Secant TI86 Dec 9 06

[Pages:3]A Secant Line Program for a TI-85 or TI-86 Calculator

The program

(8/23/06)

1. PROGAM: SECANT 2. : ClrDrw 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 F2 for and follow the steps below. If you are editing a previously entered program, select its abbreviated name from the menu and press ENTER . Then follow the instructions below. Commands typed in slanted bold

type can be obtained from the calculator's catalog, which is reached with 2nd CATALOG on a TI-85

and with 2nd CATALOG F1 on a TI-86. Press the key for the first letter in the command, scroll down

to the command if necessary, and press ENTER to enter it. For example, to enter ClDrw on line 2 of

the program use the keys 2nd CATALOG C

ENTER ENTER , and for FnOff on line 3 press 2nd

CATALOG F followed by eight times (on a TI-85) or nine times (on a TI-86) and ENTER ENTER . Most of the commands can also be found in the menus.

To make a correction, move the cursor to the error and use DEL and 2nd INS as needed. To

return to the program from other screens, press EXIT or follow the steps in the first paragraph. To

interrupt the running of the program, press ON and then F5 for .

To transfer a program electronically from one TI-85 calculator to another TI-85 or TI-86 or from a TI-86 to another TI-86, 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 ond F1

for . The screen should display "Waiting." On the transmitting calculator press 2nd LINK

and F1 for , press F2 for , and scroll down to the name of the program. Press

F2 for . The triangle beside the program name should be changed to an arrow. Press F1 for to transmit the program. Select on the receiving calculator to replace any old program that has the same name.

1. Press S E C A N T ENTER .

2. Enter ClDrw from the catalog and press ENTER . This command clears the graphics screen.

TI-86 secant line program, p. 2

3. Enter FnOff from the catalog and press ENTER . This command unselects all the formulas in the y= menu so their graphs are not generated when the program is run.

4. Enter FnOn and press 1 ENTER . This selects y1 so its graph is generated.

5. Enter Disp and press 2nd STRING F1 (for "). Press ALPHA ALPHA to lock the calculator in

upper-case alpha mode and U S E with the space on the (-) key. Press ALPHA to leave upper-case alpha mode and 2nd alpha to enter lower-case alpha mode. Press Y 1 ( x-VAR

) F1 (for ") ENTER to finish the line.

6. Enter Prompt and press ALPHA A , ALPHA B ENTER . The prompts A =? and B =? will appear so the user can assign values to A and B.

7. Press ALPHA A STO x-VAR ENTER to set x = A.

8. Press 2nd alpha Y 1 STO W ENTER . There is no ALPHA before W because the calculator is locked in upper-case alpha mode after STO . Here the value at x (= A) of y1 in the y= menu is stored as W .

9. Press ALPHA B STO x-VAR ENTER to give x the value B.

10. Press 2nd alpha Y 1 STO V ENTER . y1(B) is stored as V .

11. Use ( ALPHA V - ALPHA W ) ? ( ALPHA B - ALPHA A ) STO 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 stored as M .

12. Enter DrawF and press ALPHA W + ALPHA M ? ( x-VAR - ALPHA A ) ENTER . The secant line y = W + M (x - A) is drawn.

13. Enter Pause ENTER to stop the program until the user presses ENTER .

14. Enter Disp and press 2nd STRING F1 (for ") ALPHA ALPHA S L O P E = F1 ENTER . SLOPE = appears when the program is run.

15. Enter Disp and press ALPHA M ENTER to displays the slope of the line on the home screen.

TI-86 secant line program, p. 3

Running the program

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 F1 for and the key under the program's abbreviated name. 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, and yScale = 1 in the Range 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 from the tangent line 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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