You may have noticed that all the results so far have been improper fractions. For example the first calculation shown right gives the answer as 22/15 rather than 1 7. The fraction setting of Mixed Fraction is 15 essentially the same but answers are given as mixed fractions instead of improper fractions, as shown.
If you want to use the Fraction setting to convert decimals to fractions, here are some tips
if converting a recurring decimal to a fraction, then make sure you include at least one more digit in the decimal than the setting of Fraction in MODES. As you can see right, failing to include enough decimal places does not produce the desired result.
if you are converting an exact decimal to a fraction, then set a Fraction n value of at least one more than the number of decimal places in the value entered. Both examples in the third screen shot to the right were done at Fraction 6.
Not understanding the significance of the setting of Fraction can produce some unfortunate effects. For example, at Fraction 2, the value of 123.456 becomes 123, with the 0.456 dropped entirely. An example of this is shown right. If you use a setting of only Fraction 2 to perform the calculation shown, you will find to your amazement that 1/3 + 4/5 = 8/7 , whereas using Fraction 6 gives the correct answer.
The reason for this error is that the 1/3 and 4/5 were converted to decimals and added to give
1.133333. This was converted back to a fraction using Fraction 2 to give 8/7 (1.1428.).
This may seem odd but it does match sufficiently closely in Fraction 2 to be accepted.
Generally it is not a good idea to go below the default setting of
Fraction 4. In fact, a Fraction 6 setting tends to be more reliable.
Fraction in the MODES view.
A new feature of the hp 39gs and hp 40gs is the setting of Mixed
The results of this new setting can be seen in the image to the right. Using the setting of Mixed Fraction the result is 4+1/7 ( 4
the answer of 29/7 is obtained using the old Fraction setting.

1 ) whereas 7

Calculator Tip If you scroll back through the History and re-use a result such as the 4+1/7 shown above then dont forget to put brackets around it to ensure that no order of operations errors occur.

The HOME History

The HOME page maintains a record of all your calculations called the History. You can re-use any of the calculations or their results in subsequent calculations.

Summary

The up/down arrow key moves the history highlight through the record of previous calculations. key can be used to retrieve any earlier results for editing When the highlight is visible, the using the left/right arrow keys and the DEL key. Care must be taken to ensure the your idea of order of operations agrees with the calculators. For example, (-5) 2 must be entered as (-5) 2 rather than as -52, and (5+4) rather than 5 + 4.

5 + 4 must be entered as

The ANS key can be used to retrieve the results of the calculation immediately preceding the one youre working on. E.g. (5+Ans) The DEL key can be used to erase single characters in the editing line or single lines in the HOME history. The SHIFT CLEAR key will delete the entire history. Regular clearing will ensure that memory is not gradually eroded. The key displays a calculation as you would see it written and is available in many views.
The MODES view can be used to set the format in which numbers are displayed on the HOME page, and to choose the angle measure which is to be used. Make sure you understand Fraction mode before using it. Remember that the angle and numeric mode settings may change if you change aplets in the APLET view. Numbers are stored in memory using the key labeled. The stored values can then be used by simply putting the letter in the expression in place of the number. You can easily reboot the calculator if it locks up, generally without loss of memory. Make sure you know how to do this in case it happens during a test or an examination. Regularly saving your information to a PC will ensure that you dont lose anything important. Additionally, it is a good idea to completely reset the calculator occasionally so that any instability in the operating system has no chance to grow. Many extra functions are available via the MATH menu. For more information on the complete set of mathematical functions available in the HOME view (and anywhere else) see the chapter The MATH menu on page 165.

8 THE FUNCTION APLET

The Function aplet is probably the one that you will use most of all. It allows you to:
graph equations find intercepts find turning points (maxima/minima) find areas under curves find areas between curves find gradients find derivatives algebraically find simple integrals algebraically evaluate functions at particular values graph and evaluate algebraically expressions such as f(g(x)) or f(x+2)

Now move the highlight back to A (the value youre trying to find) and button. You should find that you obtain the answer to press the our problem of m/s2.
The INFO report process has finished, you can obtain a report on it by When the button. The result in this case may not seem very pressing the informative but there is more about these messages on page 106. The information they supply can be critical and you should develop the habit of checking them.
Multiple solutions and the initial guess Our first example was fairly simple because there was only one solution so it did not much matter where we began looking for it. When there is more than one possible answer you are required to supply an initial estimate or guess. The Solve aplet will then try to find a solution which is near to the estimate.
Example 1 The volume of a cylinder is given by V = 2 r ( r + h ). Find the radius of a cylinder which has a volume of 1 liter and a height of 10cm.
Enter the equation into E1 as shown right. When you are entering the equation, ensure that you put a * sign between the R and the bracket. See page 79 for more information on the reason for this.
Change to the NUM view and enter the known values, remembering that 1 liter=1000cm3. Position the highlight over R, enter a positive value as to find the solution shown right of your estimate, and press 8.57cm. The equation is a quadratic in R which means two solutions are possible. If you enter an initial estimate of -10 you will obtain the negative solution, which is physically invalid in this case.
Example 2 If f ( x ) = x 3 2x 2 5x + 2 find all values of x for which f ( x ) = 1.
Although you may have a clear picture in your mind and can provide Solve with the estimates it needs, Ill assume that, like me, you would find it helpful to see a graph first.
It is also possible to solve this in the Function aplet, which offers more powerful tools. The PLOT view in the Solve aplet, although powerful, can be deceptive if you dont understand it and I sometimes find it easier to work in the Function aplet. In this case we will continue to work in Solve. Graphing in Solve In the SYMB view, enter the equation Y=X^3-2X2-5X+2 into E1. In the NUM view, enter the known value of Y=1, ensure that the highlight is on X, making it the active variable, and then press PLOT. If your view does not look like this then you may not have had the highlight on the X, or your axes may not be set the same as mine in PLOT SETUP.
The PLOT view on the previous page shows two curves. The horizontal line is the left side of the equation which, when the known value of Y=1 is substituted, forms a constant straight line. The other curve is the right hand side of the equation which, since X is the active variable, forms a cubic. In this case the scale chosen is appropriate but this will not always be the case and some adjustment might be required in the PLOT SETUP view. Transferring approximate solutions We require values where the two curves intersect. Using the arrow keys, move the cursor near to the first intersection point. I found (see right) that -1.6 seemed to be a good approximation. Now change back to the NUM view and you will find that this approximation has been carried to find the true value. back as the initial estimate. Press

the Statistics aplet initially opens in the NUM view, offering easy input and editing of When you press value. The SYMB view is reserved for specifying which columns contain data and which columns frequencies or, in the case of bivariate data, for indicating pairing of columns. If you have not already done so, go to the APLET view, highlight, and then the Statistics aplet. Uni-variate vs. Bi-variate data or On the screen you will see a key labeled either Pressing the key under this label changes from univariate ( ) and back. Make sure the key is showing bivariate ( before proceeding. Clearing data If your NUM view had some data in it, you could press CLEAR (above DEL) and choose All columns. The DEL key is used to delete individual data points, rather than whole columns. ) to
Let's use the following set of data and obtain all the usual statistics on it, and also plot a histogram and a box & whisker graph. { 2, 3, 1, 0, -2, 3, 4, 2, 2, 0, 6, 2, 3, 1, 0, 4, 1, 3, 3, 2 }
Move the highlight into column C1 and enter the data, pressing the ENTER key after each piece of data.
Looking at the bottom of the calculator screen you will see a series of tools provided for you. really worth bothering with because it is generally easier just to retype a number than it is to press then use the arrow keys and DEL to change it.

is not and

Sorting data inserts space for a new number by shifting all the The key labeled does exactly what it says it sorts the numbers down one space. data into ascending or descending order. The extra fields in the screen shot right are used with bivariate sorts or frequency tables and will be to stop the sort. explained in that section of the notes. Press
key provides access to a larger font size and The is the really useful one. last key labeled
we have already discussed. The
The STATS key key and Making sure the highlight is in column C1, press the you will see the screen shown right. If you use the down arrow, you can scroll down and see the rest of the screen (below right).
NOTE: If you get an error message instead of summary statistics, you the aplet before beginning this process. If may have forgotten to the SYMB view defines columns which dont actually have any data in them then errors will result.
As you can see in the screens above right, the calculator gives not only the standard statistics that any scientific calculator would give, but also the minimum and maximum values, the median and the upper and lower quartile cutoffs. The mode is not given, but this is easily obtained from the histogram as we will see later. Functions of columns Let's create a second column of data with all its values exactly double the values in the first column. We can use the HOME view to avoid having to retype the values as follows

The reason for the last instruction is that only one histogram can be drawn at a time and if more than one data ed then only the first one is drawn. set is Auto scale Now use VIEWS Auto Scale to plot the graph. You will hopefully find that it looks like the one on the right. The Auto Scale function is always very effective in the Statistics aplet and is recommended.
If you use the left/right arrows and look at the bottom of the screen youll see that the frequencies and ranges are listed. It is probably worth tidying up this graph up a little by going into PLOT SETUP and (on the second page) setting the YTick value to be 5 instead of 1. In the graph ed. to the right the Labels option has also been
You probably noticed a lot of other options in the first page of PLOT SETUP. Their explanations follow.
Plot Setup options The setting of Statplot controls what type of graph is drawn. There two choices are Hist (short for histogram) or BoxW (Box and Whisker). key while Statplot is highlighted will switch between Pressing the these two, or you use the button to pick from a menu. Box and whisker graphs Unlike histograms, it is possible to have more than one box and whisker graph plotted. This makes comparisons between data sets very easy. If you look for the cursor (circled) in the diagram shown right, you will see is turned on then information about the graph is given that when at the bottom of the screen. As usual the up/down arrows change from graph to graph, while the left/right arrows move within the graph.
key produces the normal tools of
As an aside, pressing the and. They all behave in the normal manner as ,
tool was discussed in detail in the Function aplet chapter. The can be quite useful by displaying information on which columns make up each graph if you lose track. Looking again at the screen shot of the first page of PLOT SETUP (near the top of the page) you will see that there are three ranges. As with the Parametric and Polar aplets, XRng and YRng control how much of the graph is seen. If your histogram has frequencies of (say) up to 30 then you need to make sure your YRng reaches at least that value or the top of the histogram will be cut off. In the same way, if your data has a minimum value of -5 and a maximum of 35 then your XRng will need to cover at least that range of values. This is normally not worth worrying about since using VIEWS Auto Scale generally produces very satisfactory results.

A standardized test is available for which it is known that the normal performance of hearing-impaired students at the same stage of study has a mean of 53.6% and a standard deviation of 12.2%. When he applies this test to his class of 23 students their scores are shown below. The teacher believes that this data shows that his students are scoring significantly better and wishes to test this at a level of 5%. Test results: {57, 72, 42, 50, 55, 58, 59, 38, 45,53, 77,57, 52, 69, 50, 55, 59, 68, 62, 63, 53, 56}
As usual we begin by entering the data into column C1 of the Statistics aplet.
Changing to the Inference aplet, we choose a Hypothesis test using Ztest: 1 , since we know the population standard deviation.
The hypotheses are: H0: The sample is drawn from a population whose mean is the same as the standardized population ( = 0 ). The sample is drawn from a population whose mean is larger than that of the standardized population ( > 0 ).
Change to the NUM SETUP view, you can use the import facility to import the summary statistics from the Statistics aplet.
Enter the values for the mean and standard deviation of the standardized test, and the significance level of 0.05 (5%).
If we now change to the NUM view we can see that the test z score is less than the required critical z*, and the probability of obtaining a mean of the value found is 0.1080, which is larger than the required test value of 0.05.
In the PLOT view, we can see visually that the vertical line representing the sample mean is not within the region of rejection marked by the R.
From the evidence the teacher must reject the alternate hypothesis and conclude that it is not possible to say at the 5% level of significance that his class has averaged significantly higher than the standardized population from which the test was drawn. He should re-think his proposed paper or his new teaching method. Alternatively, from the diagram in the PLOT view it seems that his mean is not far from being significant. Perhaps he simply needs to collect more data in the hopes that this may back up his view. The result he has obtained is, after all, only a probability and further investigation may give a different view.
23 THE EXPERT: CHI2 TESTS & FREQUENCY TABLES
We will start with a small digression to look at a simple inferential problem which can be solved using only the Statistics and Solve aplets. Using the Chi2 test on a frequency table Four coins are tossed 400 times and the number of heads noted for each toss.

In both cases the procedure is to supply sufficient information to allow the triangle to be solved, hence the message to Fill 3 out of 6 values. This request should be taken with a pinch of salt. For example, in the case of a right triangle it is actually only necessary to supply 2 values despite what is stated. 7cm 115 15cm
Solve the triangle shown right. Use the Aplet view to select and the aplet.
The second is to ensure that we are working in degree mode. Change to the MODES view and choose Degrees.
Now press SYMB (or NUM or PLOT) to change back to the view shown right.
Since this is not a right triangle, the first step is to ensure that is not selected, as is shown right. Any of the three angles , or can be used to represent the 115o angle. In this case I will use for no other reason than that it is at the top of the illustration, just as it is in the diagram of the triangle. This means that the 15 cm goes into the A field and the 7 cm into the B field. Enter those values, using the arrow keys to move from one to another. The result should be the screen shown right.
Pressing the button labeled being filled in, as shown.
will result in the remaining 3 values
The calculated values are highlighted for convenience.
Find the length of the hypotenuse for the triangle shown right.

12 cm 25 cm

Since we dont want the sizes of the angles it doesnt really matter what angle mode the aplet is set to. If you
worked the previous example then it is probably still in degree mode.
button to change the screen into the right triangle Press the
format as shown right. Pressing SHIFT CLEAR will remove the remaining values from the previous problem. Use the arrow keys to move to the A and B fields and enter the values of. 25 cm and 12 cm respectively. Then press
The result should be as shown right, giving a length for the hypotenuse of 27.73 cm. In the example screen I have also pressed the button (with the highlight on C) so that I can see more than 2 decimal places.
Solve the triangle shown right.
This is an example of a triangle that has two possible solutions, generally referred to as The Ambiguous Case. The calculator will give both possible solutions.
Begin by setting the calculator into Degree mode, if it is not already. Change into the SYMB view and ensure that the non-right triangle is selected as shown.
Purely to maintain orientation, we will select C as the side that is 10cm long and enter the values shown right. Notice that as soon as sufficient information has been entered the message Solution Found appears.
and the calculator will fill in the missing values. The Press will appear to announce that an additional button label of alternate solution is available.

will alternate repeatedly between the two solutions.

26 THE FINANCE APLET

This aplet is designed to allow users to solve time-value-of-money (TVM) and amortization style problems quickly and easily, as well as ordinary compound interest problems. Compound interest problems involve bank accounts, mortgages and similar situations where money earns money. TVM problems involve the use of the idea that the value of money changes with time - a dollar today is worth more than the same dollar some years from now. For example, that a dollar invested today can generate more money than the same dollar invested later.
The calculator manual contains a lengthier explanation including cash flow diagrams for those who need it, as does any high school or college textbook.

When you

the aplet you will see the initial view shown right.
Pressing SYMB, NUM or PLOT will make no difference to this aplet as it is quite limited and only has the one view, consisting of two related pages. Parameters There are a number of parameters or variables which must be either supplied or solved for. These are:
The total number of compounding payments or payments.
This has the value of Beg(inning) or End depending on when payments occur relative to the compounding periods - at the beginning or the end.
The number of payments per year.
The nominal interest rate or investment rate per year. This is then divided by P/YR to find the nominal interest per compounding period. This is the rate actually used in the internal calculations.
This is the present value of the initial flow of cash. In a loan, this is the amount of the loan. In an investment, the amount invested. PV is always the amount at the start of the first period, however long that may be.
This is the size of the periodic payment. The assumptions made are that all payments are the same size and that no payments will be skipped. Payments can occur at the beginning or the end of a compounding period, depending on the setting of Mode.
The future value of the investment or loan. This could be the amount in a bank account after a period of years, the residual on a lease, the amount still owing on a loan after N repayments, or the remaining value of an investment which has been paying income as an annuity.
When using the aplet is it important to visualize the cash flow in terms of positive cash (inwards) or negative cash (outwards). This can be illustrated simply via the following example. Always bear this principle in mind when deciding how to plan your setup of the aplet.

<var_name>(<expression>) This function will differentiate the expression with respect to the variable specified. This can be done in two ways. When done in the HOME view the result is numeric because the derivative is evaluated for the current value of the variable in memory. For example, if X currently has the value of 3 then the result is as shown right. When done in the Function aplet, or using a symbolic variable (S1S5), the result is the algebraic derivative (see pages 59 to 75).
TAYLOR(<expression>,<var_name>,<num>) Briefly, a Taylor polynomial allows you to approximate a complicated function via a simpler polynomial function. The <expression> supplied is approximated with respect to <var_name> by terms of a polynomial up to <num> power. The screen shot on the right shows the calculator deriving the Taylor polynomial for sin(x) up to the 7th power. The SIN(X) function can be approximated by taking terms from the polynomial:

sin( x) = x = x

x3 3! 1 6

x5040 x 7

In this example, the result is shown twice. The first is calculated with MODES set to Standard, the second with MODES set to Fraction 4. The second screen shot shows the fractional polynomial in more detail after highlighting it and pressing.
The Complex group of functions
Complex numbers on the hp 39gs & hp 40gs can be entered in either of two ways. Firstly, in the same way as they are commonly written in mathematical workings: a + bi. Secondly, as an ordered pair: (a,b).
For example, 3 + 2i could be entered into the calculator exactly as it is written, with the i obtained using SHIFT ALPHA to get a lowercase i. Alternatively you can enter it directly as an ordered pair.
As soon as you press ENTER, the calculator immediately converts the a + bi form into an ordered pair. The History retains the original in case you need to it later for re-use.
The exception is when you enter a complex number in polar form using button). When you the (angle) sign on the keyboard (above the do this the calculator converts into the two other common forms of rcis format and (a,b) format as shown right. In the example right, the lowest line shows how the number was been entered. The first two lines show how the result is stored in the History as rcis format and as (a,b) format.
Complex numbers can be used with all trigonometric and hyperbolic function, as well as with matrices, lists and some real-number and keyboard functions.
Just as real numbers can be stored into the alphabetic memories A to Z, there are 10 special memories Z1,Z2.Z9,Z0 which are provided to store complex numbers.
In addition to the trig functions, there are other functions that take complex arguments.

INVERSE(<matrix>) This function produces the inverse matrix of an n x n square matrix, where possible. A fully worked example of the use of an inverse matrix to solve a 3 by 3 system of equations is given in the chapter on Using Matrices on page 211 and in Appendix A on page 302. An error message is given (see right) when the matrix is singular (det. zero).
Note: Some people write the inverse matrix as a fraction (one over the
determinant) multiplied by a matrix, so as to avoid decimals and fractions within the inverse matrix. The calculator does not do this. If you want the matrix with the determinant factored out, then evaluate DET(matrix) first, record the fraction and then evaluate DET(matrix) * INVERSE(matrix) to obtain (usually) a non-fractional matrix.

A= A = 2

Remember that the inverse matrix is not just the matrix, but the fraction times the matrix. See also: RREF, DET
LQ(<matrix>) This function takes an mxn matrix, factors it and returns a list containing three matrices which are (in order):
an mxn lower trapezoidal matrix an nxn orthogonal matrix an mxm permutation matrix.
If you want to separate these matrices for later use then you should store them into a list variable. For example, if M1 was [[1,2,3],[4,5,6],[7,8,9]] then LQ(M1) L1 would store the three resulting matrices into list variable L1. In the HOME view you could now enter L1(1) M2 to store the first of the result matrices into M2 and so on.
LSQ(<matrix1>,<matrix2>) The least squares function displays the minimum norm least squares matrix (or vector).
LU(<matrix>) This LU Decomposition function is similar to the LQ function on the previous page. It factors a square matrix into three matrices, returning them in the form of a list variable. {[[lower triangular]],[[upper triangular]],[[permutation]]} The upper triangular has ones on its diagonal. The matrices can be separated in the same method outlined for the LQ function.
MAKEMAT(<expression>,<rows>,<columns>) The MAKEMAT function is used, mainly by programmers to manufacture a matrix with dimensions rows columns, using the supplied expression to calculate each element. Eg.
MAKEMAT(0,3,3) returns a 33 zero matrix,
Note: If the expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J during the calculation.
4 MAKEMAT(I+J,3,3) returns the matrix 5 6
QR(<matrix>) The QR function is similar to the LQ function on the previous page. It factors an m x n matrix into three matrices, returning them in the form of a list variable. {[[mm orthogonal]],[[mn uppertrapezoidal]],[[nn permutation]]}

The next program code we will look at belongs to the 1st option on the VIEWS menu of Plot axes.
A message is first given to the user of how to proceed if they want to use different axes. The flag value of G is then set to 1 so that the next program can tell that the axes are ready to use. The function is also re-entered in case the user has changed the SYMB view. Users have an annoying habit of changing things so try to allow for this in your programs by making them fool-proof.
The next program below runs when the user chooses the second menu option of Explore, and illustrates a very important technique. A copy of the PLOT view is stored in the aplets sketch view and then retrieved and modified using the various graphics commands. The program is broken into parts for discussion purposes.
The reason for the IF G==0 THEN is to check that the blank axes have been plotted and are available for use. If not then the user receives a message to tell them what to do and the remainder of the program is bypassed using the IFTHENELSE statement. Trying to capture a PLOT view that doesnt exist is a major error and will result in the program crashing abruptly. It is possible to allow for errors like this using the IFERR statement but in a teaching example like this it makes the code more difficult to follow.
Still referring to the code on the previous page, you will see that it refers to PageNum. The sketches in the calculators SKETCH view are numbered 1, 2, 3etc. Sketch number 1 is always present but after that only sketches that have been created are available and the program will crash if you try to access one that does not exist.
The aplet variable PageNum is the pointer to the sketch you want and the actual sketch page itself is called Page. Thus the two lines after ELSE are telling the program to store the PLOT view into the first page of the SKETCH view using the command PLOT. This command stores the PLOT view into whatever graphics variable you specify. In this case into Page.
The PLOT view must exist before this can be done or the program will crash. This is the reason for setting up the flag G discussed earlier by doing that we ensure that this section of code only runs if something has been plotted. If you run the program and then later change to the SKETCH view you will be able to see this stored image. Finally, the user is presented with two messages which tell them what to do.

INPUT <variable>;<title>;<prompt>;<message>;<default value> This command puts up an input view which can be used to obtain responses from the user. The degree of control over appearance is quite high as can be seen in the example. If you want the default value to be whatever the user last input then use
INPUT N;.; N instead. If you do this then you should consider storing an initial reasonable value into N before the first use of the INPUT command.
MSGBOX <expression> This puts up a box with the text/expression you specify. If you want a new line started within the box then just enclose a pressing of the ENTER key within the quotes.
PROMPT <variable> This is a short form of the INPUT statement for those that dont require such precision of control over appearance. The default value is the current value of the variable. Using the PROMPT command you dont have control of the title and prompts at the bottom of the screen and to the left of the input field.
WAIT <duration> This command pauses execution for the specified number of seconds. Execution resumes at the next statement after the WAIT command.
42 APPENDIX A: SOME WORKED EXAMPLES
The examples which follow are intended to illustrate the ways in which the calculator can be used to help solve some typical problems. In some cases more than one method is shown. In some cases the method is chosen more to illustrate the capabilities of the calculator than because it is necessarily the most efficient method. Sometimes these problems are quoted elsewhere in the book and repeated here for convenience.
Finding the intercepts of a quadratic
Find the x intercepts of the quadratic equation

g ( x) = 2 x 2 + 2 x 1

Method 1 - Using the QUAD function in HOME.
key in the bottom view. This method is shown right, using the This is probably not a method that one would use in general but it has the slight advantage that the answer is given in the same form that you the result, would see it if you used the Quadratic formula. Just edit and square the decimal part to find the value of the discriminant if you need the result in surd format. The S1 is the calculators version of the result and remove the S1 to obtain the the sign. Just positive solution, replacing the + with a - to obtain the other. This method is only of use if the question said Show working because it doesnt give the answer directly.
Method 2 - Using the Function aplet. Shown right. Enter the function into the SYMB view, use the VIEWS key and choose Decimal. If the axes dont suit, then use the option of Root to find the two roots. One options. Now use the result is shown. This is clearly the best method and has the advantage that you can see the graph clearly. Root method does not depend on the graph Note: Using the being on the screen. The algorithm will still find roots even if they are not currently visible.

Step by step mode might appear to be quite useful for students but is quite limited in what it actually
displays. Those hoping for the CAS to show complete working such as that required by a teacher will be disappointed. Choose Step by step mode to view some details of the calculations, displayed on to proceed to the next stage. The the screen. After each step you are requested to press alternative is Direct mode, in which only the result is displayed.
Incredible as it may seem, the CAS is capable of infinite precision when manipulating integers (memory permitting). To see this in action try evaluating 200 factorial and then press VIEWS. You can now scroll through all 375 digits of the result! Dont use a summation variable of lower-case value - the positive root of x2+1=0.
This is assumed by the CAS to be the unit imaginary
Although you can use the integration symbol provided on the keyboard it has disadvantages outlined on page 74. Use the INTVX function instead. See the example on page 339. The COLLECT function referred to earlier will factorize over the set of integers. For example, COLLECT(x2-4) will result in (x+2)(x-2), whereas COLLECT(X2+4) will result in X2+4 back again. On the other hand the FACTOR function will factorize over the irrational and complex sets too. Entering FACTOR(X2+2) will result in the expression
( x + 2i )( x 2i ) in complex mode.
The infinity symbol can be found in the Constants section of the MATH menu but can also be
obtained by pressing SHIFT 0. Pressing (-) first will produce -, while pressing (-) twice will give +. These are often needed for use in the LIMITS function. For example, evaluating LIMIT(
x + x + x x ,+) will give (after a very long wait).
As with the infinity symbol there is also a shortcut for the symbol i. Just press SHIFT 1. See page 333 for more keyboard shortcuts.

HP 40gs

Graphing Calculator
This ideal classroom graphing tool uses Computer Algebra System (CAS), familiar algebraic entry-system logic and displays answers in symbolic, numeric, and graphing views. Create and store Aplets with 2.25MB total memory**.
Enhanced classroom power Math and science students will benefit from algebraic entry-system logic and easy-to-use interactive tools. Perform complex arithmetic and calculus functions with Computer Algebra System (CAS) Improve problem solving and learning opportunities with symbolic, numeric and graphic views Easily create and use Aplets to assist in learning Review and work with your data using interactive history, notes and sketch capabilities Complex problem solver Complex problem solving is easier on a large, dynamic split screen with adjustable contrast and 2.25MB of total memory**. Easy readability on dynamic split screen with adjustable contrast Get outstanding performance and ample storage with 2.25MB of total memory (2MB Flash + 256KB RAM)** Tackle tough problems with over 750 built-in functions plus powerful HP solvers and applications Use a built-in library of 29 constants and easy metric unit conversions for math and science Designed to be efficient Access online applications and share data through a variety of connectivity options. Improve accuracy with HP click-style keys. Download and share data with PCs and other devices using USB and serial ports Reduce keying errors and improve accuracy with unique HP click-and-rotate keys Increase protection and improve portability using slide-on hard cover Get added flexibility using on-screen dynamic menu options HP quality and support Have confidence that every time you turn on your HP calculator, every calculation you make, results in dependable, worry-free performance and accurate results. Rely on HP quality and award-wining support online and by phone Get the most from your calculator, visit www.hp.com/calculators for downloads, tutorials and more

Specifications

The HP 40gs Graphing Calculator includes all the features of the HP 9G plus: Computer Algebra System (CAS) Symbolic, numeric and graphic views Linear equation solver and triangle solver 2.25MB total memory (2MB Flash ROM + 256KB RAM)** Enhanced connectivity with serial port, USB Adjustable contrast for greater readability Built-in constant library Slide-on hard cover included
HP Part Number CPU Display size Display Type Connectivity Contrast Entry-system logic Built-in functions Menus, prompts, etc. Internal precision Memory Keyboard Power Power off memory protection Auto power off Size (L x W x D) Enclosure material Key top material Weight What's in the box Warranty Subject suitability Permitted for use on
F2225AA 75Mhz ARMx 64 pixels (7 lines x 33 characters + 2 line header + 1 line menu) LCD USB and serial ports for connectivity to PCs, other HP 40gs calculators and peripherals Adjustable Algebraic Over 750 Yes 15 digits 2.25MB total memory (2MB Flash + 256KB RAM)** Alphanumeric AAA x 4 + CR2032 Yes 5 minutes 18.7 x 9.4 x 3.1 cm (7.4 x 3.7 x 1.2 inches) Plastic Plastic Approximately 249 g (8.8 oz)
Calculator, slide-on protective cover, batteries, user manual, USB cable, unit-tounit cable and CD with connectivity software, Aplets and advanced user manual
1-year warranty (may vary by region) General mathematics, Algebra, Trigonometry, Statistics, Geometry, Biology, Chemistry, Physics, Earth Sciences SAT Reasoning and SAT Subject TestsTM in Math 1 & 2, ACT, PSAT/NMSQT, AP Chemistry/Physics, AP Calculus/Statistics, PLAN, EXPLORE*
2007 Hewlett-Packard Development Company, L.P. The information contained herein is subject to change without notice. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. Nothing herein should be construed as constituting an additional warranty. HP shall not be liable for technical or editorial errors or omissions contained herein. *ACT, PLAN and EXPLORE are registered trademarks of ACT, Inc., which was not involved in the production of and does not endorse this product. For more information, go to www.act.org. AP Calculus requires a graphing calculator. Any scientific or graphing calculator (Excludes models with QWERTY (i.e. typewriter) keyboards, electronic writing pads, and pen-input/stylus-driven devices) is permitted for the following College Board tests: AP Chemistry, AP Physics, AP Statistics (a graphing calculator with statistical capabilities is expected), PSAT/NMSQT, SAT Reasoning and SAT Subject Tests in Mathematics Level 1 and Level 2. For more information, go to www.collegeboard.com. Policies are subject to change. AP and SAT are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of both the College Board and National Merit Scholarship Corporation which were not involved in the production of and do not endorse this product. **Flash ROM memory is for system upgrades only and is not available to the user.

To learn more, visit www.hp.com/calculators

4AA1-0863ENUC, June 2007