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HP 50g graphing calculator user’s manual Edition 1 HP part number F2229AA-90001...
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Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE.
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This manual contains examples that illustrate the use of the basic calculator functions and operations. The chapters in this user’s manual are organized by subject in order of difficulty: from the setting of calculator modes, to real and complex number calculations, operations with lists, vectors, and matrices, graphics, calculus applications, vector analysis, differential equations, probability and statistics.
Chapter 1 - Getting started Basic Operations, 1-1 Batteries, 1-1 Turning the calculator on and off, 1-2 Adjusting the display contrast, 1-2 Contents of the calculator’s display, 1-3 Menus, 1-3 The TOOL menu, 1-3 Setting time and date, 1-4 Introducing the calculator’s keyboard, 1-4...
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Creating algebraic expressions, 2-4 Using the Equation Writer (EQW) to create expressions, 2-5 Creating arithmetic expressions, 2-5 Creating algebraic expressions, 2-7 Organizing data in the calculator, 2-8 The HOME directory, 2-8 Subdirectories, 2-9 Variables, 2-9 Typing variable names , 2-9...
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Defining and using functions, 3-15 Reference, 3-16 Chapter 4 - Calculations with complex numbers Definitions, 4-1 Setting the calculator to COMPLEX mode, 4-1 Entering complex numbers, 4-2 Polar representation of a complex number, 4-3 Simple operations with complex numbers, 4-4...
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The PROOT function, 5-9 The QUOT and REMAINDER functions, 5-9 The PEVAL function , 5-9 Fractions, 5-9 The SIMP2 function, 5-10 The PROPFRAC function, 5-10 The PARTFRAC function, 5-10 The FCOEF function, 5-10 The FROOTS function, 5-11 Step-by-step operations with polynomials and fractions, 5-11 Reference, 5-12 Chapter 6 - Solution to equations Symbolic solution of algebraic equations, 6-1...
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Addition, subtraction, multiplication, division, 7-2 Functions applied to lists, 7-4 Lists of complex numbers, 7-4 Lists of algebraic objects, 7-5 The MTH/LIST menu, 7-5 The SEQ function, 7-7 The MAP function, 7-7 Reference, 7-7 Chapter 8 - Vectors Entering vectors , 8-1 Typing vectors in the stack, 8-1 Storing vectors into variables in the stack, 8-2 Using the Matrix Writer (MTRW) to enter vectors, 8-3...
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Solution by “division” of matrices, 9-11 References, 9-12 Chapter 10 - Graphics Graphs options in the calculator, 10-1 Plotting an expression of the form y = f(x), 10-2 Generating a table of values for a function, 10-4 Fast 3D plots, 10-5...
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Solution to linear and non-linear equations, 14-1 Function LDEC, 14-1 Function DESOLVE, 14-3 The variable ODETYPE, 14-3 Laplace Transforms, 14-4 Laplace transform and inverses in the calculator, 14-4 Fourier series, 14-5 Function FOURIER, 14-5 Fourier series for a quadratic function, 14-6 Reference, 14-7 Chapter 15 - Probability Distributions The MTH/PROBABILITY..
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Reference, 15-4 Chapter 16 - Statistical Applications Entering data, 16-1 Calculating single-variable statistics, 16-2 Sample vs. population, 16-2 Obtaining frequency distributions, 16-3 Fitting data to a function y = f(x), 16-5 Obtaining additional summary statistics, 16-6 Confidence intervals, 16-7 Hypothesis testing, 16-9 Reference, 16-11 Chapter 17 - Numbers in Different Bases The BASE menu, 17-1...
Insert 4 new AAA (LR03) batteries into the main compartment. Make sure each battery is inserted in the indicated direction. To install the backup battery a. Make sure the calculator is OFF. Press down the holder. Push the plate to the shown direction and lift it. Page 1-1...
The $ key is located at the lower left corner of the keyboard. Press it once to turn your calculator on. To turn the calculator off, press the right- shift key @ (first key in the second row from the bottom of the keyboard), followed by the $ key.
Contents of the calculator’s display Turn your calculator on once more. At the top of the display you will have two lines of information that describe the settings of the calculator. The first line shows the characters: For details on the meaning of these symbols see Chapter 2 in the calculator’s user’s guide.
TOOL menu is to press the I key (third key from the left in the second row of keys from the top of the keyboard). Setting time and date See Chapter 1 in the calculator’s user’s guide to learn how to set time and date. Introducing the calculator’s keyboard The figure on the next page shows a diagram of the calculator’s keyboard...
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For example, the P key, key(4,4), has the following six functions associated with it: Main function, to activate the SYMBolic menu Left-shift function, to activate the MTH (Math) menu „´ Right-shift function, to activate the CATalog function …N ALPHA function, to enter the upper-case letter P ALPHA-Left-Shift function, to enter the lower-case letter p ~„p Page 1-5...
Press the H button (second key from the left on the second row of keys from the top) to show the following CALCULATOR MODES input form: Press the !!@@OK#@ soft menu key to return to normal display. Examples of selecting different calculator modes are shown next.
The calculator offers two operating modes: the Algebraic mode, and the Reverse Polish Notation (RPN) mode. The default mode is the Algebraic mode (as indicated in the figure above), however, users of earlier HP calculators may be more familiar with the RPN mode.
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Notice that the display shows several levels of output labeled, from bottom to top, as 1, 2, 3, etc. This is referred to as the stack of the calculator. The different levels are referred to as the stack levels, i.e., stack level 1, stack level 2, etc.
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Let's try some other simple operations before trying the more complicated expression used earlier for the algebraic operating mode: 123/32 ( 27) Note the position of the y and x in the last two operations. The base in the exponential operation is y (stack level 2) while the exponent is x (stack level 1) before the key Q is pressed.
To select a number format, first open the CALCULATOR MODES input form by pressing the H button. Then, use the down arrow key, ˜, to select the option Number format.
—˜, select, say, 3 decimals. Press the !!@@OK#@ soft menu key to complete the selection: Press the !!@@OK#@ soft menu key return to the calculator display. The number now is shown as: Notice how the number is rounded, not truncated.
Fixed number of decimals in the example above). Press the !!@@OK#@ soft menu key return to the calculator display. The number now is shown as: This result, 1.23E2, is the calculator’s version of powers-of-ten notation, i.e., 1.235...
Press the !!@@OK#@ soft menu key return to the calculator display. The number now is shown as: Because this number has three figures in the integer part, it is shown with four significative figures and a zero power of ten, while using the Engineering format.
Angle Measure Trigonometric functions, for example, require arguments representing plane angles. The calculator provides three different Angle Measure modes for working with angles, namely: • Degrees: There are 360 degrees (360 ) in a complete circumference. • Radians: There are 2 •...
To see the optional CAS settings use the following: • Press the H button to activate the CALCULATOR MODES input form. • To change CAS settings press the @@CAS@@ soft menu key. The default values of the CAS setting are shown below: •...
• After having selected and unselected all the options that you want in the CAS MODES input form, press the @@@OK@@@ soft menu key. This will take you back to the CALCULATOR MODES input form. To return to normal calculator display at this point, press the @@@OK@@@ soft menu key once more.
The calculator display can be customized to your preference by selecting different display modes. following: • First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key to display the DISPLAY MODES input form.
Practice changing the display fonts to sizes 7 and 6. Press the OK soft menu key to effect the selection. When done with a font selection, press the @@@OK@@@ soft menu key to go back to the CALCULATOR MODES input form. To return to normal calculator display at this point, press the @@@OK@@@ soft menu key once more and see how the stack display change to accommodate the different font.
Selecting properties of the Stack First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key (D) to display the DISPLAY MODES input form. Press the down arrow key, ˜, twice, to get to the Stack line. This line shows two properties that can be modified.
Selecting properties of the equation writer (EQW) First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key to display the DISPLAY MODES input form. Press the down arrow key, ˜, three times, to get to the EQW (Equation Writer) line.
In this chapter we present a number of basic operations of the calculator including the use of the Equation Writer and the manipulation of data objects in the calculator. Study the examples in this chapter to get a good grasp of the capabilities of the calculator for future applications.
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– see Chapter 1): In this case, when the expression is entered directly into the stack, as soon as you press `, the calculator will attempt to calculate a value for the expression. If the expression is preceded by a tickmark, however, the calculator will reproduce the expression as entered.
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An alternative way to evaluate the expression entered earlier between quotes is by using the option …ï. We will now enter the expression used above when the calculator is set to the RPN operating mode. We also set the CAS to Exact, the display to Textbook, and the number format to Standard.
Algebraic expressions include not only numbers, but also variable names. As an example, we will enter the following algebraic expression: We set the calculator operating mode to Algebraic, the CAS to Exact, and the display to Textbook. To enter this algebraic expression we use the following keystrokes: ³2*~l*R„Ü1+~„x/...
The six soft menu keys for the Equation Writer activate functions EDIT, CURS, BIG, EVAL, FACTOR, SIMPLIFY, CMDS, and HELP. Detailed information on these functions is provided in Chapter 3 of the calculator’s user’s guide. Creating arithmetic expressions Entering arithmetic expressions in the Equation Writer is very similar to entering an arithmetic expression in the stack enclosed in quotes.
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Suppose that you want to replace the quantity between parentheses in the denominator (i.e., 5+1/3) with (5+ /2). First, we use the delete key (ƒ) delete the current 1/3 expression, and then we replace that fraction with /2, as follows: ƒƒƒ„ìQ2 When hit this point the screen looks as follows: In order to insert the denominator 2 in the expression, we need to highlight...
First, we need to highlight the entire first term by using either the right arrow (™) or the upper arrow (—) keys, repeatedly, until the entire expression is highlighted, i.e., seven times, producing: NOTE: Alternatively, from the original position of the cursor (to the right of the 2 in the denominator of combination ‚—, interpreted as (‚...
Chapter 2 of the calculator’s user’s guide. Organizing data in the calculator You can organize data in your calculator by storing variables in a directory tree. The basis of the calculator’s directory tree is the HOME directory described next.
Valid examples of variable names are: ‘A’, ‘B’, ‘a’, ‘b’, ‘ ’, ‘ ’, ‘A1’, ‘AB12’, ‘ A12’, ’Vel’, ’Z0’, ’z1’, etc. A variable can not have the same name as a function of the calculator. Some of the reserved calculator variable names are the following: ALRMDAT, CST, EQ, EXPR, IERR, IOPAR, MAXR, MINR, PICT, PPAR, PRTPAR, VPAR, ZPAR, der_, e, i, n1,n2, …, s1, s2, …, DAT, PAR, , .
To unlock the upper-case locked keyboard, press ~. Try the following exercises: ~~m„a„t„h` ~~m„~at„h` The calculator display will show the following (left-hand side is Algebraic mode, right-hand side is RPN mode): Creating variables The simplest way to create a variable is by using the K. The following...
The following are the keystrokes for entering the remaining variables: A12: 3V5K~a12` Q: ~„r/„Ü ~„m+~„r™™K~q` R: „Ô3‚í2‚í1™K~r` z1: 3+5*„¥K~„z1` (Accept change to Complex mode if asked). p1: å‚é~„r³„ì* ~„rQ2™™™K~„p1`. The screen, at this point, will look as follows: You will see six of the seven variables listed at the bottom of the screen: p1, z1, R, Q, A12, a.
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To enter the value 3 10 into A12, we can use a shorter version of the procedure: 3V5³~a12`K Here is a way to enter the contents of Q: Q: ~„r/„Ü ~„m+~„r™™³~q`K To enter the value of R, we can use an even shorter version of the procedure: R: „Ô3#2#1™...
Checking variables contents The simplest way to check a variable content is by pressing the soft menu key label for the variable. For example, for the variables listed above, press the following keys to see the contents of the variables: Algebraic mode Type these keystrokes: J@@z1@@ ` @@@R@@ `@@@Q@@@ `.
Listing the contents of all variables in the screen Use the keystroke combination ‚˜ to list the contents of all variables in the screen. For example: Press $ to return to normal calculator display. Deleting variables The simplest way of deleting variables is by using function PURGE. This function can be accessed directly by using the TOOLS menu (I), or by using the FILES menu „¡@@OK@@ .
(in RPN mode, the elements of the list need not be separated by commas as in Algebraic mode): J „ä³ @@@R!@@ ™³ @@@Q!@@ ` Then, press I@PURGE@ use to purge the variables. Additional information on variable manipulation is available in Chapter 2 of the calculator’s user’s guide. Page 2-15...
Soft MENUs, and vice versa, through an exercise. Although not applied to a specific example, the present exercise shows the two options for menus in the calculator (CHOOSE boxes and soft MENUs). In this exercise, we use the ORDER command to reorder variables in a directory.
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There is an alternative way to access these menus as soft MENU keys, by setting system flag 117. (For information on Flags see Chapters 2 and 24 in the calculator’s user’s guide). To set this flag try the following: H@FLAGS! ———————...
References For additional information on entering and manipulating expressions in the display or in the Equation Writer see Chapter 2 of the calculator’s user’s guide. For CAS (Computer Algebraic System) settings, see Appendix C in the calculator’s user’s guide. For information on Flags see, Chapter 24 in the calculator’s user’s guide.
Chapter 3 Calculations with real numbers This chapter demonstrates the use of the calculator for operations and functions related to real numbers. The user should be acquainted with the keyboard to identify certain functions available in the keyboard (e.g., SIN, COS, TAN, etc.).
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6.3#8.5- 4.2#2.5* 2.3#4.5/ • Parentheses („Ü) can be used to group operations, as well as to enclose arguments of functions. In ALG mode: „Ü5+3.2™/„Ü7- In RPN mode, you do not need the parenthesis, calculation is done directly on the stack: 5`3.2+7`2.2-/ In RPN mode, typing the expression between single quotes will allow you to enter the expression like in algebraic mode:...
• The power function, ^, is available through the Q key. When calculating in the stack in ALG mode, enter the base (y) followed by the Q key, and then the exponent (x), e.g., 5.2Q1.25` In RPN mode, enter the number first, then the function, e.g., 5.2`1.25Q •...
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ALOG, LN, EXP, SIN, COS, TAN, ASIN, ACOS, ATAN, can be combined with the fundamental operations (+-*/) to form more complex expressions. The Equation Writer, whose operations is described in Chapter 2, is ideal for building such expressions, regardless of the calculator operation mode. S30` T45` U135` 135U 0.25„¼...
1. We will describe in detail the use of the 4. HYPERBOLIC.. menu in this section with the intention of describing the general operation of calculator menus. Pay close attention to the process for selecting different options. 2. To quickly select one of the numbered options in a menu list (or CHOOSE box), simply press the number for the option in the keyboard.
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For example, in ALG mode, the keystroke sequence to calculate, say, tanh(2.5), is the following: „´4@@OK@@ 5@@OK@@ 2.5` In the RPN mode, the keystrokes to perform this calculation are the following: 2.5`„´4@@OK@@ 5@@OK@@ The operations shown above assume that you are using the default setting for system flag 117 (CHOOSE boxes).
TANH(2.5) = 0.98661.. EXPM(2.0) = 6.38905…. Operations with units Numbers in the calculator can have units associated with them. Thus, it is possible to calculate results involving a consistent system of units and produce a result with the appropriate combination of units.
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Option 1. Tools.. contains functions used to operate on units (discussed later). Options 2. Length.. through 17.Viscosity.. contain menus with a number of units for each of the quantities described. For example, selecting option 8. Force.. shows the following units menu: The user will recognize most of these units (some, e.g., dyne, are not used very often nowadays) from his or her physics classes: N = newtons, dyn = dynes, gf = grams –...
NOTE: Use the L key or the „«keystroke sequence to navigate through the menus. Available units For a complete list of available units see Chapter 3 in the calculator’s user’s guide. Attaching units to numbers To attach a unit object to a number, the number must be followed by an underscore (‚Ý, key(8,5)).
(*) In the SI system, this prefix is da rather than D. Use D for deka in the calculator, however. To enter these prefixes, simply type the prefix using the ~ keyboard. For example, to enter 123 pm (picometer), use: 5‚Û8@@OK@@ @@OK@@...
123‚Ý~„p~„m Using UBASE (type the name) to convert to the default unit (1 m) results in: Operations with units Here are some calculation examples using the ALG operating mode. Be warned that, when multiplying or dividing quantities with units, you must enclosed each quantity with its units between parentheses.
Examples of function CONVERT are shown below. Examples of the other UNIT/TOOLS functions are available in Chapter 3 of the calculator’s user’s guide. For example, to convert 33 watts to btu’s use either of the following entries:...
Physical constants in the calculator The calculator’s physical constants are contained in a constants library activated with the command CONLIB. To launch this command you could simply type it in the stack: ~~conlib`, or, you can select the command CONLIB from the command catalog, as follows: launch the catalog by using: ‚N~c.
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(English units selected in this case): To copy the value of Vm to the stack, select the variable name, and press @²STK, then, press @QUIT@. For the calculator set to the ALG, the screen will look like this: The display shows what is called a tagged value, Vm:359.0394. In here, Vm, is the tag of this result.
‘LN(x+1) + EXP(x)’ >> This is a simple program in the default programming language of the calculator. This programming language is called UserRPL (See Chapters 20 and 21 in the calculator’s user’s guide). The program shown above is Page 3-15...
2@@@H@@@ . The other examples shown above can be entered by using: 1.2@@@H@@@ , 2`3/@@@H@@@. Reference Additional information on operations with real numbers with the calculator is contained in Chapter 3 of the user’s guide. enter a value that is temporarily...
(x) axis. Similarly, the negative of z, –z = –x –iy = –re can be thought of as the reflection of z about the origin. Setting the calculator to COMPLEX mode To work with complex numbers select the CAS complex mode: H) @ @CAS@ ˜˜™...
Press @@OK@@ , twice, to return to the stack. Entering complex numbers Complex numbers in the calculator can be entered in either of the two Cartesian representations, namely, x+iy, or (x,y). calculator will be shown in the ordered-pair format, i.e., (x,y).
= r e . You can enter this complex number into the calculator by using an ordered pair of the form (r, ). The angle symbol ( ) can be entered as ~‚6. For example, the complex 1.5i...
(+-*/). The results follow the rules of algebra with the caveat that i2= -1. Operations with complex numbers are similar to those with real numbers. For example, with the calculator in ALG mode and the CAS set to Complex, try the following operations: (3+5i) + (6-3i) = (9,2);...
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The first menu (options 1 through 6) shows the following functions: Examples of applications of these functions are shown next in RECT RE(z) Real part of a complex number IM(z) Imaginary part of a complex number C R(z) Separates a complex number into its real and imaginary parts R C(x,y) Forms the complex number (x,y) out of real numbers x and...
CMPLX menu in keyboard A second CMPLX menu is accessible by using the right-shift option associated with the 1 key, i.e., ‚ß. With system flag 117 set to CHOOSE boxes, the keyboard CMPLX menu shows up as the following screens: The resulting menu include some of the functions already introduced in the previous section, namely, ARG, ABS, CONJ, IM, NEG, RE, and SIGN.
A(5, -3) and B(6, 2) can be found as follows (example in Algebraic mode): Function DROITE is found in the command catalog (‚N). calculator is in APPROX mode, the result will be Y = 5.*(X-5.)-3. Reference Additional information on complex number operations is presented in Chapter 4 of the calculator’s user’s guide.
Chapter 5 Algebraic and arithmetic operations An algebraic object, or simply, algebraic, is any number, variable name or algebraic expression that can be operated upon, manipulated, and combined according to the rules of algebra. Examples of algebraic objects are the following: •...
Simple operations with algebraic objects Algebraic objects can be added, subtracted, multiplied, divided (except by zero), raised to a power, used as arguments for a variety of standard functions (exponential, logarithmic, trigonometry, hyperbolic, etc.), as you would any real or complex number. To demonstrate basic operations with algebraic objects, let’s create a couple of objects, say ‘...
CHOOSE boxes, the ALG menu shows the following functions: Rather than listing the description of each function in this manual, the user is invited to look up the description using the calculator’s help facility: IL@) H ELP@`. To locate a particular function, type the first letter of the function.
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To complete the operation press @@OK@@. Here is the help screen for function COLLECT: We notice that, at the bottom of the screen, the line See: EXPAND FACTOR suggests links to other help facility entries, the functions EXPAND and FACTOR. To move directly to those entries, press the soft menu key @SEE1! for EXPAND, and @SEE2! for FACTOR.
At this point, select function TEXPAND from menu ALG (or directly from the catalog ‚N), to complete the operation. Operations with transcendental functions The calculator offers a number of functions that can be used to replace expressions containing logarithmic and exponential functions („Ð), as well as trigonometric functions (‚Ñ).
Information and examples on these commands are available in the help facility of the calculator. For example, the description of EXPLN is shown in the left-hand side, and the example from the help facility is shown to the right: Expansion and factoring using trigonometric functions The TRIG menu, triggered by using ‚Ñ, shows the following...
SIMP2 in the ARITHMETIC menu(IL@HELP): FACTORS: The functions associated with the ARITHMETIC submenus: INTEGER, POLYNOMIAL, MODULO, and PERMUTATION, are presented in detail in Chapter 5 in the calculator’s user’s guide. The following sections show some applications to polynomials and fractions. Page 5-7 SIMP2:...
The variable VX Most polynomial examples above were written using variable X. This is because a variable called VX exists in the calculator’s {HOME CASDIR} directory that takes, by default, the value of ‘X’. This is the name of the preferred independent variable for algebraic and calculus applications.
ARITHMETIC menu, instead use the CALC/DERIV&INTEG Menu. Example: PEVAL([1,5,6,1],5) = 281. Additional applications of polynomial functions are presented in Chapter 5 in the calculator’s user’s guide. Fractions Fractions can be expanded and factored by using functions EXPAND and FACTOR, from the ALG menu (‚×). For example: EXPAND(‘(1+X)^3/((X-1)*(X+3))’)=‘(X^3+3*X^2+3*X+1)/(X^2+2*X-3)’...
FACTOR(‘(X^3-9*X)/(X^2-5*X+6)’ )=‘X*(X+3)/(X-2)’ The SIMP2 function Function SIMP2, in the ARITHMETIC menu, takes as arguments two numbers or polynomials, representing the numerator and denominator of a rational fraction, and returns the simplified numerator and denominator. For example: SIMP2(‘X^3-1’,’X^2-4*X+3’) = {‘X^2+X+1’,‘X-3’} The PROPFRAC function The function PROPFRAC converts a rational fraction into a “proper”...
This is very useful to see the steps of a synthetic division. The example of dividing is shown in detail in Appendix C of the calculator’s user’s guide. The following example shows a lengthier synthetic division (DIV2 is available in...
Reference Additional information, definitions, and examples of algebraic and arithmetic operations are presented in Chapter 5 of the calculator’s user’s guide. Page 5-12...
Finally, function ZEROS provides the zeros, or roots, of a polynomial. Function ISOL Function ISOL(Equation, variable) will produce the solution(s) to Equation by isolating variable. For example, with the calculator set to ALG mode, to solve for t in the equation at -bt = 0 we can use the following:...
the figure to the left. After applying ISOL, the result is shown in the figure to the right: The first argument in ISOL can be an expression, as shown above, or an equation. For example, in ALG mode, try: NOTE: To type the equal sign (=) in an equation, use ‚Å (associated with the \ key).
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SOLVE produces four solutions, shown in the last output line. The very last solution is not visible because the result occupies more characters than the width of the calculator’s screen. However, you can still see all the solutions by using the down arrow key (˜), which triggers the line editor (this operation can be used to access any output line that is wider than the calculator’s screen):...
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.
(mainly, polynomial equations). If the equation to be solved for has all numerical coefficients, a numerical solution is possible through the use of the Numerical Solver features of the calculator. Numerical solver menu The calculator provides a very powerful environment for the solution of single algebraic or transcendental equations.
A polynomial equation is an equation of the form: an = 0. For example, solve the equation: 3s We want to place the coefficients of the equation in a vector: [3,2,0,-1,1]. To solve for this polynomial equation using the calculator, try the following: ‚Ï˜˜@@OK@@ „Ô3‚í2‚í0...
0.766, 0.632), (-0.766, -0.632). Generating polynomial coefficients given the polynomial's roots Suppose you want to generate the polynomial whose roots are the numbers [1, 5, -2, 4]. To use the calculator for this purpose, follow these steps: ‚Ï˜˜@@OK@@ ˜„Ô1‚í5 ‚í2\‚í4@@OK@@ @SOLVE@ Solve for coefficients Press ` to return to stack, the coefficients will be shown in the stack.
Generating an algebraic expression for the polynomial You can use the calculator to generate an algebraic expression for a polynomial given the coefficients or the roots of the polynomial. resulting expression will be given in terms of the default CAS variable X.
Solving equations with one unknown through NUM.SLV The calculator's NUM.SLV menu provides item 1. Solve equation.. solve different types of equations in a single variable, including non-linear algebraic and transcendental equations. For example, let's solve the equation: ex-sin( x/3) = 0.
The equation we stored in variable EQ is already loaded in the Eq field in the SOLVE EQUATION input form. Also, a field labeled x is provided. To solve the equation all you need to do is highlight the field in front of X: by using ˜, and press @SOLVE@.
The final solution is X = 1.8238, Y = -0.9681. Reference Additional information on solving single and multiple equations is provided in Chapters 6 and 7 of the calculator’s user’s guide. Page 6-11...
Chapter 7 Operations with lists Lists are a type of calculator’s object that can be useful for data processing. This chapter presents examples of operations with lists. To get started with the examples in this Chapter, we use the Approximate mode (See Chapter Creating and storing lists To create a list in ALG mode, first enter the braces key „ä...
Addition, subtraction, multiplication, division Multiplication and division of a list by a single number is distributed across the list, for example: Subtraction of a single number from a list will subtract the same number from each element in the list, for example: Addition of a single number to a list produces a list augmented by the number, and not an addition of the single number to each element in the list.
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The division L4/L3 will produce an infinity entry because one of the elements in L3 is zero, and an error message is returned. NOTE: If we had entered the elements in lists L4 and L3 as integers, the infinite symbol would be shown whenever a division by zero occurs.
Functions applied to lists Real number functions from the keyboard (ABS, e , LN, 10 , LOG, SIN, x , COS, TAN, ASIN, ACOS, ATAN, y ) as well as those from the MTH/ HYPERBOLIC menu (SINH, COSH, TANH, ASINH, ACOSH, ATANH), and MTH/REAL menu (%, etc.), can be applied to lists, e.g., INVERSE (1/x) Lists of complex numbers...
Lists of algebraic objects The following are examples of lists of algebraic objects with the function SIN applied to them (select Exact mode for these examples -- See Chapter The MTH/LIST menu The MTH menu provides a number of functions that exclusively to lists. With system flag 117 set to CHOOSE boxes, the MTH/LIST menu offers the following functions: With system flag 117 set to SOFT menus, the MTH/LIST menu shows the...
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Examples of application of these functions in ALG mode are shown next: SORT and REVLIST can be combined to sort a list in decreasing order: If you are working in RPN mode, enter the list onto the stack and then select the operation you want.
In both cases, you can either type out the MAP command (as in the examples above) or select the command from the CAT menu. Reference For additional references, examples, and applications of lists see Chapter 8 in the calculator’s user’s guide. Page 7-7...
['t','t^2','SIN(t)'] Typing vectors in the stack With the calculator in ALG mode, a vector is typed into the stack by opening a set of brackets („Ô) and typing the components or elements of the vector separated by commas (‚í). The screen shots below show the entering of a numerical vector followed by an algebraic vector.
Storing vectors into variables in the stack Vectors can be stored into variables. The screen shots below show the vectors = [1, 2] , u = [-3, 2, -2] , v Stored into variables @@@u2@@, @@@u3@@, @@@v2@@, and @@@v3@@, respectively. First, in ALG mode: Then, in RPN mode (before pressing K, repeatedly): NOTE: The apostrophes (‘) are not needed ordinarily in entering the...
Using the Matrix Writer (MTRW) to enter vectors Vectors can also be entered by using the Matrix Writer „² (third key in the fourth row of keys from the top of the keyboard). This command generates a species of spreadsheet corresponding to rows and columns of a matrix (Details on using the Matrix Writer to enter matrices will be presented in Chapter 9).
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@+ROW@ @-ROW @+COL@ @-COL@ The @+ROW@ key will add a row full of zeros at the location of the selected cell of the spreadsheet. The @-ROW key will delete the row corresponding to the selected cell of the spreadsheet. The @+COL@ key will add a column full of zeros at the location of the selected cell of the spreadsheet.
Simple operations with vectors To illustrate operations with vectors we will use the vectors u2, u3, v2, and v3, stored in an earlier exercise. Also, store vector A=[-1,-2,-3,-4,-5] to be used in the following exercises. Changing sign To change the sign of a vector use the key \, e.g., Addition, subtraction Addition and subtraction of vectors require that the two vector operands have the same length:...
Multiplication by a scalar, and division by a scalar Multiplication by a scalar or division by a scalar is straightforward: Absolute value function The absolute value function (ABS), when applied to a vector, produces the magnitude of the vector. For example: ABS([1,-2,6]), ABS(A), ABS(u3), will show in the screen as follows: The MTH/VECTOR menu The MTH menu („´) contains a menu of functions that specifically to...
Magnitude The magnitude of a vector, as discussed earlier, can be found with function ABS. This function is also available from the keyboard („Ê). Examples of application of function ABS were shown above. Dot product Function DOT (option 2 in CHOOSE box above) is used to calculate the dot product of two vectors of the same length.
Attempts to calculate a cross product of vectors of length other than 2 or 3, produce an error message: Reference Additional information on operations with vectors, including applications in the physical sciences, is presented in Chapter 9 of the calculator’s user’s guide. Page 8-8...
Entering matrices in the stack In this section we present two different methods to enter matrices in the calculator stack: (1) using the Matrix Writer, and (2) typing the matrix directly into the stack. Using the Matrix Writer As with the case of vectors, discussed in Chapter 8, matrices can be entered into the stack by using the Matrix Writer.
If you have selected the textbook display option (using H@) D ISP! and checking off Textbook ), the matrix will look like the one shown above. Otherwise, the display will show: The display in RPN mode will look very similar to these. Typing in the matrix directly into the stack The same result as above can be achieved by entering the following directly into the stack:...
To illustrate the operations we will create a number of matrices that we will store in the following variables. Here are the matrices A22, B22, A23, B23, A33 and B33 (The random matrices in your calculator may be different): In RPN mode, the steps to follow are:...
Addition and subtraction Four examples are shown below using the matrices stored above (ALG mode). In RPN mode, try the following eight examples: A22 ` B22`+ A23 ` B23`+ A32 ` B32`+ A33 ` B33`+ Multiplication There are a number of multiplication operations that involve matrices. These are described next.
Matrix-vector multiplication Matrix-vector multiplication is possible only if the number of columns of the matrix is equal to the length of the vector. A couple of examples of matrix- vector multiplication follow: Vector-matrix multiplication, on the other hand, is not defined. multiplication can be performed, however, as a special case of matrix multiplication as defined next.
Term-by-term multiplication Term-by-term multiplication of two matrices of the same dimensions is possible through the use of function HADAMARD. The result is, of course, another matrix of the same dimensions. This function is available through Function catalog ( ‚N ), or through the MATRICES/OPERATIONS sub- menu ( „Ø...
= I , where I is the identity matrix of the same dimensions as A . The inverse of a matrix is obtained in the calculator by using the inverse function, INV (i.e., the Y key). Examples of the inverse of some of the matrices stored...
The matrix NORM (NORMALIZE) menu is accessed through the keystroke sequence „´ . This menu is described in detail in Chapter 10 of the calculator’s user’s guide. Some of these functions are described next. Function DET Function DET calculates the determinant of a square matrix. For example,...
Using the numerical solver for linear systems There are many ways to solve a system of linear equations with the calculator. One possibility is through the numerical solver ‚Ï . From the numerical solver screen, shown below (left), select the option 4. Solve lin sys.., and press @@@OK@@@ .
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can be written as the matrix equation A x = b , if ⎡ ⎢ ⎢ ⎢ ⎣ This system has the same number of equations as of unknowns, and will be referred to as a square system. In general, there should be a unique solution to the system.
While the operation of division is not defined for matrices, we can use the calculator’s / key to “divide” vector b by matrix A to solve for x in the matrix equation A x = b . The procedure for the case of “dividing” b by A is illustrated below for the example above.
References Additional information on creating matrices, matrix operations, and matrix applications in linear algebra is presented in Chapters 10 and 11 of the calculator’s user’s guide. Page 9-12...
Right in front of the TYPE field you will, most likely, see the option Function highlighted. This is the default type of graph for the calculator. To see the list of available graph types, press the soft menu key labeled @CHOOS . This...
Function is selected as the TYPE , and that ‘X’ is selected as the independent variable ( INDEP ). Press L@@@OK@@@ to return to normal calculator display. The PLOT SET UP window should look similar to this: •...
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VIEW, then press @AUTO to generate the V-VIEW automatically. The PLOT WINDOW screen looks as follows: • Plot the graph: @ERASE @DRAW (wait till the calculator finishes the graphs) • To see labels: @EDIT L @LABEL @MENU • To recover the first graphics menu: LL@) P ICT •...
‘X/(X+10)’. Press ` . • To accept the changes made to the PLOT SETUP screen press L@@@OK@@@ . You will be returned to normal calculator display. • The next step is to access the Table Set-up screen by using the keystroke combination „õ...
• With the option In highlighted, press @@@OK@@@ . The table is expanded so that the x-increment is now 0.25 rather than 0.5. Simply, what the calculator does is to multiply the original increment, 0.5, by the zoom factor, 0.5, to produce the new increment of 0.25. Thus, the zoom in option is useful when you want more resolution for the values of x in your table.
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• Keep the default plot window ranges to read: NOTE : The Step Indep: and Depnd: values represent the number of gridlines to be used in the plot. The larger these number, the slower it is to produce the graph, although, the times utilized for graphic generation are relatively fast.
• When done, press @EXIT . • Press @CANCL to return to PLOT WINDOW. • Press $ , or L@@@OK@@@ , to return to normal calculator display. Try also a Fast 3D plot for the surface z = f(x,y) = sin (x •...
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...
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Function lim is entered in ALG mode as lim(f(x),x=a) to calculate the limit In RPN mode, enter the function first, then the expression ‘x=a’, and finally function lim. Examples in ALG mode are shown next, including some limits to infinity, and one-sided limits. The infinity symbol is associated with the 0 key, i.e.., „è...
= dF/dx, and C = constant. Functions INT, INTVX, RISCH, SIGMA and SIGMAVX The calculator provides functions INT, INTVX, RISCH, SIGMA and SIGMAVX to calculate anti-derivatives of functions. Functions INT, RISCH, and SIGMA work with functions of any variable, while functions INTVX, and SIGMAVX utilize functions of the CAS variable VX (typically, ‘x’).
Please notice that functions SIGMAVX and SIGMA are designed for integrands that involve some sort of integer function like the factorial (!) function shown above. Their result is the so-called discrete derivative, i.e., one defined for integer numbers only. Definite integrals In a definite integral of a function, the resulting anti-derivative is evaluated at the upper and lower limit of an interval (a,b) and the evaluated values ∫...
Infinite series A function f(x) can be expanded into an infinite series around a point x=x by using a Taylor’s series, namely, where f (x) represents the n-th derivative of f(x) with respect to x, f f(x). If the value x = 0, the series is referred to as a Maclaurin’s series.
RPN stack before and after using the TAYLR function, as illustrated above: The keystrokes that generate this particular example are: ~!s`!ì2/- S~!s`6!Ö˜$OK$ ˜˜˜˜$OK$ Reference Additional definitions and applications of calculus operations are presented in Chapter 13 in the calculator’s user’s guide. Page 11-6...
You can use the derivative functions in the calculator: DERVX, DERIV, , described in detail in Chapter 11 of this manual, to calculate partial derivatives (DERVX uses the CAS default variable VX, typically, ‘X’). Some examples of first-order partial derivatives are shown next. The functions used in the first two examples are f(x,y) = x cos(y), and g(x,y,z) = sin(z).
∫∫ Calculating a double integral in the calculator is straightforward. double integral can be built in the Equation Writer (see example in Chapter 2 in the user’s guide), as shown below. This double integral is calculated directly in the Equation Writer by selecting the entire expression and using function @EVAL .
Chapter 13 Vector Analysis Applications This chapter describes the use of functions HESS, DIV, and CURL, for calculating operations of vector analysis. The del operator The following operator, referred to as the ‘del’ or ‘nabla’ operator, is a vector-based operator that can be applied to a scalar or vector function: When applied to a scalar function we can obtain the gradient of the function, and when applied to a vector function we can obtain the divergence and the curl of that function.
. The curl of vector field can be calculated with function CURL. For example, for the function F (X,Y,Z) = [XY,X ,YZ], the curl is calculated as follows: CURL([X*Y,X^2+Y^2+Z^2,Y*Z],[X,Y,Z]) Reference For additional information on vector analysis applications see Chapter 15 in the calculator’s user’s guide. Page 13-2...
Differential Equations In this Chapter we present examples of solving ordinary differential equations (ODE) using calculator functions. A differential equation is an equation involving derivatives of the independent variable. In most cases, we seek the dependent function that satisfies the differential equation.
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• the characteristic equation of the ODE Both of these inputs must be given in terms of the default independent variable for the calculator’s CAS (typically X). The output from the function is the general solution of the ODE. The examples below are shown in the RPN mode: Example 1 –...
Function DESOLVE The calculator provides function DESOLVE (Differential Equation SOLVEr) to solve certain types of differential equations. The function requires as input the differential equation and the unknown function, and returns the solution to the equation if available. You can also provide a vector containing the differential equation and the initial conditions, instead of only a differential equation, as input to DESOLVE.
Laplace transform, respectively, of a function f(VX), where VX is the CAS default independent variable (typically X). The calculator returns the transform or inverse transform as a function of X. The functions LAP and ILAP are available under the CALC/DIFF menu. The examples are worked out in the RPN mode, but translating them to ALG mode is straightforward.
LAP you get back a function of X, which is the Laplace transform of f(X). Example 2 – Determine the inverse Laplace transform of F(s) = sin(s). Use: The calculator returns the result: ‘X e Fourier series A complex Fourier series is defined by the following expression where ∫...
= (t-1) +(t-1), with period T = 2. Using the calculator in ALG mode, first we define functions f(t) and g(t): Next, we move to the CASDIR sub-directory under HOME to change the value of variable PERIOD, e.g., „...
) exp(2 i t)]. Reference For additional definitions, applications, and exercises on solving differential equations, using Laplace transform, and Fourier series and transforms, as well as numerical and graphical methods, see Chapter 16 in the calculator’s user’s guide. Page 14-7...
Chapter 15 Probability Distributions In this Chapter we provide examples of applications of the pre-defined probability distributions in the calculator. The MTH/PROBABILITY.. sub-menu - part 1 The MTH/PROBABILITY.. sub-menu is accessible through the keystroke sequence „´ . With system flag 117 set to CHOOSE boxes, the following functions are available in the PROBABILITY..
RAND from the MTH/PROBABILITY sub- menu. The following screen shows a number of random numbers produced using RAND. (Note: The random numbers in your calculator will differ from these). Additional details on random numbers in the calculator are provided in Chapter 17 of the user’s guide.
The Student-t distribution The Student-t, or simply, the t-, distribution has one parameter , known as the degrees of freedom of the distribution. The calculator provides for values of the upper-tail (cumulative) distribution function for the t- distribution, function UTPT, given the parameter and the value of t, i.e.,...
The Chi-square ( ) distribution has one parameter , known as the degrees of freedom. The calculator provides for values of the upper-tail (cumulative) distribution function for the -distribution using UTPC given the value of x and the parameter . The definition of this function is, therefore, UTPC( ,x) = P(X>x) = 1 - P(X<x).
Chapter 16 Statistical Applications The calculator provides the following pre-programmed statistical features accessible through the keystroke combination ‚Ù (the 5 key): Entering data Applications numbered 1, 2, and 4 in the list above require that the data be available as columns of the matrix DAT.
Minimum values) that you want as output of this program. When ready, press @@@OK@@ . The selected values will be listed, appropriately labeled, in the screen of your calculator. For example: Sample vs. population The pre-programmed functions for single-variable statistics used above can be applied to a finite population by selecting the Type: Population in the SINGLE-VARIABLE STATISTICS screen.
Obtaining frequency distributions The application 2. Frequencies.. in the STAT menu can be used to obtain frequency distributions for a set of data. The data must be present in the form of a column vector stored in variable DAT. To get started, press ‚Ù˜@@@OK@@@ .
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DAT, by using function STO (see example above). Next, obtain single- variable information using: ‚Ù @@@OK@@@ . The results are: This information indicates that our data ranges from -9 to 9. To produce a frequency distribution we will use the interval (-8, 8) dividing it into 8 bins of width 2 each.
Fitting data to a function y = f(x) The program 3. Fit data.. , available as option number 3 in the STAT menu, can be used to fit linear, logarithmic, exponential, and power functions to data sets (x, y), stored in columns of the DAT matrix. For this application, you need to have at least two columns in your DAT variable.
1 shows the covariance of x-y. definitions of these parameters see Chapter 18 in the user’s guide. For additional information on the data-fit feature of the calculator see Chapter 18 in the user’s guide. Obtaining additional summary statistics The application 4.
• Press @@@OK@@@ to obtain the following results: Confidence intervals The application 6. Conf Interval can be accessed by using ‚Ù—@@@OK@@@ . The application offers the following options: These options are to be interpreted as follows: 1. Z-INT: 1 .: Single sample confidence interval for the population mean, , with known population variance, or for large samples with unknown population variance.
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Press @HELP to obtain a screen explaining the meaning of the confidence interval in terms of random numbers generated by a calculator. To scroll down the resulting screen use the down-arrow key ˜ . Press @@@OK@@@ when done with the help screen.
(21.98424 and 24.61576). Press @TEXT to return to the previous results screen, and/or press @@@OK@@@ to exit the confidence interval environment. The results will be listed in the calculator’s display. Additional examples of confidence interval calculations are presented in Chapter 18 in the calculator’s user’s guide.
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H Press ‚Ù——@@@OK@@@ to access the confidence interval feature in the calculator. Press @@@OK@@@ to select option 1. Z-Test: 1 . Enter the following data and press @@@OK@@@ : You are then asked to select the alternative hypothesis: 150.
Then, we reject H = 150, against H 150. The test z value is = 5.656854. The P-value is 1.54 10 . The critical values of = 1.959964, corresponding to critical x range of {147.2 152.8}. This information can be observed graphically by pressing the soft-menu key @GRAPH : Reference Additional materials on statistical analysis, including definitions of...
With system flag 117 set to SOFT menus, the BASE menu shows the following: This figure shows that the LOGIC, BIT, and BYTE entries within the BASE menu are themselves sub-menus. These menus are discussed in detail in Chapter 19 of the calculator’s user’s guide. Page 17-1...
Writing non-decimal numbers Numbers in non-decimal systems, referred to as binary integers, are written preceded by the # symbol ( „â ) in the calculator. To select the current base to be used for binary integers, choose either HEX (adecimal), DEC (imal), OCT (al), or BIN (ary) in the BASE menu.
If you are holding the HP 50g with the keyboard facing up, then this side of the SD card should face down or away from you when being inserted into the HP 50g.
4. When the formatting is finished, the HP 50g displays the message "FORMAT FINISHED. PRESS ANY KEY TO EXIT". To exit the system menu, hold down the ‡ key, press and release the C key and then release the ‡ key.
Note that if the name of the object you intend to store on an SD card is longer than eight characters, it will appear in 8.3 DOS format in port 3 in the Filer once it is stored on the card. Recalling an object from the SD card To recall an object from the SD card onto the screen, use function RCL, as follows:...
Purging all objects on the SD card (by reformatting) You can purge all objects from the SD card by reformatting it. When an SD card is inserted, @FORMA appears an additional menu item in File Manager. Selecting this option reformats the entire card, a process which also deletes every object on the card.
Chapter 19 Equation Library The Equation Library is a collection of equations and commands that enable you to solve simple science and engineering problems. The library consists of more than 300 equations grouped into 15 technical subjects containing more than 100 problem titles. Each problem title contains one or more equations that help you solve that type of problem.
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View the five equations in the Projectile Motion set. All five are Step 4: used interchangeably in order to solve for missing variables (see the next example). #EQN# #NXEQ# #NXEQ# #NXEQ# #NXEQ# Step 5: Examine the variables used by the equation set. #VARS# and —...
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Notice that pressing the right-shifted version of a variable’s menu key causes the calculator to recall its value to the stack. (The small square next to the R on the menu label indicates that it was used in the previous calculation.)
Replacement products may be either new or like-new. 2. HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase, for the period specified above, due to defects in material and workmanship when properly installed and used.
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8. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services.
Service Europe Country : Austria Belgium Denmark Eastern Europe countries Finland France Germany Greece Holland Italy Norway Portugal Spain Sweden Switzerland Turkey Czech Republic South Africa Luxembourg Other European countries +420-5-41422523 Asia Pacific Country : Australia Singapore Page W-3 Telephone numbers +43-1-3602771203 +32-2-7126219 +45-8-2332844...
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Guatemala Puerto Rico Costa Rica N.America Country : U.S. Canada ROTC = Rest of the country Please logon to http://www.hp.com for the latest service and support information. Telephone numbers 0-810-555-5520 Sao Paulo 3747-7799; ROTC 0-800-157751 Mx City 5258-9922; ROTC 01-800-472-6684...
Regulatory information Federal Communications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation.
Or, call 1-800-474-6836 For questions regarding this FCC declaration, contact: Hewlett-Packard Company P. O. Box 692000, Mail Stop 510101 Houston, Texas 77269-2000 Or, call 1-281-514-3333 To identify this product, refer to the part, series, or model number found on the product. Canadian Notice This Class B digital apparatus meets all requirements of the Canadian Interference-Causing Equipment Regulations.
Japanese Notice Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment.
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