Secant TI83 Dec 9 06

[Pages:3]The program

A Secant Line Program for a TI-83 Calculator

(8/23/06)

1. PROGRAM: SECANT 2. : ClrDraw 3. : FnOff 4. : FnOn 1

5. : Disp "USE Y1(X)"

6. : Prompt A, B 7. : A X 8. : Y1 W 9. : B X 10. : Y1 V 11. : (V - W )/(B - A) M 12. : DrawF W + M (X - A) 13. : Pause

14. : Disp "SLOPE ="

15. : Disp M

Entering the program

To enter the program, press 2nd QUIT to display the home screen. Then press PRGM for the menu of programs. Press twice so that NEW is highlighted and press 1 or ENTER . Then carry out the line by line instructions listed below. The line numbers are not used on the calculator. To make a correction, move the cursor to the error and use INS and DEL as needed. To return to the program from other screens, press CLEAR or follow the steps in the previous paragraph.

To edit a previously entered program, press PRGM and to highlight EDIT. Then press the number or letter of the program, or scroll down to its name and press ENTER .

To delete a program, press 2nd MEM 2 for Delete, 6 for Prgm, put the cursor on the name of the program, and press ENTER 2nd QUIT .

To transfer a program electronically from one TI-83 calculator to another, turn both calculators on and connect them with the wire that is provided, pressing the connectors in firmly. On the calculator to receive the program, press 2nd LINK , select , and press ENTER . The screen should display "Waiting. . ." On the transmitting calculator press 2nd LINK , scroll down to , press ENTER , and scroll down to the name of the program. Press ENTER to select it. The triangle beside its name should changed to an square. Press for and ENTER to transmit the program. Select on the receiving calculator if necessary to replace any old program that has the same name.

1. Press S E C A N T ENTER . The calculator is automatically in alpha mode here. This title identifies the program in the program menu.

2. Press 2nd DRAW 1 ENTER . ClearDraw clears the graphics screen.

TI-83 secant line program, p. 2

3. Press VARS

4 2 ENTER . FnOff unselects all the formulas in the Y= menu so their graphs

are not generated when the program is run.

4. Press VARS

4 1 1 ENTER . This command selects Y1 so its graph will be generated.

5. Press PRGM to display CTL (control) commands and then for I/O

(input/output) commands. Press 3 to enter the word Disp and then 2nd A-LOCK to lock the

calculator in alpha mode. Press " U S E

VARS

1 1 ( X, T, , n ) ALPHA "

ENTER with the space on the zero key.

6. Press PRGM

2 for the word Prompt. Press ALPHA A , ALPHA B ENTER to complete

the line, which causes the prompts A = ? and B =? to appear when the program is run so the

user can supply values of A and B.

7. Press ALPHA A STO X, T, , n ENTER . This assigns the value of A to X.

8. Press VARS

1 1 STO ALPHA W ENTER . Here the function Y1 in the Y= menu is

evaluated at X(= A) and the result is stored as W .

9. Press ALPHA B STO X, T, , n ENTER to give X the value B.

10. Press VARS

1 1 STO ALPHA V ENTER . Y1(B) is stored as V .

11. Use ( ALPHA V - ALPHA W ) ? ( ALPHA B - ALPHA A ) STO ALPHA M ENTER . The slope (V - W )/(B - A) of the secant line through (A, W ) = (A, Y1(A)) and (B, V ) = (B, Y1(B)) on the graph is calculated and stored as M .

12. Press 2nd DRAW 6 ALPHA W + ALPHA M ( X, T, , n - ALPHA A ) ENTER This draws the secant line, y = W + M (x - A).

13. Press PRGM and then either press 8 ENTER or scroll down to and press ENTER ENTER This stops the program until the user presses ENTER .

14. Press PRGM

3 and then 2nd A-LOCK to lock the calculator in alpha mode. Press " S

L O P E 2nd TEST 1 ALPHA " ENTER . SLOPE = appears when the program is run.

15. Press PRGM

3 ALPHA M ENTER for the last command, which displays the slope of the

line on the home screen.

TI-83 secant line program, p. 3

Running the program

When you finish entering the program, compare what you hsve entered with the listing above. The function to be studied should be entered as Y1 in the Y = menu and a suitable window for the graph of the function and the secant line should be chosen. To run the program press PRGM , the program's

number, and ENTER . Give the values of A and B when requested, followed by the ENTER key. The

curve and the secant line will be drawn. Press ENTER to display the slope of the line. You can then

press ENTER to rerun the program if you do not perform any other operations first. To interrupt the

running of the program, press ON and then 2 for QUIT.

Example 1

Use the secant-line program with the window -1 x 5, -1 y 5 to calculate the slopes of the secant lines to y = 4x - x2 through the points at x = 1 and at

x = B for B = 2, 1.5, 1.1, 1.001, and 1.00001. Use the results to predict the derivative of y = 4x - x2 at x = 1.

Solution

Set Y1 = 4x - x2 in the Y = menu and Xmin = -1, Xmax = 5, Xscale = 1, Ymin = -1, Ymax = 5, Yscale = 1, and Xres = 1 in the Window menu. Run the

program with A = 1 and the given values of B.You should obtain the secant lines in

Figures 1 through 6.The secant lines in Figures 5 and 6 are indistinguishable because

B is very close to 1 in these cases. The slopes seem to approach 2 as x approaches 1, so we predict that the derivative of y = 4x - x2 at x = 1 is 2.

y 4 3 2 1

1234 x

a = 1, b = 2.5 Slope = 0.5 FIGURE 1

y 4 3 2 1

1234 x

a = 1, b = 2 Slope = 1 FIGURE 2

y 4 3 2 1

1234 x

a = 1, b = 1.5 Slope = 1.5 FIGURE 3

y 4 3 2 1

1234 x

a = 1, b = 1.1 Slope = 1.9 FIGURE 4

y 4 3 2 1

1234 x

a = 1, b = 1.001 Slope = 1.999

FIGURE 5

y 4 3 2 1

1234 x

a = 1, b = 1.00001 Slope = 1.99999

FIGURE 6

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