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HP 49g Chapter Calculus Applications, Calc Calculus menu, Limits and derivatives, Function lim

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Chapter 11

Calculus Applications

In this Chapter we discuss applications of the calculator’s functions to operations related to Calculus, e.g., limits, derivatives, integrals, power series, etc.

The CALC (Calculus) menu

Many of the functions presented in this Chapter are contained in the calculator’s CALC menu, available through the keystroke sequence „Ö (associated with the 4 key):

The first four options in this menu are actually sub-menus that apply to (1) derivatives and integrals, (2) limits and power series, (3) differential equations, and (4) graphics. The functions in entries (1) and (2) will be presented in this Chapter. Functions DERVX and INTVX are discussed in pages 11-2 and 11-3, respectively..

Limits and derivatives

Differential calculus deals with derivatives, or rates of change, of functions and their applications in mathematical analysis. The derivative of a function is defined as a limit of the difference of a function as the increment in the independent variable tends to zero. Limits are used also to check the continuity of functions.

Function lim

The calculator provides function lim to calculate limits of functions. This function uses as input an expression representing a function and the value

Page 11-1

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HP 49g manual Chapter Calculus Applications, Calc Calculus menu, Limits and derivatives, Function lim

Contents

User’s manual Hp 49g+ graphing calculatorPrinting History Preface Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbersOperations with lists Solution to equationsMatrices and linear algebra VectorsVector Analysis Applications GraphicsCalculus Applications Multi-variate Calculus ApplicationsDifferential Equations Probability DistributionsStatistical Applications Using SD cards Limited Warranty W-1Numbers in Different Bases Chapter Getting started Basic OperationsBatteries Contents of the calculator’s display Tool menu MenusIntroducing the calculator’s keyboard Setting time and datePage Selecting calculator modes 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 settingsSelecting the display font Selecting properties of the line editor Selecting properties of the Stack Selecting properties of the equation writer EQW ReferencesCreating arithmetic expressions Chapter Introducing the calculatorCalculator objects Editing expressions in the stackPage Page 2L 1 + + 2 L + y Creating algebraic expressionsUsing the Equation Writer EQW to create expressions Page + 2 ⋅ 5 + + e  x + 2µ ⋅ ∆y Organizing data in the calculator Home directorySubdirectories Typing variable names VariablesCreating variables Page Page Checking variables contents Page Deleting variables Using function Purge in the stack in Algebraic modeUsing function Purge in the stack in RPN mode Undo and CMD functionsChoose boxes vs. Soft Menu Show Prog menu list and select Memory Page References Examples of real number calculations Chapter Calculations with real numbersPage Page Using powers of 10 in entering data Page Hyperbolic functions and their inverses Real number functions in the MTH menuPage Units menu Operations with unitsPage Available units Attaching units to numbers Operations with units Page Unit conversions Physical constants in the calculatorEngl Defining and using functions ‘LNx+1 + EXPx ‘ Reference Setting the calculator to Complex mode Chapter Calculations with complex numbersDefinitions Polar representation of a complex number Entering complex numbersSimple operations with complex numbers Cmplx menu through the MTH menu Cmplx menusCmplx menu in keyboard Function Droite equation of a straight line Functions applied to complex numbersReference Entering algebraic objects Chapter Algebraic and arithmetic operationsSimple operations with algebraic objects `‚¹ Collect Functions in the ALG menuPage Expansion and factoring using log-exp functions Expansion and factoring using trigonometric functionsOperations with transcendental functions Functions in the Arithmetic menu Horner function PolynomialsQuot and Remainder functions VariablePcoef function Proot functionFractions Peval functionSIMP2 function Propfrac function Partfrac functionFcoef function Step-by-step operations with polynomials and fractions Froots function− 5X 2 + 3X − Reference Chapter Solution to equations Symbolic solution of algebraic equationsFunction Isol Function Solve Page Function Zeros Function SolvevxNumerical solver menu @SOLVE@ Polynomial EquationsSolve for coefficients ˜@SYMB@ Solving equations with one unknown through NUM.SLV Financial calculationsSolution to simultaneous equations with Mslv Page Reference Changing sign Chapter Operations with listsCreating and storing lists Operations with lists of numbersAddition, subtraction, multiplication, division Functions applied to lists Lists of complex numbers Lists of algebraic objectsMTH/LIST menu ∆LIST MAP function SEQ functionChapter Vectors Entering vectorsTyping vectors in the stack Storing vectors into variables in the stack Using the Matrix Writer Mtrw to enter vectorsPage Page Addition, subtraction Simple operations with vectorsAbsolute value function Multiplication by a scalar, and division by a scalarMTH/VECTOR menu MagnitudeDot product Cross product Using the Matrix Writer Chapter Matrices and linear algebraEntering matrices in the stack Typing in the matrix directly into the stack Addition and subtraction Operations with matricesMultiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Page Function Trace Solution of linear systemsCharacterizing a matrix The matrix Norm menu Function DETUsing the numerical solver for linear systems =  a M x2 Solution by division of matrices Solution with the inverse matrixGraphs options in the calculator Chapter Graphics= 1 exp− x Plotting an expression of the form y = fxGenerating a table of values for a function Page Fast 3D plots Left-1 Right1 Near-1 Far Low High Step Indep Depnd Page Reference Function lim Chapter Calculus ApplicationsCalc Calculus menu Limits and derivativesFunctions Deriv and Dervx Anti-derivatives and integrals Xdx = F x + CFunctions INT, INTVX, RISCH, Sigma and Sigmavx Definite integrals Infinite seriesFunctions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus ApplicationsΦ x, ydydx Multiple integrals∇ = i ⋅ ∂ + j ⋅ ∂ + k ⋅ ∂ ∂x ∂y ∂z Chapter Vector Analysis ApplicationsDel operator GradientCurl DivergenceSolution to linear and non-linear equations Chapter Differential EquationsCALC/DIFF menu Function Ldec Yx = 5 ⋅ exp−x3 / 3 ⋅ expx3 / 3 ⋅ dx + C0 Function DesolveDesolve Variable OdetypeLaplace transform and inverses in the calculator Laplace TransformsFourier series for a quadratic function Fourier series= ∑ c n Function FourierPage Reference − 2... − + 1 = − r Chapter Probability DistributionsMTH/PROBABILITY.. sub-menu part Factorials, combinations, and permutationsRandom numbers MTH/PROB menu part Normal distributionStudent-t distribution F distribution Chi-square distributionChapter Statistical Applications Entering dataCalculating single-variable statistics Page Obtaining frequency distributions Fitting data to a function y = fx 195238095238 + 2.00857242857*X Correlation Covariance Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Chapter Numbers in Different Bases Base menuWriting non-decimal numbers HEX DEC OCT BIN Using SD cards ChapterStoring objects in the SD card Purging an object from the SD card Recalling an object from the SD cardLimited Warranty Service HP Invent USA Regulatory information