About the Sequence aplet, Open the Sequence aplet

Sequence aplet

About the Sequence aplet

The Sequence aplet allows you to explore sequences.

You can define a sequence named, for example, U1:

•in terms of n

•in terms of U1( n-1)

•in terms of U1( n-2)

•in terms of another sequence, for example, U2( n)

•in any combination of the above.

Getting started with the Sequence aplet

Open the Sequence aplet

The following example defines and then plots an expression in the Sequence aplet.

1.Open the Sequence aplet.

>$3/( @ Select

67Sequence$57

The Sequence aplet starts in the Symbolic view.

Sequence aplet

6-1

Page 79

Image 79

HP 40G manual About the Sequence aplet, Getting started with the Sequence aplet, Open the Sequence aplet

Contents

USER’S Guide Page Contents Parametric aplet Importing Sample Statistics from the Statistics aplet Inference aplet Variables and memory management Programming Index +,7@CLEAR, 6+,7@MODES, 6+,7@ACOS, etc PrefaceManual conventions @, &26@, +20@, etc Preface Getting started On/off, cancel operationsHome Display To adjust the contrast To clear the displayParts of the display Menu keys KeyboardAnnunciator Description Key Meaning Aplet control keys 75@ +,7@$/3+$@ 175@ +,7@$/3+$@ Shifted keystrokesHelpwith Key Description Math keys Program commands Inactive keys Menus To cancel a menuTo search a menu Input forms Mode settingsReset input form values Setting Options Setting Options Aplets E-lessons Setting a modePress+20@ to return to Home Aplet Use this aplet to explore Name N T Quad Explorer aplet *,*A, keys Trig Explorer aplet Aplets are stored in the Aplet library Symbolic view Plot view Numeric viewAplet library Aplet views Views menu contains the Plot-Table view To change views Aplet view configurationPlot Setup Numeric Setup Symbolic Configuration Example Mathematical calculationsEntering expressions Long results Negative numbers Explicit and implicit multiplication Scientific notation powers@4 6+,7@EEX @13@ @@6 6+,7@EEX 23@ j@ 3 6+,7@EEX 175@ +,7@√ @85 @9 @ Entering Calculates@ 45 @6+,7@π +,7@√ 85@9 Clearing numbers Using previous results 50175@ @25 175@175@ 175@ updates ANS from 50 to 75 to $/3+$@ a 175@ Accessing the display historyKey Function Clearing the display history Using fractionsSetting Fraction mode See Setting fraction precision below for more information Setting fraction precision Evaluate the calculation Fraction calculations Converting decimals to fractionsReturn to Home and enter the calculation @@@2@3 + iy Complex numbersConverting a number to a fraction Complex results To enter complex numbers Catalogs and editors Catalog/Editor ContentsStoring complex numbers Trig Explorer and Quadratic Explorer aplets Differences between the HP 38G and the HP 39G/40GMemory manager Plot Goto function Statistics Pred functionPage Aplet views About the Symbolic viewDefining an expression Symbolic view Aplets and their views Aplets and their views Aplets Evaluating expressionsHome +,7@CLEAR Symb view keys$56@ $7+@ 175@ or Setting up the plot Plot view setupPlot view settings About the Plot view Reset plot settings Plot view keys Exploring the graph+,7@*A Zoom options Trace a graphZoom within a graph To jump directly to a value To turn trace on/ off Multiplies vertical scale only, using Divides horizontal scale only, usingMultiplies horizontal scale, using Divides vertical scale only, using =220Zoom Out 018Zoom=220Un-zoom Press *k, to move to the bottom of the Zoom list =220Y-Zoom Out =220X-Zoom=220X-Zoom Out =220Y-Zoom To box zoom To set zoom factors Options Other views for scaling and splitting the graph Menu key copies the right plot to the left Integer scaling Trigonometric scaling About the numeric viewOverlay plots Decimal scaling Numeric view settings Setting up the table numeric view setupReset numeric settings NUM view menu keys Exploring the table of numbersZoom within a table 175@, the values for the dependent variables are Building your own table of numbersArrow keys to place the cursor in the independent variable Column, then enter the value to jump to Clear data Build Your Own menu keys $3/7@ Select Example plotting a circle+,7@√@9 Open the Function aplet Function apletAbout the Function aplet Getting started with the Function aplet Plot the functions Define the expressionsPlot the functions @75@175@ Times Change the scale Trace a graphWith FCN functions Trace the linear function SelectRoot Find the greater of the two roots of the quadratic functionRoot value is displayed at the bottom of the screen @.2 2Select.SlopeMove the cursor to x = 1 by pressing the *A,or Choose the end value for Display the numeric view Display the numeric view Set up the tableDisplay the numeric setup To find the extremum of the quadratic Move to X = Match the table settings to the pixel columns in the graphExplore the table Display a table of numeric values Area Extremum Isect Root Slope Function aplet interactive analysis Function Description Access FCN variables FCN functions Cursor. You need to have at least Symbolic view. DisplaysTwo selected expressions =  Plotting a piecewise defined function example$3/ @ Select Page Open the Parametric aplet Define the expressions Parametric apletAbout the Parametric aplet Getting started with the Parametric aplet +,7@PLOT Set angle measure Set up the plot Plot the expression360 120 Overlay plot Display the numbersPlot a triangle graph over the existing circle graph +,7@ PlotPage +,7@CLEAR 46+,7@π 2.a Polar apletGetting started with the polar aplet Open the Polar aplet Explore the graph Display the numbers Getting started with the Sequence aplet Sequence aplet starts in the Symbolic viewSequence aplet About the Sequence aplet Keys to assist in the entry of equations Define the expression Select Cobweb Plot Setup, set the Seqplot option to CobwebPlot the sequence Display the table Plot the Fibonacci sequencePage About the Solve aplet Solve aplet Open the Solve aplet Getting started with the Solve apletDefine the equation Define known variables Solve for the unknown variable a Solve the unknown variable Plot the equation@ Select Auto ≈20 times Solve aplet’s NUM view keys Number format Use an initial guess Message Condition Interpreting results Root- Finder at work 180@ 30 175@ 2175@ *e,4175@ *e,*e, to highlight T Plotting to find guessesAt2 x = v0t + $/3+$@X To move cursor to the intersection Plot the graph 3175@*k,*k,*k Using variables in equationsHome variables Initial guess 1400 920 1100 2265 2890 2200 Statistics apletAbout the Statistics aplet Getting started with the Statistics aplet 1400 175@920 175@ 1100 175@2265 175@ 2890 175@2200 175@ Open the Statistics aplet Enter data175@1 175@ 175@5 175@ 175@4 175@ To move to the next column Select a fit in the Symbolic setup view Choose fit and data columns Explore statistics Setup plotSelect2. Linear To move to the FIT1 +2field Display the equation for the best linear fit 6175@ Entering and editing statistical data$7+@ S to highlight To highlight +,7@ FXUVRU Statistics aplet’s NUM view keys 160 175@ 165 175@ 170 175@ 175 175@ 180 175@ $56@ Before re-use Sets will need to be selected againHeight cm Frequency Save data Angle SettingDelete data Select the Sort Order option. You can choose either Defining a regression model 2VARInsert data Sort data values To choose the fit = ax3+bx2+cx+d. Needs at least Fit models To define your own fitFit model Meaning = m lnx + b One-variable Computed statisticsStatistic Definition Columns for a linear fit only Two-variable To plot statistical data PlottingYou can plot Histogram Box and Whisker Plot Scatter Plot Plot types Coefficient Relative ErrorFitting a curve to0182VAR data Correlation Plotting mark 2VAR Connected points 2VAR Setting up the plot Plot setup view Trouble-shooting a plot Statistics aplet’s Plot view keys Find predicted values Calculating predicted valuesPage Example data Default the input form contains example data. This exampleInference aplet About the Inference aplet Hypothesis Tests Confidence Intervals Getting started with the Inference apletOpen the Inference aplet Inference aplet’s Symb view keys ∝.a∝ Define the inferential method Field name Definition Open the Statistics aplet Open Statistics aplet. Note Reset current settingsImporting Sample Statistics from the Statistics aplet Plot test results @529 175@ @295 175@ @952 175@ @259 175@ @925 175@ @592 175@ Calculate statistics Open Inference aplet Import the data Choose inference method and type2one.a Display the confidence interval in the Plot view Display Numeric view Display Plot viewSpecify a 90% confidence interval in the C field E, to move to Field Inputs Hypothesis testsOne-Sample Z-Test Menu name Results Two-Sample Z-TestResult Description One-Proportion Z-Test Successes in the two populations is equal Two-Proportion Z-TestH0 π1 = π2 Hypothesis is that the sample mean has some assumed value One-Sample T-TestTest 1 ∝ Selected hypothesis against the null hypothesis. The null Two-Sample T-Test Sample 2 standard deviation Sample 1 standard deviation Confidence level Confidence intervalsConfidence interval calculations that the HP 39G/40G can Perform are based on the Normal Z-distribution or Student’s Deviations, σ1 and σ2, are known Two populations, ∝1 ∝2, when the population standardTwo-Sample Z-Interval Confidence interval for the difference between the means Sample success count One-Proportion Z-Interval Sample 2 success count Two-Proportion Z-IntervalSuccesses in two populations Sample 1 success count One-Sample T-Interval Two-Sample T-Interval Page Math functions Using mathematical functionsMath menu Function categories To select a functionCalculus Loop Stat-Two Complex Matrices Syntax Math functions by categoryFunctions common to keyboard and menus Keyboard functions +,7@√ +,7@ASIN+,7@ACOS +,7@ATAN +,7@ n Valuepower+,7@ABS ABSvalue Lower,upper,expression,variable Calculus functionsTaylor Variableexpression ARG Complex number functionsConj Hyperbolic trigonometry Constants EXPM1 List functionsAlog EXP Recurse Loop functionsMatrix functions Iterate Polyform Polynomial functionsPolycoef Polyeval Random Probability functionsComb Perm Utpt UtpcUtpf Utpn Real-number functions Mant HMS→→HMS INT RAD→DEG MODChange Total Xpon Statistics-TwoSign Truncate Quad Symbolic functionsIsolate LINEAR? Quote Trigonometry functions Home Symbolic calculationsSymbolic calculations in the Function aplet Using formal variables Evaluate the function Finding derivativesTo find derivatives GG@$/3+$@S1 GG@@$/3+$@ To find derivatives in the Function aplet’s Symbolic view Thus, substituting X for S1, it can be seen that To find the indefinite integral using formal variables+,7@GG@0 @ $/3+$@ S1 @ 3 @ Show the result format 10-26 Introduction Variables and memory management Numeric Precision Storing and recalling variablesTo store a value To store the results of a calculation 65 @$/3+$@A 175@ Vars menuTo use variables Calculations +,7@LIST Names or values of variables into programs List names directly from the keyboard 2contents,.a is copied to the command line$56@ *e,*e,*e,*A $/3+$@L3175@ Category Available names Aplet variables To access an aplet variableTo copy the value of the variable into the edit line +,7@MEMORY Memory ManagerStart the Memory Manager. a list of variable categories Is displayedPage Matrix Variables MatricesVectors Matrices +,7@*e, or Creating and storing matricesMatrix Catalog keys + 7@CLEAR Select the type of matrix to create To create a matrix in the matrix catalog +,7@*k, *e Working with matricesTo transmit a matrix Clears all elements from the matrix 728 672? 175@ 8 175@ Matrix arithmeticTo multiply and divide by a scalar 175@ 2175@*e 175@ 4175@ $/3+$@M1 j@$/3+$@M2 175@ $/3+$@M1@ $/3+$@M2 175@ +,7@MATRIX Solving systems of linear equations+,7@MATRIX1 175@ 175@7 175@ About functions Matrix functions and commands Argument conventions Inverse EigenvalEigenvv Idenmat Schur RankRownorm Rref Identity Matrix Transposing a Matrix ExamplesTrace TRN Reduced-Row Echelon Form Open the List catalog ListsCreating lists Create a list in the List Catalog List catalog keys List edit keys Create a list @ /@ Displaying and editing listsTo display a list To display one element To edit a list To insert an element in a list To store one element 16a*e To delete all lists Deleting listsTransmitting lists To delete a list List functions $/3+$@A @ $/3+$@L 5175@ $7+@L *A$/3+$@L5175@ $7+@L *A,Select Sorts elements in ascending order Calculates the product of all elements in listPOSlist, element Calculates the number of elements in a list 89@65@ 0@89 Finding statistical values for list elements$/3+$@ L1 175@ Go to the Numeric view To display calculated statistics 180@67$76aPage Your work is automatically saved. Press any view key Aplet note viewTo write a note in Note view +,7@letter +,7@ Cmds +,7@%.63$= Sketch keys Aplet sketch viewTo draw a line Draw keys Where you want any corner of the box to beYou can adjust the size of the box by moving the cursor To draw a box Press 2.again to affix the label KeysHighlight2. the variable name you want to use and press Name of the note is ‘MYNOTE’ To import a graphics variableTo create a note +,7@NOTEPAD Another HP 39G/40G or PC Opens the selected note forBegins a new note, and asks for Transmits the selected note to 14-8 Programming Contents of a Program Structured Programming Open Program catalog Program catalog +,7@*k, or *e Program catalog keys Create a new program Creating and editing programs To enter functions more to come Enter commands Edit a program+,7@CMDS A,*e Editing keys Debug a program Stop a program Using programsRun a program From HOME, type RUN programname. or Transmit a program Delete a program Working with programsCopy a Program Programs Delete the contents of a programAbout customizing an aplet Delete all Customizing an aplet example Aplet naming convention$3/7@Select Configuring the Setviews menu option programs Setviews ’’’’’’’’18 Programming 15-13 Select Programming commandsAplet commands Check Syntax for the command is as follows Command syntax Auto-run programs If test-clause Branch commandsUncheck IF...THEN...END END Iferr trap-clause Then error-clause ENDIF... then ELSE... END CASE...END Iferr Then Drawing commands Graphic commands Grobxor →GROBGrobnot Grobor Loop commands Matrix commands Scaleadd RandmatRedim Scale Prompt commands Print commands Editmat matrixname DispDisptime Disp linenumbertextitem Getkey Input nametitle,labelhelpdefaultInput Wait seconds MsgboxPrompt Wait Stat-One commands Stat-One and Stat-Two commandsStat-Two commands Axes Storing and retrieving variables in programsPlot-view variables Area Grid CoordExtremum FastRes Isect HwidthIndep InvCross S1mark-S5mark Nmin / NmaxRecenter Root Umin/Umax SimultSlope StatPlot Xcross Tmin / TmaxTracing Tstep Ymin / Ymax XtickYtick Xmin / Xmax Angle Symbolic-view variablesXzoom Yzoom E1...E9, E0 X1, Y1...X9,Y9 X0,Y0R1...R9, R0 U1...U9, U0 C1...C9, C0 Numeric-view variablesDigits NumIndep FormatNumCol NumFont NumType NumRowNumStart NumStep PageNum Creating new aplets based on existing aplets Extending aplets $/3+$@ H 175@ $1@ $/3+$@ θ @ Aplet Keys$/3+$@ C @ 175@ 180@ 35 175@ $3/ @Select Length of the ladder is approximately 8.72 metres Resetting an apletDownloading e-lessons from the web Solve for the missing To transmit an aplet Sending and receiving aplets To sort the aplet list Sorting items in the aplet library menu listTo delete an aplet Regulatory information Reference informationCanada Warranty LED safety Reference information To reset using the keyboard Resetting the HP 39G/40G If the calculator does not turn on To erase all memory and reset defaults21@ key Cross matrix1,matrix2 Glossary Operating details Operating temperature 0 to 45C 32 to 113FBatteries Home variables are Menu maps of the Vars menuCategory Available name Function aplet variables are Function aplet variablesUser-named Modes Plot-FCN Parametric aplet variablesParametric aplet variables are Polar aplet variables are Polar aplet variables Sequence aplet variables are Sequence aplet variables Solve aplet variables are Solve aplet variables Statistics aplet variables are Statistics aplet variablesStat-One Calculus Menu maps of the Math menuMath functions Math functions are = = Polynom Program constants Category Command Program commands Message Meaning Selected status messages+,7@ Memory Or intersection is not visible Function value, root, extremumCurrent screen Index Index Index Index Index Index Index Index Index Index Index Index Index