Parametric aplet | HP 40G guide

3 Function aplet
About the Function aplet	3-1
Getting started with the Function aplet	3-1
Function aplet interactive analysis	3-8
Plotting a piecewise defined function example	3-11

4	Parametric aplet
	About the Parametric aplet	4-1
	Getting started with the Parametric aplet	4-1
5	Polar aplet
	Getting started with the polar aplet	5-1
6	Sequence aplet
	About the Sequence aplet	6-1
	Getting started with the Sequence aplet	6-1
7	Solve aplet
	About the Solve aplet	7-1
	Getting started with the Solve aplet	7-2
	Use an initial guess	7-5
	Interpreting results	7-6
	Plotting to find guesses	7-8
	Using variables in equations	7-10
8	Statistics aplet
	About the Statistics aplet	8-1
	Getting started with the Statistics aplet	8-1
	Entering and editing statistical data	8-5
	Defining a regression model (2VAR)	8-11
	Computed statistics	8-13
	Plotting	8-15
	Plot types	8-16
	Fitting a curve to 2VAR data	8-17
	Setting up the plot (Plot setup view)	8-18
	Trouble-shooting a plot	8-19
	Exploring the graph	8-20
	Calculating predicted values	8-21

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Contents

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HP 40G manual Parametric aplet

Contents

USER’S Guide Page Contents Parametric aplet Inference aplet Importing Sample Statistics from the Statistics aplet Variables and memory management Programming Index Preface Manual conventions@, &26@, +20@, etc +,7@CLEAR, 6+,7@MODES, 6+,7@ACOS, etc Preface Getting started On/off, cancel operationsHome Display To adjust the contrast To clear the displayParts of the display Menu keys KeyboardAnnunciator Description Aplet control keys Key Meaning +,7@ $/3+$@175@ 75@ Shifted keystrokes HelpwithKey Description +,7@$/3+$@ Program commands Inactive keys Math keys Menus To cancel a menuTo search a menu Mode settings Reset input form valuesSetting Options Input forms Setting Options Aplets E-lessons Setting a modePress+20@ to return to Home Aplet Use this aplet to explore Name Quad Explorer aplet N T Trig Explorer aplet *,*A, keys Symbolic view Plot view Numeric view Aplet libraryAplet views Aplets are stored in the Aplet library Views menu contains the Plot-Table view Aplet view configuration Plot Setup Numeric Setup SymbolicConfiguration To change views Mathematical calculations Entering expressionsLong results Negative numbers Example Explicit and implicit multiplication Scientific notation powers@4 6+,7@EEX @13@ @@6 6+,7@EEX 23@ j@ 3 6+,7@EEX 175@ Entering Calculates @ 45 @6+,7@π+,7@√ 85@9 +,7@√ @85 @9 @ Clearing numbers Using previous results 175@ updates ANS from 50 to 75 to 50175@ @25 175@175@ $/3+$@ a 175@ Accessing the display historyKey Function Using fractions Setting Fraction modeSee Setting fraction precision below for more information Clearing the display history Setting fraction precision Fraction calculations Converting decimals to fractions Return to Home and enter the calculation@@@2@3 Evaluate the calculation Complex numbers Converting a number to a fractionComplex results To enter complex numbers + iy Catalogs and editors Catalog/Editor ContentsStoring complex numbers Differences between the HP 38G and the HP 39G/40G Memory manager Plot Goto functionStatistics Pred function Trig Explorer and Quadratic Explorer apletsPage About the Symbolic view Defining an expression Symbolic viewAplets and their views Aplet views Aplets and their views Aplets Evaluating expressionsHome Symb view keys $56@$7+@ +,7@CLEAR Setting up the plot Plot view setup Plot view settingsAbout the Plot view 175@ or Reset plot settings Plot view keys Exploring the graph+,7@*A Trace a graph Zoom within a graphTo jump directly to a value To turn trace on/ off Zoom options Divides horizontal scale only, using Multiplies horizontal scale, usingDivides vertical scale only, using Multiplies vertical scale only, using 018Zoom =220Un-zoomPress *k, to move to the bottom of the Zoom list =220Zoom Out =220X-Zoom =220X-Zoom Out=220Y-Zoom =220Y-Zoom Out To box zoom To set zoom factors Other views for scaling and splitting the graph Options Menu key copies the right plot to the left About the numeric view Overlay plotsDecimal scaling Integer scaling Trigonometric 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 Building your own table of numbers Arrow keys to place the cursor in the independent variableColumn, then enter the value to jump to 175@, the values for the dependent variables are Build Your Own menu keys Clear data $3/7@ Select Example plotting a circle+,7@√@9 Function aplet About the Function apletGetting started with the Function aplet Open the Function aplet Define the expressions Plot the functions@75@175@ Plot the functions Change the scale Trace a graph With FCN functionsTrace the linear function Times SelectRoot Find the greater of the two roots of the quadratic functionRoot value is displayed at the bottom of the screen 2Select.Slope Move the cursor to x = 1 by pressing the *A,orChoose the end value for @.2 Display the numeric view Set up the table Display the numeric setupTo find the extremum of the quadratic Display the numeric view Match the table settings to the pixel columns in the graph Explore the tableDisplay a table of numeric values Move to X = Function aplet interactive analysis Area Extremum Isect Root Slope Access FCN variables FCN functions Function Description Cursor. You need to have at least Symbolic view. DisplaysTwo selected expressions =  Plotting a piecewise defined function example$3/ @ Select Page Parametric aplet About the Parametric apletGetting started with the Parametric aplet Open the Parametric aplet Define the expressions +,7@PLOT Set angle measure Set up the plot Plot the expression360 Overlay plot Display the numbers Plot a triangle graph over the existing circle graph+,7@ Plot 120Page Polar aplet Getting started with the polar apletOpen the Polar aplet +,7@CLEAR 46+,7@π 2.a Explore the graph Display the numbers Sequence aplet starts in the Symbolic view Sequence apletAbout the Sequence aplet Getting started with the Sequence aplet Define the expression Keys to assist in the entry of equations Plot Setup, set the Seqplot option to Cobweb Plot the sequence Display the tablePlot the Fibonacci sequence Select CobwebPage Solve aplet About the Solve aplet Open the Solve aplet Getting started with the Solve apletDefine the equation Define known variables Solve for the unknown variable a Solve the unknown variable Plot the equation@ Select Auto Solve aplet’s NUM view keys ≈20 times Use an initial guess Number format Interpreting results Message Condition Root- Finder at work Plotting to find guesses At2 x = v0t +$/3+$@X 180@ 30 175@ 2175@ *e,4175@ *e,*e, to highlight T Plot the graph To move cursor to the intersection Using variables in equations Home variablesInitial guess 3175@*k,*k,*k Statistics aplet About the Statistics apletGetting started with the Statistics aplet 1400 920 1100 2265 2890 2200 Open the Statistics aplet Enter data 175@1 175@ 175@5 175@ 175@4 175@To move to the next column 1400 175@920 175@ 1100 175@2265 175@ 2890 175@2200 175@ Select a fit in the Symbolic setup view Choose fit and data columns Explore statistics Setup plotSelect2. Linear Display the equation for the best linear fit To move to the FIT1 +2field Entering and editing statistical data $7+@ S to highlightTo highlight 6175@ Statistics aplet’s NUM view keys +,7@ FXUVRU 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 Defining a regression model 2VAR Insert data Sort data valuesTo choose the fit Select the Sort Order option. You can choose either Fit models To define your own fit Fit model Meaning= m lnx + b = ax3+bx2+cx+d. Needs at least One-variable Computed statisticsStatistic Definition Two-variable Columns for a linear fit only To plot statistical data PlottingYou can plot Plot types Histogram Box and Whisker Plot Scatter Plot Relative Error Fitting a curve to0182VAR dataCorrelation Coefficient Setting up the plot Plot setup view Plotting mark 2VAR Connected points 2VAR Trouble-shooting a plot Statistics aplet’s Plot view keys Calculating predicted values Find predicted valuesPage Default the input form contains example data. This example Inference apletAbout the Inference aplet Example data Getting started with the Inference aplet Open the Inference apletInference aplet’s Symb view keys Hypothesis Tests Confidence Intervals Define the inferential method ∝.a∝ Field name Definition Open Statistics aplet. Note Reset current settings Importing Sample Statistics from the Statistics apletPlot test results Open the Statistics aplet Calculate statistics Open Inference aplet @529 175@ @295 175@ @952 175@ @259 175@ @925 175@ @592 175@ Import the data Choose inference method and type2one.a Display Numeric view Display Plot view Specify a 90% confidence interval in the C fieldE, to move to Field Display the confidence interval in the Plot view Hypothesis tests One-Sample Z-TestMenu name Inputs Results Two-Sample Z-TestResult Description One-Proportion Z-Test Successes in the two populations is equal Two-Proportion Z-TestH0 π1 = π2 One-Sample T-Test Test 1 ∝Selected hypothesis against the null hypothesis. The null Hypothesis is that the sample mean has some assumed value Two-Sample T-Test Sample 1 standard deviation Sample 2 standard deviation Confidence intervals Confidence interval calculations that the HP 39G/40G canPerform are based on the Normal Z-distribution or Student’s Confidence level Two populations, ∝1 ∝2, when the population standard Two-Sample Z-IntervalConfidence interval for the difference between the means Deviations, σ1 and σ2, are known One-Proportion Z-Interval Sample success count Two-Proportion Z-Interval Successes in two populationsSample 1 success count Sample 2 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@ASIN +,7@ACOS+,7@ATAN +,7@√ Valuepower +,7@ABSABSvalue +,7@ n Calculus functions TaylorVariableexpression Lower,upper,expression,variable ARG Complex number functionsConj Constants Hyperbolic trigonometry List functions AlogEXP EXPM1 Loop functions Matrix functionsIterate Recurse Polynomial functions PolycoefPolyeval Polyform Probability functions CombPerm Random Utpc UtpfUtpn Utpt Real-number functions HMS→ →HMSINT Mant MOD ChangeTotal RAD→DEG Statistics-Two SignTruncate Xpon Symbolic functions IsolateLINEAR? Quad Quote Trigonometry functions Symbolic calculations Symbolic calculations in the Function apletUsing formal variables Home Finding derivatives To find derivativesGG@$/3+$@S1 Evaluate the function To find derivatives in the Function aplet’s Symbolic view GG@@$/3+$@ To find the indefinite integral using formal variables +,7@GG@0 @ $/3+$@ S1 @ 3 @Show the result format Thus, substituting X for S1, it can be seen that 10-26 Variables and memory management Introduction Numeric Precision Storing and recalling variablesTo store a value To store the results of a calculation Vars menu To use variablesCalculations 65 @$/3+$@A 175@ Names or values of variables into programs +,7@LIST 2contents,.a is copied to the command line $56@ *e,*e,*e,*A$/3+$@L3175@ List names directly from the keyboard Category Available names Aplet variables To access an aplet variableTo copy the value of the variable into the edit line Memory Manager Start the Memory Manager. a list of variable categoriesIs displayed +,7@MEMORYPage Matrices VectorsMatrices Matrix Variables Creating and storing matrices Matrix Catalog keys+ 7@CLEAR +,7@*e, or To create a matrix in the matrix catalog Select the type of matrix to create Working with matrices To transmit a matrixClears all elements from the matrix +,7@*k, *e 728 672? Matrix arithmetic To multiply and divide by a scalar175@ 2175@*e 175@ 4175@ 175@ 8 175@ $/3+$@M1@ $/3+$@M2 175@ $/3+$@M1 j@$/3+$@M2 175@ Solving systems of linear equations +,7@MATRIX1 175@175@7 175@ +,7@MATRIX Matrix functions and commands About functions Argument conventions Eigenval EigenvvIdenmat Inverse Rank RownormRref Schur Examples TraceTRN Identity Matrix Transposing a Matrix Reduced-Row Echelon Form Lists Creating listsCreate a list in the List Catalog Open the List catalog List catalog keys Create a list List edit keys Displaying and editing lists To display a listTo display one element To edit a list @ /@ 16a*e To insert an element in a list To store one element Deleting lists Transmitting listsTo delete a list To delete all lists List functions $/3+$@L 5175@ $7+@L *A $/3+$@L5175@$7+@L *A,Select $/3+$@A @ Calculates the product of all elements in list POSlist, elementCalculates the number of elements in a list Sorts elements in ascending order 89@65@ 0@89 Finding statistical values for list elements$/3+$@ L1 175@ 180@67$76a Go to the Numeric view To display calculated statisticsPage Aplet note view To write a note in Note view+,7@letter Your work is automatically saved. Press any view key +,7@%.63$= +,7@ Cmds Sketch keys Aplet sketch viewTo draw a line Where you want any corner of the box to be You can adjust the size of the box by moving the cursorTo draw a box Draw keys Press 2.again to affix the label KeysHighlight2. the variable name you want to use and press To import a graphics variable To create a note+,7@NOTEPAD Name of the note is ‘MYNOTE’ Opens the selected note for Begins a new note, and asks forTransmits the selected note to Another HP 39G/40G or PC 14-8 Contents of a Program Structured Programming Programming Program catalog Open Program catalog Program catalog keys +,7@*k, or *e Creating and editing programs Create a new program Enter commands Edit a program +,7@CMDSA,*e To enter functions more to come Editing keys Debug a program Stop a program Using programsRun a program From HOME, type RUN programname. or Working with programs Copy aProgram Transmit a program Delete a program Delete the contents of a program About customizing an apletDelete all Programs Customizing an aplet example Aplet naming convention$3/7@Select Configuring the Setviews menu option programs Setviews ’’’’’’’’18 Programming 15-13 Programming commands Aplet commandsCheck Select Command syntax Syntax for the command is as follows Auto-run programs Branch commands UncheckIF...THEN...END If test-clause Iferr trap-clause Then error-clause END IF... thenELSE... END CASE...END Iferr Then END Drawing commands Graphic commands →GROB GrobnotGrobor Grobxor Loop commands Matrix commands Randmat RedimScale Scaleadd Print commands Prompt commands Disp DisptimeDisp linenumbertextitem Editmat matrixname Getkey Input nametitle,labelhelpdefaultInput Msgbox PromptWait Wait seconds Stat-One commands Stat-One and Stat-Two commandsStat-Two commands Storing and retrieving variables in programs Plot-view variablesArea Axes Coord ExtremumFastRes Grid Hwidth IndepInvCross Isect Nmin / Nmax RecenterRoot S1mark-S5mark Simult SlopeStatPlot Umin/Umax Tmin / Tmax TracingTstep Xcross Xtick YtickXmin / Xmax Ymin / Ymax Symbolic-view variables XzoomYzoom Angle X1, Y1...X9,Y9 X0,Y0 R1...R9, R0U1...U9, U0 E1...E9, E0 C1...C9, C0 Numeric-view variablesDigits Format NumColNumFont NumIndep NumRow NumStartNumStep NumType PageNum Extending aplets Creating new aplets based on existing aplets $/3+$@ H 175@ $1@ $/3+$@ θ @ Aplet Keys$/3+$@ C @ 175@ $3/ @Select 180@ 35 175@ Resetting an aplet Downloading e-lessons from the webSolve for the missing Length of the ladder is approximately 8.72 metres Sending and receiving aplets To transmit an aplet To sort the aplet list Sorting items in the aplet library menu listTo delete an aplet Regulatory information Reference informationCanada LED safety Warranty Reference information Resetting the HP 39G/40G To reset using the keyboard If the calculator does not turn on To erase all memory and reset defaults21@ key Glossary Cross matrix1,matrix2 Operating details Operating temperature 0 to 45C 32 to 113FBatteries Home variables are Menu maps of the Vars menuCategory Available name Function aplet variables User-namedModes Function aplet variables are Plot-FCN Parametric aplet variablesParametric aplet variables are Polar aplet variables Polar aplet variables are Sequence aplet variables Sequence aplet variables are Solve aplet variables Solve aplet variables are Statistics aplet variables are Statistics aplet variablesStat-One Menu maps of the Math menu Math functionsMath functions are Calculus Polynom = = Program constants Program commands Category Command 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