Step ExamplesIntroduction This chapter illustrates the power of CAS, and the Equation Writer, by working though a

16-2 Step-by-Step ExamplesPress to simplify the numerator.Press to select the entire fraction.Press to simplify the selected fraction, giving the

Step-by-Step Examples 16-3Press to factor 20 into .Press to select and to simplify it.Press to select and to exchange with .Press to se

16-4 Step-by-Step ExamplesPress to evaluate the selection.It remains to transform and combine it with . Follow the same procedure as undertaken a

Step-by-Step Examples 16-5Press to select the entire equation, then press to reduce it to .Press , select FACTOR, press and then . The result is

1-16 Getting startedAplet libraryAplets are stored in the Aplet library.To open an aplet Press to display the Aplet library menu. Select the aplet a

16-6 Step-by-Step ExamplesPress , select LINSOLVE and press .Enter 17 X 20 Y 90 10 X 25 Y 90 X YIf you are working in step b

Step-by-Step Examples 16-71. Find the exact length of AB in centimetres.2. Determine the equation of the line AB.First method Type:STORE((-1,3),A)and

16-8 Step-by-Step ExamplesPress again to simplify the result toY = 2X+5.Second method Type:(-3,-1 )-(-1,3)The answer is –(2+4i).With the answer stil

Step-by-Step Examples 16-94. Show that for every integer n > 0, bn × cn = a2n.5. Deduce the prime factor decomposition of a6.6. Show that GCD(bn,cn

16-10 Step-by-Step ExamplesShow that the whole numbers k such that: have digits in decimal notation.We have:so have digits in decimal notation.Mo

Step-by-Step Examples 16-11Now consider the product of two of the definitions entered above: B(N) × C(N): B N C N . Press , to select

16-12 Step-by-Step ExamplesPart 2Given the equation:[1]where the integers x and y are unknown and b3 and c3 are defined as in part 1 above:1. Show tha

Step-by-Step Examples 16-13so, , or The calculator is not needed for finding the general solution to equation [1].We started with and have established

16-14 Step-by-Step Examplesthe circle C, M will move on a curve Γ. In this exercise we will study and plot Γ.1. Let and m be the point on C of affix

Step-by-Step Examples 16-15Selecting the entire expression and pressing gives the result at the right:Now linearize the result by applying the LIN com

Getting started 1-17Numeric view Press to display the aplet’s Numeric view.In this view, the functions that you have defined are displayed in tabula

16-16 Step-by-Step ExamplesDEF command to it. Press to complete the definition.To calculate the real part of the expression, apply the IM command (a

Step-by-Step Examples 16-17Then press to produce the result at the right: In other words, .If is part of , then is also part of .Since and

16-18 Step-by-Step ExamplesPart 4 To calculate , begin by typing: DERVX(Y(t)). Pressing returns:Press again to simplify the result:Select FACTOR a

Step-by-Step Examples 16-19Now press to see the graphs.Part 6 To find the values of and for return to CAS, type each function in turn and pres

16-20 Step-by-Step ExamplesThe example at the right shows the case for t = 0. Select the entire expression and press to get the answer:0The example

Step-by-Step Examples 16-21Now we will graph Γ, which is a parametric curve.In the Equation Writer, type X(t) + i × Y(t).Select the entire expression

16-22 Step-by-Step ExamplesExercise 8 For this exercise, make sure that the calculator is in exact real mode with X as the current variable.Part 1 For

Step-by-Step Examples 16-23Solution 1Start by defining G(X):DEF G X = 2 X 3 X 2Now press :Press and to select the numerator and deno

16-24 Step-by-Step ExamplesNow press and scroll down the screen to:Now press to obtain the table of variations.If you are not in step-by -step mod

Step-by-Step Examples 16-25We can now see that:To justify the preceding calculation, we must assume that is a primitive of .If you are not sure, you

iiiContentsPrefaceManual conventions ... P-1Notice ...

1-18 Getting startedNote view Press NOTE to display the aplet’s note view. This note is transferred with the aplet if it is sent to another calculato

16-26 Step-by-Step ExamplesNOTE: The variable VX is now set to N. Reset it to X by pressing (to display CAS MODES screen) and change the INDEP VAR

Step-by-Step Examples 16-27Solution 1Start by defining the following: Now type PROPFRAC(G(X)). Note that PROPFRAC can be found on the POLYNOMIAL subm

16-28 Step-by-Step ExamplesSolution 3The calculator is not needed here. Simply stating that increases for is sufficient to yield the inequality:Solu

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Variables and memory management 17-117Variables and memory managementIntroductionThe HP 40gs has approximately 200K of user memory. The calculator use

17-2 Variables and memory managementStoring and recalling variablesYou can store numbers or expressions from a previous input or result into variables

Variables and memory management 17-35. Enter a name for the variable. A6. Press to store the result.The results of a calculation can also be stored d

17-4 Variables and memory managementThe VARS menuYou use the VARS menu to access all variables in the calculator. The VARS menu is organised by catego

Variables and memory management 17-55. Choose whether to place the variable name or the variable value on the command line.– Press to indicate that

Getting started 1-19To change views Each view is a separate environment. To change a view, select a different view by pressing , , keys or select

17-6 Variables and memory management4. Enter data for L2.55 48 86 90 77 5. Press to access HOME.6. Open the variable menu and select L1. 7. Copy

Variables and memory management 17-7Home variables It is not possible to store data of one type in a variable of another type. For example, you use th

17-8 Variables and memory managementAplet variables Most aplet variables store values that are unique to a particular aplet. These include symbolic ex

Variables and memory management 17-9Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You c

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Matrices 18-118MatricesIntroductionYou can perform matrix calculations in HOME and in programs. The matrix and each row of a matrix appear in brackets

18-2 MatricesCreating and storing matricesYou can create, edit, delete, send, and receive matrices in the Matrix catalog.To open the Matrix catalog, p

Matrices 18-32. Highlight the matrix variable name you want to use and press . 3. Select the type of matrix to create.– For a vector (one-dimensional

18-4 MatricesTo transmit a matrixYou can send matrices between calculators just as you can send aplets, programs, lists, and notes. 1. Connect the cal

Matrices 18-5To display a matrix • In the Matrix catalog ( MATRIX), highlight the matrix name and press .• In HOME, enter the name of the matrix vari

1-20 Getting startedExample Calculate :Long results If the result is too long to fit on the display line, or if you want to see an expression in textb

18-6 MatricesTo store one elementIn HOME, enter, value matrixname(row,column).For example, to change the element in the first row and second column o

Matrices 18-7 M1 M2 To multiply and divide by a scalarFor division by a scalar, enter the matrix first, then the operator, then the scalar. For mul

18-8 MatricesTo divide by a square matrixFor division of a matrix or a vector by a square matrix, the number of rows of the dividend (or the number of

Matrices 18-93. Return to the Matrix Catalog. MATRIX In this example, the vector you created is listed as M1.4. Create a new matrix. Select Real matri

18-10 MatricesMatrix functions and commandsAbout functions • Functions can be used in any aplet or in HOME. They are listed in the MATH menu under the

Matrices 18-11COND Condition Number. Finds the 1-norm (column norm) of a square matrix.COND(matrix)CROSS Cross Product of vector1 with vector2.CROSS(v

18-12 MatricesLU LU Decomposition. Factors a square matrix into three matrices: {[[lowertriangular]],[[uppertriangular]],[[permutation]]}The uppertri

Matrices 18-13SPECNORM Spectral Norm of matrix.SPECNORM(matrix)SPECRAD Spectral Radius of a square matrix.SPECRAD(matrix)SVD Singular Value Decomposit

18-14 Matricescolumn 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on.For example, TRN([[1,2],[3,4]]) creates the ma

Matrices 18-15The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutions.

Getting started 1-21However, for clarity, it is better to include the multiplication sign where you expect multiplication in an expression. It is clea

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Lists 19-119ListsYou can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matri

19-2 Lists3. Enter the values you want in the list, pressing after each one. Values can be real or complex numbers (or an expression). If you enter

Lists 19-3List edit keys When you press to create or change a list, the following keys are available to you:Create a list in HOME1. Enter the list o

19-4 ListsDisplaying and editing listsTo display a list • In the List catalog, highlight the list name and press .• In HOME, enter the name of the lis

Lists 19-5To insert an element in a list1. Open the List catalog. LIST.2. Press or to highlight the name of the list you want to edit (L1, etc.) a

19-6 ListsDeleting listsTo delete a list In the List catalog, highlight the list name and press . You are prompted to confirm that you want to delete

Lists 19-7variable name (such as L1) or the actual list. For example, REVERSE({1,2,3}).• If Decimal Mark in Modes is set to Comma, use periods to sepa

19-8 ListsMAKELIST Calculates a sequence of elements for a new list. Evaluates expression with variable from begin to end values, taken at increment s

Lists 19-9SIZE Calculates the number of elements in a list.SIZE(list)Also works with matrices.ΣLIST Calculates the sum of all elements in list. ΣLIST(

1-22 Getting startedAlgebraic precedence order of evaluationFunctions within an expression are evaluated in the following order of precedence. Functio

19-10 Lists3. Start the Statistics aplet, and select 1-variable mode (press , if necessary, to display ).Select StatisticsNote: Your list values are

Notes and sketches 20-120Notes and sketchesIntroductionThe HP 40gs has text and picture editors for entering notes and sketches.• Each aplet has its o

20-2 Notes and sketchesNote edit keysKey Meaning Space key for text entry.Displays next page of a multi-page note. Alpha-lock for letter entry. Lowe

Notes and sketches 20-3Aplet sketch viewYou can attach pictures to an aplet in its Sketch view ( SKETCH). Your work is automatically saved with the ap

20-4 Notes and sketchesTo draw a box 1. In Sketch view, press and move the cursor to where you want any corner of the box to be.2. Press . 3. Move t

Notes and sketches 20-5To label parts of a sketch1. Press and type the text on the edit line. To lock the Alpha shift on, press (for uppercase) or

20-6 Notes and sketchesTo import a graphics variableYou can copy the contents of a graphics variable into the Sketch view of an aplet.1. Open the Sket

Notes and sketches 20-74. Write your note.See “Note edit keys” on page 20-2 for more information on the entry and editing of notes.5. When you are fin

20-8 Notes and sketchesTo import a note You can import a note from the Notepad into an aplet’s Note view, and vice versa. Suppose you want to copy a n

Programming 21-121Programming IntroductionThis chapter describes how to program using the HP 40gs. In this chapter you’ll learn about:• using the Prog

Getting started 1-23When you highlight a previous input or result (by pressing ), the and menu labels appear. To copy a previous lineHighlight the

21-2 ProgrammingExample RUN GETVALUE: RUN CALCULATE: RUN "SHOW ANSWER":This program is separated into three main tasks, each an individual p

Programming 21-3Program catalog keysThe program catalog keys are:Key Meaning Opens the highlighted program for editing.Prompts for a new program name,

21-4 ProgrammingCreating and editing programsCreate a new program1. Press PROGRM to open the Program catalog.2. Press .The HP 40gs prompts you for a

Programming 21-52. On the left, use or to highlight a command category, then press to access the commands in the category. Select the command th

21-6 ProgrammingEditing keys The editing keys are:Key Meaning Inserts the character at the editing point.Inserts space into text.Displays previous p

Programming 21-7Using programsRun a program From HOME, type RUN program_name.orFrom the Program catalog, highlight the program you want to run and pre

21-8 ProgrammingCopy a program You can use the following procedure if you want to make a copy of your work before editing—or if you want to use one pr

Programming 21-9Delete a programTo delete a program:1. Press PROGRM to open the Program catalog.2. Highlight a program to delete, then press .Delete

21-10 Programming4. Develop a program that uses the SETVIEWS command to modify the aplet’s VIEWS menu. The menu options provide links to associated pr

Programming 21-11Save the aplet 1. Open the Function aplet and save it as “EXPERIMENT”. The new aplet appears in the Aplet library.Select Function EX

1-24 Getting startedHINTWhen you retrieve a number from ANS, you obtain the result to its full precision. When you retrieve a number from the HOME’s d

21-12 Programming6. Open the Program catalog and create a program named “EXP.SV”. Include the following code in the program. Each entry line after the

Programming 21-13’’ ’’;’’ EXP.ANG’’;0;The program EXP.ANG is a small routine that is called by other programs that the aplet uses. This entry specifie

21-14 ProgrammingAplet commandsCHECK Checks (selects) the corresponding function in the current aplet. For example, Check 3 would check F3 if the cur

Programming 21-15options use, or the program that defines the aplet’s VIEWS menu. • You can include a “Start” option in the VIEWS menu to specify a pr

21-16 ProgrammingProgramNameProgramName is the name of the program that runs when the corresponding menu entry is selected. All programs that are iden

Programming 21-17View numbersThe Function aplet views are numbered as follows:View numbers from 15 on will vary according to the parent aplet. The lis

21-18 ProgrammingExample1XA :IF A==1 THEN MSGBOX " A EQUALS 1" :END: IF... THEN... ELSE... ENDExecutes the true-clause sequence of commands

Programming 21-19IFERR...THEN...ELSE...END allows a program to intercept error conditions that otherwise would cause the program to abort. Its syntax

21-20 ProgrammingExampleARC 0;0;2;0;2π:FREEZE:Draws a circle centered at (0,0) of radius 2. The FREEZE command causes the circle to remain displayed o

Programming 21-21ExampleTLINE 0;0;3;3:Erases previously drawn 45 degree line from (0,0) to (3,3), or draws that line if it doesn’t already exist.Graph

Getting started 1-25Accessing the display historyPressing enables the highlight bar in the display history. While the highlight bar is active, the f

21-22 ProgrammingGROBXOR Using the logical XOR, superimposes graphicname2 onto graphicname1. The upper left corner of graphicname2 is placed at positi

Programming 21-23Loop commandsLoop hp allow a program to execute a routine repeatedly. The HP 40gs has three loop structures. The example programs bel

21-24 ProgrammingMatrix commandsThe matrix commands take variables M0–M9 as arguments.ADDCOL Add Column. Inserts values into a column before column_nu

Programming 21-25REPLACE Replaces portion of a matrix or vector stored in name with an object starting at position start. start for a matrix is a list

21-26 ProgrammingPRVAR Prints name and contents of variablename.PRVAR variablename:You can also use the PRVAR command to print the contents of a progr

Programming 21-27ExampleIf you have stored {1,2,3,4} in variable L1, entering CLVAR L1 will clear L1.DISP Displays textitem in a row of the display

21-28 ProgrammingExamples5.152000X DATE(sets the date to May 15, 2000).10.1500X TIME (sets the time to 10:15 am).EDITMAT Matrix Editor. Opens the Matr

Programming 21-29ExampleINPUT R; "Circular Area"; "Radius"; "Enter Number";1: MSGBOX Displays a message bo

21-30 ProgrammingStat-One commandsDO1VSTATS Calculates STATS using datasetname and stores the results in the corresponding variables: NΣ, TotΣ, MeanΣ,

Programming 21-31Storing and retrieving variables in programsThe HP 40gs has both Home variables and Aplet variables. Home variables are used for real

1-26 Getting started2. Select Number Format, press to display the options, and highlight Fraction or Mixed Fraction. 3. Press to select the Numb

21-32 ProgrammingCoordFunctionParametricPolarSequenceSolveStatisticsTurns the coordinate-display mode in Plot view on or off.From Plot view, use the M

Programming 21-33HwidthStatisticsSets the width of histogram bars.From Plot Setup in 1VAR stats set a value for HwidthorIn a program, typen X HwidthIn

21-34 ProgrammingNmin / NmaxSequenceDefines the minimum and maximum independent variable values. Appears as the NRNG fields in the Plot Setup input fo

Programming 21-35SimultFunctionParametricPolarSequenceEnables you to choose between simultaneous and sequential graphing of all selected expressions.

21-36 ProgrammingTmin / TmaxParametricSets the minimum and maximum independent variable values. Appears as the TRNG field in the Plot Setup input form

Programming 21-37XtickAAll ApletsSets the distance between tick marks for the horizontal axis.From the Plot Setup input form, enter a value for Xtick.

21-38 ProgrammingXzoomAll ApletsSets the horizontal zoom factor.From Plot-ZOOM-Set Factors, enter the value for XZOOM.orIn a program, typen X XZOOM wh

Programming 21-39X1, Y1...X9,Y9X0,Y0ParametricCan contain any expression. Independent variable is T.Example'SIN(4*T)' X Y1(T):'2*SIN(6*

21-40 ProgrammingExampleCubic X S2fit or 6 X S2fit Numeric-view variablesThe following aplet variables control the Numeric view. The value of the vari

Programming 21-411 Standard 2 Fixed3 Sci4 Eng5 Fraction6 MixFractionNote: if Fraction or Mixed Fraction is chosen, the setting will be disregarded whe

Getting started 1-27• Precision set to 1:• Precision set to 2:• Precision set to 3:• Precision set to 4Fraction calculationsWhen entering fractions:•

21-42 ProgrammingNumStartFunctionParametricPolarSequenceSets the starting value for a table in Numeric view.From Num Setup, enter a value for NUMSTART

Programming 21-43Example1VAR X StatModeor 1 X StatModeNote variablesThe following aplet variable is available in Note view. NoteTextAll ApletsUse Note

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Extending aplets 22-122Extending apletsAplets are the application environments where you explore different classes of mathematical operations. You can

22-2 Extending aplets1. Open the Solve aplet and save it under the new name.Solve| T R I A N G L E S 2. Enter the four formulas:θOHθ AHθOAABC3. De

Extending aplets 22-3Using a customized apletTo use the “Triangles” aplet, simply select the appropriate formula, change to the Numeric view and solve

22-4 Extending apletsAnnotating an aplet with notesThe Note view ( NOTE) attaches a note to the current aplet. See Chapter 20, “Notes and sketches”.An

Extending aplets 22-5To transmit an aplet1. Connect the PC or aplet disk drive to the calculator by an appropriate cable.2. Sending calculator: Open t

22-6 Extending apletsIf you are using the PC Connectivity Kit to download aplets from a PC, you will see a list of aplets in the PC’s current director

R-1RReference informationGlossaryaplet A small application, limited to one topic. The built-in aplet types are Function, Parametric, Polar, Sequence,

iv Function aplet interactive analysis... 3-9Plotting a piecewise-defined function ...

1-28 Getting started2. Enter the calculation.3234578Note: Ensure you are in the HOME view.3. Evaluate the calculation.Note that if you had selected Mi

R-2list 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 ente

R-3Resetting the HP 40gsIf the calculator “locks up” and seems to be stuck, you must reset it. This is much like resetting a PC. It cancels certain op

R-4If the calculator does not turn on If the HP 40gs does not turn on follow the steps below until the calculator turns on. You may find that the calc

R-5To install the main batteries a. Slide up the battery compartment cover as illustrated.b. Insert 4 new AAA (LR03) batteries into the main compartme

R-6VariablesHome variablesThe home variables are:Category Available name Complex Z1...Z9, Z0Graphic G1...G9, G0Library FunctionParametricPolarSequence

R-7Function aplet variablesThe function aplet variables are:Category Available name Plot AxesConnectCoordFastResGridIndepInvCrossLabelsRecenterSimultT

R-8Parametric aplet variablesThe parametric aplet variables are:Category Available name Plot AxesConnectCoordGridIndepInvCrossLabelsRecenterSimultTmin

R-9Polar aplet variablesThe polar aplet variables are:Category Available names Plot AxesConnectCoordGridIndepInvCrossLabelsRecenterSimultUminUmaxθstep

R-10Sequence aplet variablesThe sequence aplet variables are:Category Available name Plot AxesCoordGridIndepInvCrossLabelsNminNmaxRecenterSeqPlotSimul

R-11Solve aplet variablesThe solve aplet variables are:Category Available namePlot AxesConnectCoordFastResGridIndepInvCrossLabelsRecenterTracingXcross

Getting started 1-29In this example, the fraction precision is set to 6.Complex numbersComplex results The HP 40gs can return a complex number as a re

R-12Statistics aplet variablesThe statistics aplet variables are:Category Available namePlot AxesConnectCoordGridHminHmaxHwidthIndepInvCrossLabelsRece

R-13MATH menu categoriesMath functionsThe math functions are:Category Available name CalculusTAYLORComplex ARGCONJIMREConstant eiMAXREALMINREALπHyperb

R-14Matrix COLNORMCONDCROSSDETDOTEIGENVALEIGENVVIDENMATINVERSELQLSQLUMAKEMATQRRANKROWNORMRREFSCHURSIZESPECNORMSPECRADSVDSVLTRACETRNPolynom. POLYCOEFPO

R-15Program constantsThe program constants are:Tests<≤= =≠>≥ANDIFTENOTORXORTrig ACOTACSCASECCOTCSCSECCategory Available name (Continued)Categor

R-16Physical ConstantsThe physical constants are:Category Available Name Chemist • Avogadro (Avagadro’s Number, NA)• Boltz. (Boltmann, k)• mol. vo...

R-17CAS functionsCAS functions are:Category Function Algebra COLLECTDEFEXPANDFACTORPARTFRACQUOTESTORE|SUBSTTEXPANDUNASSIGNComplex iABSARGCONJDROITEIM–

R-18Polynom. EGCDFACTORGCDHERMITELCMLEGENDREPARTFRACPROPFRACPTAYLQUOTREMAINDERTCHEBYCHEFFReal CEILINGFLOORFRACINTMAXMINRewrite DISTRIBEPSX0EXPLNEXP2PO

R-19Program commandsThe program commands are:Category Command Aplet CHECKSELECTSETVIEWSUNCHECKBranch IFTHENELSEENDCASEIFERRRUNSTOPDrawing ARCBOXERASEF

Status messagesStat-Two DO2VSTATSSETDEPENDSETINDEPCategory Command (Continued)Message Meaning Bad Argument TypeIncorrect input for this operation.Bad

R-21Invalid Syntax The function or command you entered does not include the proper arguments or order of arguments. The delimiters (parentheses, comma

1-30 Getting startedCatalogs and editorsThe HP 40gs has several catalogs and editors. You use them to create and manipulate objects. They access featu

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W-1Limited WarrantyHP 40gs Graphing Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories

W-26. HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LAW, ANY IMPLIED WARRANTY OR CONDITION O

W-3ServiceEurope Country : Telephone numbers Austria +43-1-3602771203Belgium +32-2-7126219Denmark +45-8-2332844Eastern Europe countries+420-5-41422523

W-4Please logon to http://www.hp.com for the latest service and support information.hL.AmericaCountry: Telephone numbers Argentina 0-810-555-5520Brazi

W-5Regulatory NoticesFederal Commu-nications Commission NoticeThis equipment has been tested and found to comply with the limits for a Class B digital

W-6Hewlett-Packard CompanyP. O. Box 692000, Mail Stop 530113Houston, Texas 77269-2000Or, call1-800-474-6836For questions regarding this FCC declaratio

W-7Japanese Notice この装置は、 情報処理装置等電波障害自主規制協議会（VCCI） の基準に基づ く ク ラ ス B 情報技術装置です。 こ の装置は、 家庭環境で使用する こ と を目的 と し ていますが、 こ の装置がラ ジオやテ レ ビ ジ ョ ン受信機に近接 し て使用

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I-1IndexAABCUV 14-62ABS 14-45absolute value 13-6ACOS2S 14-38add 13-4ADDTMOD 14-51ALGB menu 14-10algebraic entry 1-19alpha characterstyping 1-6alphabet

Aplets and their views 2-12Aplets and their viewsAplet viewsThis section examines the options and functionality of the three main views for the Functi

I-2bad guesses error message 7-7batteries R-4Bernoulli’s number 14-65box-and-whisker plot 10-16branch commandsCASE...END 21-18IF...THEN...ELSE...END 2

I-3cosine 13-4inverse hyperbolic 13-9cotangent 13-20covariancestatistical 10-15creatingaplet 22-1lists 19-1matrices 18-2notes in Notepad 20-6programs

I-4notes 20-2programs 21-5EditlineProgram catalog 21-2editors 1-30EGCD 14-55eigenvalues 18-11eigenvectors 18-11elementstoring 18-6E-lessons 1-12engine

I-5glossary R-1graphanalyzing statistical data in 10-19auto scale 2-14box-and-whisker 10-16capture current display 21-21cobweb 6-1comparing 2-5connect

I-6using symbolic variables 13-23independent valuesadding to table 2-19independent variabledefined for Tracing mode 21-33inferenceconfidence intervals

I-7finding statistical values in list ele-ments 19-9generate a series 19-8list function syntax 19-6list variables 19-1returning position of element in

I-8redimension 21-24replacing portion of matrix or vec-tor 21-25sending or receiving 18-4singular value decomposition 18-13singular values 18-13size 1

I-9mixed fraction 1-11scientific 1-10Standard 1-10numeric precision 17-9Numeric viewadding values 2-19automatic 2-16build your own table 2-19display d

I-10labels 21-34recenter 21-34root 21-34s1mark-s5mark 21-34statplot 21-35tracing 21-33umin/umax 21-35ustep 21-35polar variablesaxes 21-31connect 21-31

I-11RE 13-8real numbermaximum 13-8minimum 13-8real part 13-8real-number functions 13-14% 13-16%CHANGE 13-16%TOTAL 13-16CEILING 13-14DEGtoRAD 13-14FNRO

2-2 Aplets and their views– For a Function definition, enter an expression to define F(X). The only independent variable in the expression is X. – For

I-12date 21-27time 21-27SEVAL 14-68SIGMA 14-68SIGMAVX 14-69SIGN 14-46sign reversal 7-6SIMPLIFY 14-32simplify 14-68, 14-70SINCOS 14-31, 14-40sine 13-4i

I-13Labels 21-34Recenter 21-34S1mark-S5mark 21-34Ycross 21-37step size of independent variable 21-36step-by-step 14-6STORE 14-14storinglist elements 1

I-14COT 13-20CSC 13-20HALFTAN 14-40SEC 13-20SINCOS 14-40TAN2CS2 14-40TAN2SC 14-41TAN2SC2 14-41TRIGCOS 14-44TRIGSIN 14-44TRIGTAN 14-44TRIGSIN 14-44TRIG

I-15in 2-9options 2-9, 3-8options within a table 2-18out 2-9redrawing table of numbers op-tions 2-18square 2-10un-zoom 2-11within Numeric view 2-18X-z

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Aplets and their views 2-3Evaluating expressionsIn aplets In the Symbolic view, a variable is a symbol only, and does not represent one specific valu

2-4 Aplets and their viewsIn HOME You can also evaluate any expression in HOME by entering it into the edit line and pressing . For example, define

Aplets and their views 2-5About the Plot viewAfter entering and selecting (check marking) the expression in the Symbolic view, press . To adjust the

2-6 Aplets and their viewsPlot view settingsThe plot view settings are:Those items with space for a checkmark are settings you can turn on or off. Pre

Aplets and their views 2-7Reset plot settingsTo reset the default values for all plot settings, press CLEAR in the Plot Setup view. To reset the defau

vAbout the Inference aplet ...11-1Getting started with the Inference aplet ...

2-8 Aplets and their viewsTrace a graph You can trace along a function using the or key which moves the cursor along the graph. The display also s

Aplets and their views 2-9To jump directly to a valueTo jump straight to a value rather than using the Trace function, use the menu key. Press , th

2-10 Aplets and their viewsY-Zoom In Divides vertical scale only, using Y-factor.Y-Zoom Out Multiplies vertical scale only, using Y-factor.Square Chan

Aplets and their views 2-11ZOOM examples The following screens show the effects of zooming options on a plot of . Plot of Zoom In: In Un-zoom: Un-z

2-12 Aplets and their viewsY-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 yo

Aplets and their views 2-13To set zoom factors 1. In the Plot view, press .2. Press . 3. Select Set Factors... and press .4. Enter the zoom factors.

2-14 Aplets and their viewsSplit the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Press . Select Plot-Detail and pr

Aplets and their views 2-15– moves the leftmost cursor to the screen’s left edge and moves the rightmost cursor to the screen’s right edge.– The

2-16 Aplets and their viewsAbout the numeric viewAfter entering and selecting (check marking) the expression or expressions that you want to explore i

Aplets and their views 2-17Reset numeric settingsTo reset the default values for all table settings, press CLEAR.Exploring the table of numbersNUM vie

vi Symbolic calculations... 13-20Finding derivatives...

2-18 Aplets and their viewsZoom within a tableZooming redraws the table of numbers in greater or lesser detail.ZOOM options The following table lists

Aplets and their views 2-19Automatic recalculationYou can enter any new value in the X column. When you press , the values for the dependent variable

2-20 Aplets and their views“Build Your Own” menu keysExample: plotting a circlePlot the circle, x 2+ y 2 = 9. First rearrange it to read .To plot both

Aplets and their views 2-21 Select Function 9 9 2. Reset the graph setup to the default settings.SETUP-PLOTCLEAR 3. Plot the two functi

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Function aplet 3-13Function apletAbout the Function apletThe Function aplet enables you to explore up to 10 real-valued, rectangular functions y in te

3-2 Function apletDefine the expressions2. There are 10 function definition fields on the Function aplet’s Symbolic view screen. They are labeled F1(X

Function aplet 3-3Change the scale6. You can change the scale to see more or less of your graphs. In this example, choose Auto Scale. (See “VIEWS menu

3-4 Function apletAnalyse graph with FCN functions9. Display the Plot view menu. From the Plot view menu, you can use the functions on the FCN menu t

Function aplet 3-512.Choose the linear function whose intersection with the quadratic function you wish to find. The coordinates of the intersection

viiAccessing CAS functions...15-12Equation Writer variables ...

3-6 Function aplet 16.Press to accept using F2(x) = (x + 3) 2 – 2 as the other boundary for the integral.17. Choose the end value for x.1 The cursor

Function aplet 3-7HINTThe Root and Extremum functions return one value only even if the function has more than one root or extremum. The function find

3-8 Function apletTo navigate around a table24.Move to X = –5.9. 6 times To go directly to a value25.Move directly to X = 10.1 0 To access the zoom

Function aplet 3-9Function aplet interactive analysisFrom the Plot view ( ), you can use the functions on the FCN menu to find roots, intersections, s

3-10 Function apletFCN functions The FCN functions are:Function Description Root Select Root to find the root of the current function nearest the curs

Function aplet 3-11Shading area You can shade a selected area between functions. This process also gives you an approximate measurement of the area sh

3-12 Function apletPlotting a piecewise-defined functionSuppose you wanted to plot the following piecewise-defined function.1. Open the Function aplet

Parametric aplet 4-14Parametric apletAbout the Parametric apletThe Parametric aplet allows you to explore parametric equations. These are equations in

4-2 Parametric apletSet angle measure3. Set the angle measure to degrees.MODESSelect Degrees Set up the plot 4. Display the graphing options.PLOTThe P

Parametric aplet 4-3Overlay plot 8. Plot a triangle graph over the existing circle graph. PLOT120 Select Overlay Plot A triangle is displayed rath

viii Aplet naming convention ... 21-10Example ...

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Polar aplet 5-15Polar apletGetting started with the Polar apletOpen the Polar aplet1. Open the Polar aplet. Select Polar Like the Function aplet, th

5-2 Polar apletExplore the graph5. Display the Plot view menu key labels.The Plot view options available are the same as those found in the Function a

Sequence aplet 6-16Sequence apletAbout the Sequence apletThe Sequence aplet allows you to explore sequences.You can define a sequence named, for examp

6-2 Sequence apletOpen the Sequence aplet1. Open the Sequence aplet. Select SequenceThe Sequence aplet starts in the Symbolic view.Define the expressi

Sequence aplet 6-3Plot the sequence4. Plot the Fibonacci sequence. 5. In Plot Setup, set the SEQPLOT option to Cobweb.SETUP-PLOT Select CobwebDisplay

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Solve aplet 7-17Solve apletAbout the Solve apletThe Solve aplet solves an equation or an expression for its unknown variable. You define an equation o

7-2 Solve apletGetting started with the Solve apletSuppose you want to find the acceleration needed to increase the speed of a car from 16.67 m/sec (6

Solve aplet 7-34. Enter the values for the known variables.2 7 7 8 1 6 6 7 1 0 0 HINTIf the Decimal Mark setting in the Modes input form ( MO

ixSolve aplet variables...R-11Statistics aplet variables ...

7-4 Solve aplet6. Plot the equation for variable A. Select Auto Scale7. Trace along the graph representing the left side of the equation until the cur

Solve aplet 7-5Use an initial guessYou can usually obtain a faster and more accurate solution if you supply an estimated value for the unknown variabl

7-6 Solve apletInterpreting resultsAfter Solve has returned a solution, press in the Numeric view for more information. You will see one of the foll

Solve aplet 7-7If Solve could not find a solution, you will see one of the following two messages.HINTIt is important to check the information relatin

7-8 Solve apletwhere X is distance, V0 is initial velocity, T is time, and A is acceleration. This is actually two equations, Y = X and Y = V0 T + (AT

Solve aplet 7-95. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial guess for T.Press until the curso

7-10 Solve apletUsing variables in equationsYou can use any of the real variable names, A to Z and θ. Do not use variable names defined for other type

Linear Solver aplet 8-18Linear Solver apletAbout the Linear Solver apletThe Linear Solver aplet allows you to solve a set of linear equations. The set

8-2 Linear Solver apletexample in the previous step). To solve a three-equation set, press . Now the input form displays three equations.If the three

Linear Solver aplet 8-3As you enter each of the remaining known values, the solution changes. The example at the right shows the final solution once a