This repetitive, calculation-heavy process is exactly what a

This repetitive, calculation-heavy process is exactly what a
This repetitive, calculation-heavy process is exactly what a calculator program would be appropriate for. To program this example into
your graphing calculator, follow these steps:
Press the
key on your calculator. You should get the following screen:
Use the right arrow key
to move over to "NEW" to get the following screen:
to create a new program. You should now see this screen:
At this point, you must name your program. You may use a combination of up to eight letters and numbers, but the first character must
be a letter. Note that the Alpha Lock is on so that you will automatically get letters when you press the calculator's keys (to tun off
Alpha Lock, press
After naming the program NEWT and pressing
, we get the following screen:
We are now ready to enter the steps in our program. The colon ( : ) indicates the beginning of a line of code. The first thing we want to
happen when we run or "execute" the program is for the calculator to ask us for our initial guess. We do this by putting an "INPUT"
line in the program. To do this, press
see the following screen:
Since Input is what we want, simply press
again and use the right arrow key
to move over to I / O, at which point you should
, and you should see the following screen:
We now need to name the variable that we want to input when we run the program. We can use any single letter we like, but X is an
obvious, easy choice, so press the
key, followed by
to get:
Next, we want the program to apply Newton's Rule and perform the calculation
. Eventually we will store
in Y1 and
in Y2 (the same Y1 and Y2 we use when graphing functions), so we need to enter our calculation in the next
step of the program, namely:
X-Y1 / Y2
We begin by entering "X-" in the next line of the program:
To access the "Y Variables," press the
to go to the standard
Since we want Y1 , just press
key, the right arrow key
to move over to the "Y-VARS" menu:
key to get the "Function" screen:
to select it, taking us back to the program screen:
We next enter the division sign ( / ), and then go back to the
"Function" screen to select Y2:
.Before leaving this line of the program, we need to store this value in another variable, call it Z. We do this by pressing
then the letter Z (don't forget to press the Alpha key first). After pressing
, you should see the following screen:
We're almost finished! The calculator now knows the result of Newton's Method, so we just have to instruct the program to tell us.
Once again, press
, and move over to I / O, and press
for Disp (short for Display). Your screen should look like this:
Since the result of our calculation is what we want to display, enter Z to get:
That's it! To quit the programming mode, press
Now, the only thing remaining is to do before we run the program is to tell it what Y1 and Y2 are. To do this, press
function in Y1 and its derivative in Y2 in the usual way:
To run the program, press
. Since EXEC is already selected and NEWT is the only program in our list, press
and enter the
begin executing or running the program. The screen will now show prgmNEWT. Press
again to start. You should get a ?
mark prompt. This is the program's way of asking you to enter your first guess. In our example, our first guess was 1. Press 1 followed
to get the following:
You should recall that 0.8 was our first answer when we did it manually.
To do a second iteration, since we are still in the execute mode, simply press
could type in .8, but we can use the ANS key (
again. You should get the ? prompt again. We
) to easily input 0.8 for X. After pressing
again, you should see the
We can continue this process iteratively as long as we want, but after just a few times, we'll discover that the answer (to 10 decimal
places) stops changing (see screen below). Newton's Method is that good (and fast!).
To do this process for a different function, all we need to do is change Y1 (the function) and Y2 (its derivative, and then simply run the
program again.
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