HP 33S Scientific Calculator
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Hewlett Packard F2216A F2216A**Hp**Hp33S Scientific Calculator**NewPocket - Scientific - HP
Powerful/advanced pocket-size programmable scientific calculator. 32K user memory. Letter+4 program line labels. Cursor keys to navigate menus. Works in both RPN and algebraic modes. Features: keystroke programming, solve function, stats one and two variable, base-n function, 27 independent memories, trig, polar-rectang.
Details
Brand: HP
Part Numbers: F2216A, HP33S
UPC: 082916014555
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Manual
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(English)HP 33S Scientific Calculator, size: 2.6 MB |
HP 33S Scientific Calculator
User reviews and opinions
| mercierb |
5:43pm on Wednesday, October 13th, 2010 ![]() |
| I am finding this guy usefull outside of school. Does what it needs to. Feels very sturdy. Tons of functionality I had to buy it for finance... | |
| gseas |
6:39am on Tuesday, September 21st, 2010 ![]() |
| The HP 10BII is a great buy. For roughly $30 I do not think that there is a more practical financial calculator on the market. | |
| zandsc |
9:10am on Friday, August 27th, 2010 ![]() |
| Good I got this calculator but due to mix up had to get another.Services are impeccable.Thanks | |
| matt.williamson |
1:22pm on Sunday, August 1st, 2010 ![]() |
| I am a finance professor and I require this calculator for my introductory classes. It has IRR and YTM. | |
| oliverst |
12:14pm on Friday, July 2nd, 2010 ![]() |
| I use the HP 10bii in my cash flow business and find that it is a user friendly calculator. Adequate Capabilities","Attractive Design". Best choice for financial courses and exams. Adequate Capabilities","Attractive Design","Clear Display","Compact Size","Easy To Use | |
| Nesami |
11:12am on Friday, May 28th, 2010 ![]() |
| This is a calculator that for the price, is beyond belief! Anyway, this is a very nice financial calculator. It fits most of my needs for in-class calculation. | |
| cadcoke3 |
8:22pm on Friday, May 14th, 2010 ![]() |
| The Batteries Died Within a Week Great calculator except for the small little fact that the batteries died the day of my test and left me scrambling h... | |
| Brazilben |
1:21am on Monday, March 22nd, 2010 ![]() |
| The calculator is easy to manage. The manual helps and is really good! HAve a hp12c financial calculator too ! Love hp! Adequate Capabilities". | |
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Documents

SCI format displays a number in scientific notation (one digit before the " " or " " radix mark) with up to 11 decimal places (if they fit) and up to three digits in the _, type in the number of decimal places to be exponent. After the prompt, 0 or 1. (The mantissa part of the displayed. For 10 or 11 places, press number will always be less than 10.) , the "2", "3", "4", and "6" are the For example, in the number decimal digits you see when the calculator is set to SCI 4 display mode. The "5" following the "E" is the exponent of 10: 1.5.
Getting Started 119
Engineering Format ({
ENG format displays a number in a manner similar to scientific notation, except that the exponent is a multiple of three (there can be up to three digits before the " " or " " radix mark). This format is most useful for scientific and engineering calculations that use units specified in multiples of 103 (such as micro, milli, and kilounits.) After the prompt, _, type in the number of digits you want after the first 0 or 1. significant digit. For 10 or 11 places, press , the "2", "3", "4", and "6" are the For example, in the number significant digits after the first significant digit you see when the calculator is set to ENG 4 display mode. The "3" following the " " is the (multiple of 3) exponent of 10: 123.46 x 103. or will cause the exponent display for the number Pressing being displayed to change in multiples of 3. and pressing will convert the For example, key in the number , which the mantissa n satisfies 1 n < 1000 and displayed value to the exponent is a multiple of 3. When you press again, the displayed value by shifting the decimal point three places to the right is converted to and converting the exponent to the next lower multiple of 3. and pressing will convert the Key in the number , which the mantissa n satisfies 0.01 n < 10 and displayed value to the exponent is a multiple of 3. When you press again, the by shifting the decimal point displayed value is converted to three places to the left and converting the exponent to the next higher multiple of 3. ALL Format ({ })
ALL format displays a number as precisely as possible (12 digits maximum). If all the digits don't fit in the display, the number is automatically displayed in scientific format.
SHOWing Full 12Digit Precision
Changing the number of displayed decimal places affects what you see, but it does not affect the internal representation of numbers. Any number stored internally always has 12 digits.
Problems that have multiple parentheses can be solved in the same manner using the automatic storage of intermediate results. For example, to solve (3 + 4) (5 + 6) on paper, you would first calculate the quantity (3 + 4). Then you would calculate (5 + 6). Finally, you would multiply the two intermediate results to get the answer. Work through the problem the same way with the HP 33s, except that you don't have to write down intermediate answersthe calculator remembers them for you.
First adds (3+4) Then adds (5+6) Then multiplies the intermediate answers together for the final answer.
Exercises
Calculate:
(16.3805x 5) = 181.0000 0.05
Solution: 16.3805 Calculate: 5.05
[(2 + 3) (4 + 5)] + [(6 + 7) (8 + 9)] = 21.5743
Solution: 8 9
Calculate: (10 5) [(17 12) 4] = 0.2500 Solution: 17 or 4
Order of Calculation
We recommend solving chain calculations by working from the innermost parentheses outward. However, you can also choose to work problems in a lefttoright order. For example, you have already calculated: 4 [14 + (7 3) 2] by starting with the innermost parentheses (7 3) and working outward, just as you would with pencil and paper. The keystrokes were 4. If you work the problem from lefttoright, press 2.
This method takes one additional keystroke. Notice that the first intermediate result is still the innermost parentheses (7 3). The advantage to working a problem lefttoright is that you don't have to use to reposition operands for nomcommutaiive functions ( and ). However, the first method (starting with the innermost parentheses) is often preferred because: It takes fewer keystrokes. It requires fewer registers in the stack.
When using the lefttoright method, be sure that no more than four intermediate numbers (or results) will be needed at one time (the stack can hold no more than four numbers).
The above example, when solved lefttoright, needed all registers in the stack at one point:
Saves 4 and 14 as intermediate numbers in the stack. At this point the stack is full with numbers for this calculation. Intermediate result. Intermediate result.
You can type almost any number as a fraction on the keyboard including an improper fraction (where the numerator is larger than the denominator). However, if you disregard these two restrictions: the calculator displays The integer and numerator must not contain more than 12 digits total. The denominator must not contain more than 4 digits.
Turns on Fractiondisplay mode. Enters 1.5; shown as a fraction. Enters 1 3/4. Displays x as a decimal number. Displays x as a fraction.
If you didn't get the same results as the example, you may have accidentally changed how fractions are displayed. (See "Changing the Fraction Display" later in this chapter.) The next topic includes more examples of valid and invalid input fractions. You can type fractions only if the number base is 10 the normal number base. See chapter 10 for information about changing the number base.
Fractions in the Display
In Fractiondisplay mode, numbers are evaluated internally as decimal numbers, then they're displayed using the most precise fractions allowed. In addition, accuracy annunciators show the direction of any inaccuracy of the fraction compared to its 12digit decimal value. (Most statistics registers are exceptions they're always shown as decimal numbers.)
Display Rules
The fraction you see may differ from the one you enter. In its default condition, the calculator displays a fractional number according to the following rules. (To change the rules, see "Changing the Fraction Display" later in this chapter.) The number has an integer part and, if necessary, a proper fraction (the numerator is less than the denominator). The denominator is no greater than 4095. The fraction is reduced as far as possible.
Examples:
These are examples of entered values and the resulting displays. For comparison, the internal 12digit values are also shown. The and annunciators in the last column are explained below.
Entered Value
2 3/15/32
54/ 12
Internal Value
2.37500000000 14.4687500000 4.50000000000 9.60000000000 2.83333333333 0.00183105469 (Illegal entry) (Illegal entry)
Displayed Fraction
6 18/5
34/ 15/ 12 8192
12345678 12345/3/16384
Accuracy Indicators
The accuracy of a displayed fraction is indicated by the and annunciators at the right of the display. The calculator compares the value of the fractional part of the internal 12digit number with the value of the displayed fraction: If no indicator is lit, the fractional part of the internal 12digit value exactly matches the value of the displayed fraction. If is lit, the fractional part of the internal 12digit value is slightly less than the displayed fraction the exact numerator is no more than 0.5 below the displayed numerator. If is lit, the fractional part of the internal 12digit value is slightly greater than the displayed fraction the exact numerator is no more than 0.5 above the displayed numerator. This diagram shows how the displayed fraction relates to nearby values means the exact numerator is "a little above" the displayed numerator, and means the exact numerator is "a little below".
Choosing a Fraction Format
The calculator has three fraction formats. Regardless of the format, the displayed fractions are always the closest fractions within the rules for that format.
Most precise fractions. Fractions have any denominator up to the /c value, and they're reduced as much as possible. For example, if you're studying math concepts with fractions, you might want any denominator to be possible (/c value is 4095). This is the default fraction format. Factors of denominator. Fractions have only denominators that are factors of the /c value, and they're reduced as much as possible. For example, if you're calculating stock prices, you might want to see and ( /c value is 8 ). Or if the /c value is 12, possible denominators are 2, 3, 4, 6, and 12. Fixed denominator. Fractions always use the /c value as the denominator they're not reduced. For example, if you're working with time ( /c value is 60 ). measurements, you might want to see
To select a fraction format, you must change the states of two flags. Each flag can be "set" or "clear," and in one case the state of flag 9 doesn't matter.
To Get This Fraction Format:
Change These Flags: 8 9
Clear Set
Most precise Factors of denominator Fixed denominator
Clear Set Set
You can change flags 8 and 9 to set the fraction format using the steps listed here. (Because flags are especially useful in programs, their use is covered in detail in chapter 13.)
to get the flag menu.
2. To set a flag, press { } and type the flag number, such as 8. To clear a flag, press { ) and type the flag number. } and type the flag number. Press To see if a flag is set, press { to clear the or response.
Examples of Fraction Displays
The following table shows how the number 2.77 is displayed in the three fraction formats for two /c values.
Fraction Format
Most Precise Factors of Denominator Fixed Denominator
How 2.77 Is Displayed
/c = 4095
2 77/1051/3153/4095
(2.7700)
/c = 16
2 10/3/12/16
(2.7692)
(2.7699)
(2.7500)
The following table shows how different numbers are displayed in the three fraction formats for a /c value of 16.
Most precise Factors of denominator Fixed denominator 2 2
Number Entered and Fraction Displayed
2 2.1/1/8/2/2/11/11/0/16 2.9999 216/9/5/10/16
2 0/16
For a /c value of 16.
Suppose a stock has a current value of 48 1/4. If it goes down 2 5/8, what would be its value? What would then be 85 percent of that value?
Accuracy of Integration
Since the calculator cannot compute the value of an integral exactly, it approximates it. The accuracy of this approximation depends on the accuracy of the integrand's function itself, as calculated by your equation. This is affected by roundoff error in the calculator and the accuracy of the empirical constants. Integrals of functions with certain characteristics such as spikes or very rapid oscillations might be calculated inaccurately, but the likelihood is very small. The general characteristics of functions that can cause problems, as well as techniques for dealing with them, are discussed in appendix E.
Specifying Accuracy
The display format's setting (FIX, SCI, ENG, or ALL) determines the precision of the integration calculation: the greater the number of digits displayed, the greater the precision of the calculated integral (and the greater the time required to calculate it). The fewer the number of digits displayed, the faster the calculation, but the calculator will presume that the function is accurate to the only number of digits specified in the display format. To specify the accuracy of the integration, set the display format so that the display shows no more than the number of digits that you consider accurate in the integrand's values. This same level of accuracy and precision will be reflected in the result of integration. If Fractiondisplay mode is on (flag 7 set), the accuracy is specified by the previous display format.
Interpreting Accuracy
After calculating the integral, the calculator places the estimated uncertainty of that to view the value of the uncertainty. integral's result in the Yregister. Press For example, if the integral Si(2) is 1.6054 0.0002, then 0.0002 is its uncertainty.
Example: Specifying Accuracy.
With the display format set to SCI 2, calculate the integral in the expression for Si(2) (from the previous example).
Sets scientific notation with two decimal places, specifying that the function is accurate to two decimal places. Rolls down the limits of integration from the Zand Tregisters into the Xand Yregisters. Displays the current Equation.
The integral approximated to two decimal places. The uncertainty of the approximation of the integral.
The integral is 1.610.0161. Since the uncertainty would not affect the approximation until its third decimal place, you can consider all the displayed digits in this approximation to be accurate. If the uncertainty of an approximation is larger than what you choose to tolerate, you can increase the number of digits in the display format and repeat the integration (provided that f(x) is still calculated accurately to the number of digits shown in the display), In general, the uncertainty of an integration calculation decreases by a factor of ten for each additional digit, specified in the display format.
Example: Changing the Accuracy.
For the integral of Si(2) just calculated, specify that the result be accurate to four decimal places instead of only two.
Specifies accuracy to four decimal places. The uncertainty from the last example is still in the display. Rolls down the limits of integration from the Z and Tregisters into the X and Yregisters. Displays the current equation.
Calculates the result.
Note that the uncertainty is about 1/100 as large as the uncertainty of the SCI 2 result calculated previously. { }4 Restores FIX 4 format.
Restores Degrees mode.
This uncertainty indicates that the result might be correct to only three decimal places. In reality, this result is accurate to seven decimal places when compared with the actual value of this integral. Since the uncertainty of a result is calculated conservatively, the calculator's approximation in most cases is more accurate than its uncertainty indicates.
This chapter gives you instructions for using integration in the HP 33s over a wide range of applications. Appendix E contains more detailed information about how the algorithm for integration works, conditions that could cause incorrect results and conditions that prolong calculation time, and obtaining the current approximation to an integral.
Operations with Complex Numbers
The HP 33s can use complex numbers in the form
x + iy.
It has operations for complex arithmetic (+, , , ), complex trigonometry (sin, cos, tan), and the mathematics functions z, 1/z, z1z 2 , ln z, and e z. (where z1 and z2 are complex numbers).
To enter a complex number: 1.
Type the imaginary part.
3. Type the real part.
Complex numbers in the HP 33s are handled by entering each part (imaginary and real) of a complex number as a separate entry. To enter two complex numbers, you enter four separate numbers. To do a complex operation, press before the operator. For example, to do (2 + i 4) + (3 + i 5), press 5 3.
The result is 5 + i 9. (The first line is the imaginary and the second is the real part.)
The Complex Stack
In RPN mode, the complex stack is really the regular memory stack split into two double registers for holding two complex numbers, z1x + i z1y and z2x + i z2y:
Since the imaginary and real parts of a complex number are entered and stored separately, you can easily work with or alter either part by itself.
Complex function
(displayed) (displayed)
When you key in numbers, the calculator will not accept more than the maximum number of digits for each base. For example, if you attempt to key in a 10digit annunciator appears. hexadecimal number, digit entry halts and the If a number entered in decimal base is outside the range given above, then it in the other base modes. In RPN mode, the produces the message original decimal value of any toobig number is used in calculations. Any operation that results in a number outside the range given above causes OVERFLOW to be briefly displayed. The display then shows the largest positive or negative integer representable in the current base. In ALG mode, any operation displays (except +/ in the entry line but not in a variable prompt) using the annunciator.
Windows for Long Binary Numbers
The longest binary number can have 36 digits three times as many digits as fit in the display. Each 12digit display of a long number is called a window.
36 - bit number
Highest window
Lowest window (displayed)
When a binary number is larger than the 12 digits, the or annunciator (or both) appears, indicating in which direction the additional digits lie. Press the or ) to view the obscured window. indicated key (
Press to display left window
Press to display right window
Statistical Operations
The statistics menus in the HP 33s provide functions to statistically analyze a set of one or twovariable data: Mean, sample and population standard deviations. Linear regression and linear estimation ( x and Weighted mean (x weighted by y). Summation statistics: n, x, y, x2, y2, and xy.
Entering Statistical Data
One and twovariable statistical data are entered (or deleted) in similar fashion using the (or ) key. Data values are accumulated as summation statistics in six statistics registers (28 through 33), whose names are displayed in the SUMS menu. (Press and see ).
Always clear the statistics registers before entering a new set of { } ). statistical data (press
Entering OneVariable Data
{} to clear existing statistical data.
2. Key in each xvalue and press
3. The display shows n, the number of statistical data values now accumulated.
actually enters two variables into the statistics registers because the Pressing value already in the Yregister is accumulated as the yvalue. For this reason, the calculator will perform linear regression and show you values based on y even when you have entered only xdata or even if you have entered an unequal number of xand yvalues. No error occurs, but the results are obviously not meaningful. To recall a value to the display immediately after it has been entered, press.
Entering TwoVariable Data
In RPN mode, when your data consist of two variables, x is the independent variable and y is the dependent variable. Remember to enter an (x, y) pair in reverse order (y x) so that y ends up in the Yregister and X in the Xregister.
You can use to move the program pointer to a specified label or line number without starting program execution.
label nnnn (nnnn < 10000). For example,
To a line number: A0005.
To a label: label but only if program entry is not active (no A. program lines displayed; PRGM off). For example,
Conditional Instructions
Another way to alter the sequence of program execution is by a conditional test, a true/false test that compares two numbers and skips the next program instruction if the proposition is false. (that is, is x equal For instance, if a conditional instruction on line A0005 is to zero?), then the program compares the contents of the Xregister with zero. If the Xregister does contain zero, then the program goes on to the next line. If the Xregister does not contain zero, then the program skips the next line, thereby branching to line A0007. This rule is commonly known as "Do if true."
Do next if true.
Skip next if false.
The above example points out a common technique used with conditional tests: the line immediately after the test (which is only executed in the "true" case) is a branch to another label. So the net effect of the test is to branch to a different routine under certain circumstances. There are three categories of conditional instructions: Comparison tests. These compare the Xand Yregisters, or the Xregister and zero.
Flag tests. These check the status of flags, which can be either set or clear. Loop counters. These are usually used to loop a specified number of times.
Tests of Comparison (x?y, x?0)
There are 12 comparisons available for programming. Pressing displays a menu for one of the two categories of tests: x?y for tests comparing x and y. x?0 for tests comparing x and 0. Remember that x refers to the number in the Xregister, and y refers to the number in the Yregister. These do not compare the variables X and Y. Select the category of comparison, then press the menu key for the conditional instruction you want. or
Selects "G" the program. SOLVE evaluates to find the value of the unknown variable. Selects P; prompts for V.
Stores 2 in V; prompts for N. Stores.005 in N; prompts for R.
.005.0821
Stores.0821 in R; prompts for T. Calculates T. Stores 297.1 in T; solves for P. Pressure is 0.0610 atm.
Example: Program Using Equation.
Write a program that uses an equation to solve the "Ideal Gas Law."
Selects Programentry mode. Moves program pointer to top of the list of programs.
H { 1 P V N R T }
Labels the program. Enables equation prompting. Evaluates the equation, clearing flag 11. (Checksum and length: EDC8 9).
Ends the program. Cancels Programentry mode. Checksum and length of program: 36FF 21
Now calculate the change in pressure of the carbon dioxide if its temperature drops by 10 C from the previous example.
Stores previous pressure. Selects program H. Selects variable P; prompts for V. Retains 2 in V; prompts for N. Retains.005 in N; prompts for R. Retains.0821 in R; prompts for T.
Calculates new T. Stores 287.1 in T; solves for new P.
Calculates pressure change of the gas when temperature drops from 297.1 K to 287.1 K (negative result indicates drop in pressure).
Using SOLVE in a Program
You can use the SOLVE operation as part of a program. If appropriate, include or prompt for initial guesses (into the unknown variable and into the Xregister) before executing the SOLVE variable instruction. The two instructions for solving an equation for an unknown variable appear in programs as:
label variable
The programmed SOLVE instruction does not produce a labeled display (variable = value) since this might not be the significant output for your program (that is, you might want to do further calculations with this number before displaying it). If you do want this result displayed, add a VIEW variable instruction after the SOLVE instruction. If no solution is found for the unknown variable, then the next program line is skipped (in accordance with the "Do if True" rule, explained in chapter 13). The program should then handle the case of not finding a root, such as by choosing new initial estimates or changing an input value.
Example: SOLVE in a Program.
The following excerpt is from a program that allows you to solve for x or y by X or Y. pressing
Setup for X. Index for X.
Branches to main routine. Checksum and length: Setup for Y. Index for Y. Branches to main routine. Checksum and length: C5EMain routine. Stores index in i. Defines program to solve. Solves for appropriate variable. Displays solution. Ends program. Checksum and length: D82E 18 Calculates f (x,y). Include INPUT or equation prompting as required.
Starts polar input routine. Defines the radius as one unit vector.
Mathematics Programs 1511
Sets T equal to 125. Sets P equal to 63. Calculates dot product. Calculates angle between resultant force vector and lever. Gets back to input routine.
Solutions of Simultaneous Equations
This program solves simultaneous linear equations in two or three unknowns. It does this through matrix inversion and matrix multiplication. A system of three linear equations
AX + DY + GZ = J BX + EY + HZ = K CX + FY + IZ = L
can be represented by the matrix equation below.
J = K L
The matrix equation may be solved for X, Y, and Z by multiplying the result matrix by the inverse of the coefficient matrix.
G J H K I L
X = Y Z
Specifics regarding the inversion process are given in the comments for the inversion routine, I.
1512 Mathematics Programs
Starting point for input of coefficients. Loopcontrol value: loops from 1 to 12, one at a time. Stores control value in index variable.
Checksum and length: 35EStarts the input loop. Prompts for and stores the variable addressed by i. Adds one to i. If i is less than 13, goes back to LBL L and gets the next value. Returns to LBL A to review values. Checksum and length: 51AB 15 This routine inverts a matrix. Calculates determinant and saves value for the division loop, J.
Calculates E' determinant = AI CG.
Calculates F' determinant = CD AF.
Mathematics Programs 1513
Calculates H' determinant = BG AH.
Calculates I' determinant = AE BD.
Calculates A' x determinant = EI FH,
Calculates B' determinant = CH BI.
Calculates C' determinant = BF CE. Stores B'.
Calculates D' determinant = FG DI.
1514 Mathematics Programs
Calculates G' determinant = DH EG. Stores D'. Stores I'. Stores E'. Stores F'. Stores H'. Sets index value to point to last element of matrix. Recalls value of determinant. Checksum and length: 0FFB 222 This routine completes inverse by dividing by determinant. Divides element. Decrements index value so it points closer to A. Loops for next value. Returns to the calling program or to Checksum and length: 1FCF 15 This routine multiplies a column matrix and a matrix. Sets index value to point, to last element in first row. Sets index value to point to last element in second.
Mathematics Programs 1515
Environmental Limits
To maintain product reliability, observe the following temperature and humidity limits: Operating temperature: 0 to 45 C (32 to 113 F). Storage temperature: 20 to 65 C (4 to 149 F). Operating and storage humidity: 90% relative humidity at 40 C (104 F) maximum.
Changing the Batteries
The calculator is powered by two 3-volt lithium coin batteries, CR2032. Replace the batteries as soon as possible when the low battery annunciator ( ) appears. If the battery annunciator is on, and the display dims, you may lose data. message is displayed. If data is lost, the
Once you've removed the batteries, replace them within 2 minutes to avoid losing stored information. (Have the new batteries readily at hand before you open the battery compartment.) To install batteries: 1.
Have two fresh buttoncell batteries at hand. Avoid touching the battery terminals handle batteries only by their edges.
2. Make sure the calculator is OFF. Do not press ON ( ) again until the entire batterychanging procedure is completed. If the calculator is ON when the batteries are removed, the contents of Continuous Memory will be erased. 3. Turn the calculator over and slide off the battery cover.
4. Never remove two old batteries at the same time, to prevent memory lose. Remove one of the two batteries. Press down the holder. Push the plate in the shown direction and lift it.
Warning
Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals.
5. Insert a new CR2032 lithium battery, making sure that the positive sign (+) is facing outward. Replace the plate and push it into its original place. 6. Remove and insert the other battery as in step 4~5. Make sure that the positive sign (+) on each battery is facing outward. 7.
Replace the battery compartment cover.
Testing Calculator Operation
Use the following guidelines to determine if the calculator is working properly. Test the calculator after every step to see if its operation has been restored. If your calculator requires service, refer to page A7.
f(x) always increases or always decreases as x increases (figure b, below).
The graph of f(x) is either concave everywhere or convex everywhere (figure c, below). If f(x) has one or more local minima or minima, each occurs singly between adjacent roots of f(x) (figure d, below).
f (x) f (x)
Function Whose Roots Can Be Found
In most situations, the calculated root is an accurate estimate of the theoretical, infinitely precise root of the equation. An "ideal" solution is one for which f(x) = 0. However, a very small nonzero value for f(x) is often acceptable because it might result from approximating numbers with limited (12digit) precision.
Interpreting Results
The SOLVE operation will produce a solution under either of the following conditions: If it finds an estimate for which f(x) equals zero. (See figure a, below.) If it finds an estimate where f(x) is not equal to zero, but the calculated root is a 12digit number adjacent to the place where the function's graph crosses the xaxis (see figure b, below). This occurs when the two final estimates are neighbors (that is, they differ by 1 in the 12th digit), and the function's value is positive for one estimate and negative for the other. Or they are (0, 10499) or (0, 10499). In most cases, f(x) will be relatively close to zero.
x a Cases Where a Root Is Found b
To obtain additional information about the result, press see the previous again to see the estimate of the root (x), which was left in the Yregister. Press value of f(x), which was left in the Zregister. If f(x) equals zero or is relatively small, it is very likely that a solution has been found. However, if f(x) is relatively large, you must use caution in interpreting the results.
Example: An Equation With One Root.
Find the root of the equation: 2x3 + 4x2 6x + 8 = 0 Enter the equation as an expression:
2 X 4 X X
Select Equation mode. Enters the equation.
Checksum and length. Cancels Equation mode. Now, solve the equation to find the root:
0 X 10 _
Initial guesses for the root. Selects Equation mode; displays the left end of the equation.
Solves for X; displays the result. Final two estimates are the same to four decimal places.
f(x) is very small, so the approximation is a good root.
Example: An Equation with Two Roots.
x<0?
x>0?
Rectangular to polar coordinates. Converts (x, y) to (r, ).
Operation Index G19
Power. Returns y raised to the xth power.
Notes: 1.
Function can be used in equations.
2. Function appears only in equations.
G20 Operation Index
Special Characters
, 65 Algebraic mode, 110 ALL format. See display format in equations, 65 in programs, 126 setting, 120 alpha characters, 13 angles between vectors, 151 converting format, 413 converting units, 413 implied units, 44, A2 angular mode, 44, A2, B3 annunciators alpha, 13 battery, 11, A2 descriptions, 111 flags, 1311 list of, 17 lowpower, 11, A2 shift keys, 12 answers to questions, A1 arithmetic binary, 102 general procedure, 116 hexadecimal, 102 intermediate results, 211 long calculations, 211 octal, 102 order of calculation, 213 stack operation, 24, 91 assignment equations, 69, 610, 611, 71
FN. See integration
% functions, 46. See equationentry cursor ~. See backspace key ". See integration z, 114 , 123 , 43, A2 annunciators binary numbers, 106 equations, 67, 126 (in fractions), 121, 51 annunciator in catalogs, 33 in fractions, 33, 52, 53 _. See digitentry cursor annunciators, 13
annunciator, 11, A2
A.Z annunciator, 13, 32, 64 absolute value (real number), 416 addressing indirect, 1320, 1321, 1322 ALG, 110 compared to equations, 124 in programs, 124
Index1
File name 33s-English-Manual-050502-Publication(Edition 3) Printed Date : 2005/5/2 Size : 13.7 x 21.2 cm Page : 388
asymptotes of functions, D8
viewing all digits, 33, 106 borrower (finance), 171 branching, 132, 1316, 147
backspace key canceling VIEW, 33 clearing messages, 15, F1 clearing Xregister, 22, 26 deleting program lines, 1218 equation entry, 15, 68 leaving menus, 15, 19 operation, 15 program entry, 126 starts editing, 68, 126, 1218 balance (finance), 171 base affects display, 104 arithmetic, 102 converting, 101 default, B3 programs, 1222 setting, 101, 1411 base mode default, B3 equations, 65, 610, 1222 fractions, 52 programming, 1222 setting, 1222, 1411 batteries, 11, A2 Bessel function, 82 bestfit regression, 117, 161
BIN annunciator, 101
%CHG arguments, 47 adjusting contrast, 11 canceling prompts, 15, 613, 1213 canceling VIEW, 33 clearing messages, 15, F1 clearing Xregister, 22, 26 interrupting programs, 1217 leaving catalogs, 15, 33 leaving Equation mode, 63, 64 leaving menus, 15, 19 leaving Program mode, 126 on and off, 11 operation, 15 stopping integration, 82, 148 stopping SOLVE, 77, 141 , 91, 92 /c value, 55, B3, B6 calculator adjusting contrast, 11 default settings, B3 environmental limits, A2 questions about, A1 resetting, A4, B2 selftest, A5 shorting contacts, A4 testing operation, A4, A5 turning on and off, 11 cash flows, 171 catalogs leaving, 15

HP 33s Scientific Calculator
Your best choice for the FE/PE exams
With 32 KB user memory, the HP 33s is the most powerful programmable 2-line scientific calculator offering the choice of both RPN* or Algebraic data entry permitted on the FE or PE series of exams. The HP 33s Scientific Calculator is available at the following national retailers: Wal-Mart, Frys Electronics and select campus bookstores
More information on HPs full line of financial, graphing and scientific calculators can be found at: www.hp.com/calculators * For details on HPs efficient and time-saving Reverse Polish Notation (RPN) data entry option, visit: www.hp.com/go/rpn
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