BGoal: We want to implement a program which allows us to estimate the limit of a function at a number, b.
Preparatory experiment: Suppose that b is 3 and that we want to generate quite a few numbers close to 3 on its right side. Further suppose that we want most of the numbers to cluster close to 3. Execute the line
3 B
and then store, in x, a first number, 6, to the right of b by
6 x
Now, we average x and B to get a new number half way toward B from x by
(x+B)/2 x
When you enter this line, you both display this new number and store it in
x, replacing the previous number in x. Without any other intervening computation,
press ENTER again several times. You should see that you are re-executing
the line (x+B)/2
x and each time producing a new number closer to B. To estimate the functionâs
limit at b, you will want a method to repeat what you have just done but to
print values of f(x) for each new x produced.
General method: This will be a two-line program which simply adjusts the value of x by moving it half way toward b and then displays the value of x and f(x). The initial values will be set up manually before the program is first run. We will execute the program repeatedly to gather our data.
Step by step method:
Choose PRGM, then EDIT, type in the name of the program (LIMIT in this case), then press ENTER. You are now ready to enter the program lines.
Enter these two lines
:(x+B)/2
x
:Disp x,y1
QUIT to the home screen.
Note 1: Disp is found by I/O while you are in program edit mode.
Note 2: The function name, y1, is entered by simply typing a lower case y (to get lower case letters, use the "alpha" option above "ALPHA" on the keypad) followed by a 1.
To use this program: Set up the calculator by placing the function, f, in the "y(x)=" screen as y1. Store the value of b in the variable B. Store the starting value in x. Now execute the program by pressing PRGM, and with EXEC selected, the number designating the program named LIMIT. After this, each time you press ENTER you will be rewarded by another execution of the program and a value of x and of f(x).
