Function Solvevx, Function Zeros | HP 49g manual

Function SOLVEVX

The function SOLVEVX solves an equation for the default CAS variable contained in the reserved variable name VX. By default, this variable is set to ‘X’. Examples, using the ALG mode with VX = ‘X’, are shown below:

In the first case SOLVEVX could not find a solution. In the second case, SOLVEVX found a single solution, X = 2.

The following screens show the RPN stack for solving the two examples shown above (before and after application of SOLVEVX):

Function ZEROS

The function ZEROS finds the solutions of a polynomial equation, without showing their multiplicity. The function requires having as input the expression for the equation and the name of the variable to solve for. Examples in ALG mode are shown next:

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HP 49g manual Function Solvevx, Function Zeros

Contents

Graphing calculator User’s manualPage Preface Page Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbers Operations with lists Solution to equations Matrices and linear algebra Vectors Vector Analysis Applications GraphicsCalculus Applications Multi-variate Calculus Applications Statistical Applications Differential EquationsProbability Distributions Numbers in Different Bases Limited Warranty W-1Service, W-2 Regulatory information, W-4 Batteries Chapter Getting startedBasic Operations Contents of the calculator’s display Associated with the six soft menu keys, F1 through F6 MenusTool menu Introducing the calculator’s keyboard Setting time and datePage ~„p Selecting calculator modesAlpha function, to enter the upper-case letter P 23.0 Operating Mode √ 3.*5.-1/3.*3./23.3+EXP2.5 Lets try now the expression proposed earlier Number Format and decimal dot or comma Page Page Page Angle Measure Coordinate System Selecting CAS settings Selecting Display modes Explanation of CAS settings Selecting the display font Selecting properties of the line editor Selecting properties of the Stack Selecting properties of the equation writer EQW References Creating arithmetic expressions Chapter Introducing the calculatorCalculator objects Editing expressions in the stack Result³5*„Ü1+1/7will be shown„ÜR3as follows -2Q3`.5 Resulting…in³5*„Ü1+1/7the output„ÜR3-2Q3`.5 + y Creating algebraic expressions Using the Equation Writer EQW to create expressions Edited expression*„Ü5+1/3looks as follows + 2 ⋅ 5 + ~‚n For this example, the Home Organizing data in the calculatorHome directory Subdirectories Typing variable names Locks the alphabetic keyboard in lower case. When lockedVariables Creating variables Name Contents Type 3V5K~a12` ³~„r/„Ü ‚å‚é~„r³„ì Checking variables contents Using the right-shift key followed by soft menu key labels @PURGE@J@@p1@@` Using function Purge in the stack in Algebraic modeUsing function Purge in the stack in RPN mode Deleting variables We use Show Prog menu list and select Memory ‚¯ Undo and CMD functionsChoose boxes vs. Soft Menu Page Not shown in this screen. To Find it we use Display now shows To activate the Order command we press the soft menu key Examples of real number calculations Operation key, namely Examples in ALG modeChapter Calculations with real numbers Directly on the stack For both, ALG and RPN modes, using the Equation Writer RPN mode, enter the number first, then the function, e.g Combination When calculating in the stack in ALG modeKey. When „¸Page \„¸45`‚¹ RPN mode Hyperbolic functions and their inverses Real number functions in the MTH menu Pressing shows the remaining options Key or With unitsUnits menu Page Key or Keystroke sequence to navigate Through the menus Available unitsFor Set of units Labels will be listed With the keyboard, e.g.,will produce the entry Attaching units to numbers Operations with units Using Ubase to convert to the default unit 1 m results 12m 3250mi Different terms in parentheses, e.g These operations produce the following output @@OK@@-˜Physical constants in the calculator Unit conversions Exit constants library When selected, constants are shown with units attachedWhen selected, constants are shown without units Copies value with or without units to the stack Which produces Defining and using functionsLike this Display shows what is called a tagged value Here ‘LNx+1 + EXPx’ ‚@@@H@@ You could try Entered by using Definitions Setting the calculator to Complex modeTo work with complex numbers select the CAS complex mode Chapter Calculations with complex numbers To enter the unit imaginary number type the I key Entering complex numbersPolar representation of a complex number Simple operations with complex numbers Cmplx menu through the MTH menu Cmplx menus Cmplx menu in the keyboard Function Droite equation of a straight line Functions applied to complex numbers Reference Function Droite is found in the command catalog Entering algebraic objects Chapter Algebraic and arithmetic operations Simple operations with algebraic objects Variable menu Press To recover Functions in the ALG menu @HELP@` Catalog To complete the operation To execute the command Operations with transcendental functions Expansion and factoring using log-exp functionsExpansion and factoring using trigonometric functions Trig menu, triggered by using Numbers or to polynomials. The remaining options 1. Integer Functions in the Arithmetic menuShows the following menu X6-1 = X5-5*X4+25X3-125X2+625X-3125X+5+15624 PolynomialsHorner function Quotient and Remainder functions VariablePcoef function Proot function SIMP2 function FractionsPeval function Fcoef function Propfrac functionPartfrac function Froots function Step-by-step operations with polynomials and fractions Reference Function Isol Chapter Solution to equationsSymbolic solution of algebraic equations Function Solve Page Function Zeros Function Solvevx Numerical solver menu Solve equation Polynomial EquationsEnter vector of coefficients Page Page Solving equations with one unknown through NUM.SLV Financial calculations Solution shown is X 4.5006E-2 Solution to simultaneous equations with MslvPage Reference Changing sign Chapter Operations with listsCreating and storing lists Addition, subtraction, multiplication, division Example When applied to lists, acts a concatenation operatorFunctions‚Napplied to lists Inverse 1/x Lists of complex numbersLists of algebraic objects MTH/LIST menu Sorts elements in increasing order Calculate increment among consecutive elements in listCalculate summation of elements in the list Calculate product of elements in the list MAP function Reference SEQ function, available through the command catalog , takesSEQ function General row vector Vector Vector of algebraics Chapter VectorsEntering vectors Typing vectors in the stack Stored into variables Mode Then, ‚íinVectors can also be entered by using the matrix writer Storing vectors into variables in the stack WID Key is used to edit the contents of a selected cell Selected Key will add a column full of zeros at the locationCell of the spreadsheet Function Delete Will delete Used in the following exercises Simple operations with vectorsAddition, subtraction Absolute value function Multiplication by a scalar, and division by a scalar Examples MTH/VECTOR menuMagnitude Dot product Cross product Entering matrices in the stack Chapter Matrices and linear algebra Typing in the matrix directly into the stack Display in RPN mode will look very similar to these Addition and subtraction Operations with matrices RPN mode, try the following eight examples Multiplication Cij = aik ⋅ bkj , for i = 1,2, , m j = 1,2, , n Page Function Trace Solution of linear systemsCharacterizing a matrix The matrix Norm menu Function DET Can be written as the matrix equation A⋅x = b, if Using the numerical solver for linear systemsPress Following input form will be provide right 2x1 + 3x2 -5x3= @SOLVE Solution by division of matrices Solution with the inverse matrix Graphs options in the calculator Chapter Graphics As an example, lets plot the function Them simultaneously if in RPN mode Use a range of -4 toPlotting an expression of the form y = fx Press Then To recover the menu, and return to the PlotAlso, check that for x = -1.48 , y = Here is picture Suggested early, namely x = You will be returned to normal calculator displayZoom factor = 0.5. Toggle To see the table, press Soft menu key To return to normal calculator display press Fast 3D plotsKey simply changes the font in the table from small to big, Option Decimal Produces x-increments Option Integer You can change Orientation Find Fast3DValues of 10 and 8 for the Step data @EDITL Press To leave the Edit environment Reference$ Function lim Chapter Calculus ApplicationsCalc Calculus menu Limits and derivatives Menu within the Calcl menu Infinity symbol is associated with Key, .eIncluding some limits If and only if, fx = dF/dx, and C = constant Anti-derivatives and integralsFunctions INT, INTVX, RISCH, Sigma and Sigmavx Xdx = F b − F a ⋅ x − x o n Functions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus Applications Y dA = b Φ x , y dydx = Multiple integrals Gradient Chapter Vector Analysis ApplicationsDel operator Alternatively, use function Deriv as follows DivergenceCurl CALC/DIFF menu Solution to linear and non-linear equationsChapter Differential Equations Function Ldec Ldec = K1⋅e-3x+ K2⋅e5x + K3⋅e2x + 450⋅x2+330⋅x+241/13500 Function DesolveWhich can be simplified to DESOLVE` Variable Odetype Laplace transform and inverses in the calculator Laplace Transforms Where Function FOURIER`Fourier series for a quadratic function Exercises. Function Collect is available in the ALG menu Thus = 1/3, c Factorials, combinations, and permutations Chapter Probability DistributionsMTH/PROBABILITY.. sub-menu part Random numbers Student-t distribution MTH/PROB menu part„´The Normal distribution F distribution Chi-square distribution Entering data‚Ù5 Chapter Statistical Applications Now Sample vs. population Obtaining frequency distributions Can be used Fitting data to a function y = fxƑ3.Fitdata Lines in RPN mode Obtaining additional summary statistics When that field is selected StatisticsTo access the summary stats… option, use Using Key select all the options for outputs, i.e Offers the following options Interpreted as follows Confidence intervalsPress to obtain the following results Interval information @GRAPH Return to the previous results screen, and/or press Corresponding interval limits 21.88424 and 24.51576. Press @@@OK@@@ Select ∝ ≠ 150. Then, press Result is With system flag 117 set to Soft menus, the Base menu shows Chapter Numbers in Different BasesBase menu Writing non-decimal numbers @HEX Storing objects in the SD card Using SD cardsChapter Purging an object from the SD card Recalling an object from the SD card Limited Warranty Service Rotc = Rest of the country Canada 905 206-4663 or 800- HP USA Regulatory information