TI-89 (and 92) Calculus Operations

Transcription

1 TI 89 1 TI-89 (and 92) Calculus Operations A Preliminaries: 1. Home Screen: This is the screen that appears when the calculator is turned on. To return to the Home screen from other screens, press HOME (green and Home on the 92). 2. Adjusting the Display Contrast: While pressing the green key, press + or. 3. Checking and Setting Modes: Press MODE to see the current settings. Notice that there is more than one page of settings. Settings showing a can be changed. Use the right arrow key (press the right side of the mouse button on the 92) and arrow down to highlight the desired setting and press ENTER. To leave the setting unchanged, press ESCAPE. Once the modes are set, press ENTER Keying in Calculations on the Home Screen: These appear in the command line at the bottom of the screen until the ENTER key is pressed (Note: the symbol must be used to designate multiplication.). At this point, calculation and answer will appear on the Home screen. If a calculation yields an exact answer, such as 2π, the decimal approximation of the answer can be obtained by bringing the calculation back to the command line and pressing the (green) and keys Stopping a Calculation: You can stop an on-going calculation by pressing ON. 6. Editing a Previous Command/Calculation: Press the Up Arrow key until the input (not the output) is highlighted and press ENTER to place it on the command line. Use the arrow keys to move the cursor to the desired point (The calculator is automatically in insert mode.). 7. Cutting, Pasting, Saving: These operations are available in the F1 (Tools) menu. 8. Available Mathematical Commands: Via Menus and Keys: Many commands are available in pull down menus accessed via Fi keys (and in some cases, by designated keys). Once a menu is selected, other menus can be accessed using left and right Arrow keys. To leave a menu, press Escape. Via the Catalog: For an alphabetical list of the commands and the format required for a selected command, press the Catalog key followed by the key below the first letter of the command name. To select a command, use the down arrow key to highlight the command, and press ENTER. The list of items required in the format will appear at the bottom of the screen. 9. List of Special Characters: For a list of characters accessible using the the (green) key, press and EE. 10. Clearing Previous Work: To clear the Home screen, command line, variables a-z, etc.: Use F6 item 2. (NewProb). 3 To clear the Command Line: Use the Clear key. To Clear the Home screen: Use F1 item 8 (Clear Home). Clearing single-character variables a-z: Use F6 item 1 (Clear a-z). 11. Trouble Shooting: If the calculator does not appear to be working correctly, try clearing the single-character variables (see above). 1 Note: A change in mode will not occur, unless this is done. In effect, you need to press ENTER twice after making a mode change. 2 By pressing MODE, you can change the answer format to decimal (or exact) form. 3 Be sure to press ENTER twice.

2 2 TI 89 B Graphing Functions Sample Exercise: Graph f 1 (x) = sin(x) and f 2 (x) = x 2 x 6 on the same screen and use the TRACE cursor to find the intersection point(s) of the two graphs. The instructions below may help. 1. Press the and Y= keys. 2. Key in the functions. For the variable x, use the X key. 3. Only the checked ( ) functions will be graphed. To check (or uncheck) a function, place the cursor on the function using the arrow keys and press F4. 4. To set the window, press and WINDOW. Set the window so that 5 x 5. Then select F2, option A. (ZoomFit) 4 to set the y-values and begin graphing. 5. Activate the TRACE cursor, by pressing F3. Then use the arrow keys to place the cursor on one of the points of intersection of the two functions. 6. To locate this intersection point more accurately, use F2 item 2 (ZoomIN). With the TRACE cursor located at the desired zoom center, press ENTER. Adjust the position of the TRACE cursor as needed. 7. Optional: Checking your solutions using the Intersection operation. (a) In the F5 (MATH) menu, select item 5 (Intersection). (b) The screen now displays First curve? and a flashing double cursor. If necessary, use the up or down arrow keys to move the cursor to one of the functions and press ENTER. (c) The screen now displays Second curve? If necessary, move the second cursor to the other desired function and press ENTER. (d) When the screen displays Lower Bound? either key in a nearby x-value or use the left or right arrow keys to move a cursor close to the intersection and press ENTER. Similarly indicate the Upper Bound. 8. Optional: Checking your solutions by using Solve: (a) From the Home screen, select F2 item 1 (Solve). (b) On the command line, key in (equation,variable) To find the intersection of the graphs of the two functions listed above, you ll need to complete the command so that it reads: solve(x 2 x 6 sin(x) = 0, x) This calculation may take awhile; if you are only interested in one solution, e.g., the solution for x > 0, you might speed up the process by keying in (equation,variable) x > 0 and pressing ENTER. C Graphing and Tabulating Sequences 1. Press the MODE key. Change the Graph setting to Sequence and press ENTER twice. 2. Change the Tb/Set Independent setting to AUTO and press ENTER twice. 3. To enter the sequence to be graphed and/or tabulated, press the and Y= keys. Note that the functions are now labeled as u1, etc. 4. Enter as ui the desired sequence using n (not x) as the variable and enter as ui1 the first n value for your sequence. 5. In the F7 Axes menu change, if necessary, the Axes setting to TIME. 6. Then use F3: GRAPH to graph your sequence and F5: TABLE to tabulate its values. 4 Scroll down to find option A.

3 TI 89 3 D Evaluating Functions and Limits of Functions 1. Enter the desired function as yi(x) using one of the methods below: Press the and Y= keys and then key in the desired function as yi for some number i. On the Home screen, key in the desired function. Then press STO and key in the expression yi(x) for some i To evaluate the function yi for a single value x = a, use one of the methods below: If you have previously stored your function as yi for some i, key in the expression yi(a) on the command line and press ENTER. Note that the value assigned to x can be a number, an alphabetical letter, or a mathematical expression involving numbers and letters, e.g., try evaluating yi(a + 3). Enter the function f(x) on the command line, press the key, and then complete the expression so that it reads f(x) x = a and press ENTER. 3. Using a table to evaluate one or more functions yi(x) for several numerical values of x: (a) The yi functions evaluated will be those that you have previously entered and checked. (b) To be able to specify the x-values, press the and TbSet keys Then select ASK on the line Independent: (c) To enter the TABLE menu, press the and TABLE keys (d) Key in the first numerical value of x at which you want to evaluate the function(s), then use the down arrow key to move to the next row, enter another value of x, etc. 4. To evaluate the limit, lim x a f(x). (a) On the Home screen enter menu F3 (Calc) and select item 3 (limit (. (b) When the command line displays limit(, complete the expression to read limit(f(x), x, a). (c) To evaluate a one-sided limit such as lim x a +f(x), proceed in the same way, but this time indicate a small numerical (positive) increment such as.1 as a final entry in the expression so that it reads limit(f(x), x, a,.1) E Derivatives and Tangent Lines 1. To compute the nth derivative f (n) (x) symbolically for a specific positive integer n: (a) Enter menu F3 (Calc) and select item 1 (d( differentiate) or press 2nd and d. (b) When the command line displays d(, complete the expression to read d(f(x), x, n). 2. To evaluate and graph f (n) (x), enter the function resulting from the differentiation as yi(x) for some i and follow the procedures in part C above. 3. To obtain the graph and equation of the tangent line to a function f(x) at a given point: (a) Enter (and check) the desired function as yi(x) for some i. (b) With the function graph onscreen (see B above), enter menu F5 (Math) and use the down arrow to scroll down to A (Tangent) and press ENTER. (c) Move the cursor to the desired point on the graph or key in the desired x-value of the point. Then press ENTER. 4. To evaluate the derivative of a function at a selected point on the graph. (a) With the function graph onscreen, enter menu F5 (Math) and select item 6 (Derivatives). (b) Move the cursor to the desired point on the graph or key in the desired x-value of the point. Then press ENTER. 5 Be sure to key in just the expression, i.e., do not include the parentheses.

4 4 TI 89 F Antiderivatives and Definite Integrals 1. To evaluate the indefinite integral F (x) = f(x) dx (a) Enter menu F3 (Calc) and select item 2 ( integrate) or press 2nd and. (b) Complete the command so that it reads (f(x), x) and press ENTER. (c) To graph an indefinite integral f(x) dx, enter the function resulting from the antidifferentiation as yi(x) for some i and follow the procedures in part C above. 2. To evaluate the definite integral b a f(x) dx (a) Enter menu F3 (Calc) and select item 2 ( integrate) or press 2nd and. (b) Complete the command so that it reads (f(x), x, a, b) and press ENTER. Note, you can use the literal expression yi(x) with a specific integer value of i if this function has been entered using the Y= key, or you can key in the algebraic expression for yi(x). 3. To evaluate the definite integral b yi(x)dx from the Graph screen: a (a) With the function graph onscreen, enter menu F5 (Math) and select item 7 ( f(x)dx). (b) When the screen displays Lower Limit? either key in the value a or move the cursor to x = a and press ENTER. Similarly indicate the Upper Limit. 4. Numerical Integration with the Numint Program: (This program is available from your instructor.) (a) Enter f(x) as the y1 function in the Y = editor. (b) From the Home screen, use the 2nd and Var-Link keys to enter the Var-Link screen. Scroll down until the the program name is highlighted and press ENTER.. (c) When the expression numint( appears on the command line, complete it so it reads numint() and press ENTER. (d) Following the program prompts, key in the lower limit of integration, a; the upper limit, b and the number of subintervals, n. Then press ENTER. (e) The left sum, right sum and trapezoid approximations then appear. Press ENTER to obtain the midpoint sum and the Simpson (SIMP) approximations. G Evaluating Partial and Infinite Sums Sample Exercise: Sum 20 k=3 7 4 k and 7 4 k k=3 1. Enter menu F3 (Calc) and select item 4 ( sum). 2. Complete the command as follows: (7/4 x, x, 3, 20) and press ENTER 6 3. With the expression (7/4 x, x, 3, 20) on the command line, 7 replace the final number 20 with the symbol and press ENTER. 4. Some sums require the use of a factorial (!). To find it, press 2nd, MATH. Select item 7 Probability and choose item 1!, or press. (On the TI-92, use 2nd w.) 6 If you are in Exact mode and want a decimal answer, you ll need to press the and keys You may need to use the up arrow key to highlight the expression and press ENTER to get it there. 4k k=3

5 TI 89 5 Prepared by JNC for St. Olaf Calculus Students comments and suggestions to: cederj Revised