Texas Instruments Titanium TI-89 Manuale utente

TI89-1

GuideforTexasInstrumentsTI-89

Graphics Calculator

This Guide is designed to offer step-by-step instruction for using your TI-89 graphing calculator with

the text Calculus Concepts: An Informal Approach to the Mathematics of Change. A technology icon

next to a particular example or discussion in the text directs you to a specific portion of this Guide.

You should also utilize the table of contents in this Guide to find specific topics on which you need

instruction.

Setup Instructions

Generally, the TI-89 will show the home screen when it is turned on. If not press

2nd ESC (QUIT)

or press

HOME .

Before you begin, check the TI-89 setup and make sure the settings described below

are chosen. Whenever you use this Guide, we assume (unless instructed otherwise) that your

calculator settings are as shown in the figures below.

• Press

MODE

and choose the settings shown in Figures 1, 2, and 3 for the basic setup. Pressing

F1 ,F2,

and

open up the three pages of the

MODE

menu that are shown below.

TI-89 Basic Setup

Figure 1 Figure 2 Figure 3

•

If you do not have the darkened choices shown in any figure, use the arrow keys to move the

blinking cursor over the setting you want to choose and press

ENTER .

When “

→

→→

→”

appears next

to a word, press

►

to see the available choices and, if necessary, use

▼

to select the one you

need. Then press

ENTER

to choose that selection and return to the mode screen.

WARNING: To save all changes when exiting from all menu boxes (such as the

MODE

screen), you

must press

ENTER

to leave that box. If you exit the box by using

ESC

or by pressing any other key,

the changes you made will disappear.

TI89-2

Chapter 1

• Check the graph format by pressing

APPS 2 [Y= Editor]

(or use

▼

to highlight the second

choice and press

ENTER ).

Press

F1 [Tools] 9 [Format]

and choose the settings in Figure 4.

Press

ENTER

andreturntothehomescreenwith

HOME .

• Beginbypressing

2nd F1 [F6: Clean Up] 2 [NewProb] ENTER

which clears single-character

variable names, turns off functions, clears graphs, and so forth. You can also clear the history

area (the main portion of the screen showing previous entries) with

F1 8 [Clear Home]

and clear

the entry line at the bottom of the screen with

CLEAR .

You may need to press

CLEAR

than once. If you clear the history area and entry line, your screen looks like the one in Figure 6.

TI-89 Graph Format Begin a New Problem Cleared Screen

Figure 4 Figure 5 Figure 6

Basic Operation

You should be familiar with the basic operation of your calculator. With your calculator in hand, go

through each of the following. We illustrate several methods – choose the ones you prefer.

1. CALCULATI NG You can type in lengthy expressions; just make sure that you use parentheses

when you are not sure of the calculator's order of operations. Always enclose in parentheses any

numerators and denominators of fractions and powers that consist of more than one term.

Evaluate

415

895

. Enclose the denominator in parentheses so

that the addition is performed before the division into 1. It is not

necessary to use parentheses around the fraction

895/7

•

The TI-89 prints the same way you should have the expression written on your paper. Always

check the left side of the screen and compare what you entered with what you have on paper.

•

To make a correction in the entry line, use

►

◄

to position the cursor to the right of

what you want to delete and then press



. The entry line is always in insert mode. You do

not need to clear the entry line before beginning to type a new expression.

Evaluate

(3)

−

8 1456

.Use

(

−

)

for the negative symbol and

−

for

the subtraction sign. The numerator and denominator must be

enclosed in parentheses and

−

≠(

−

TI-89 Guide

TI89-3

Now, evaluate e

*0.027 and e

3*0.027

. The TI-89 prints the left

parenthesis when you press



If you do not include a

right parenthesis or insert an extra parenthesis, the TI-89 gives an

error message. Press

ESC ,

fix the error, and press

ENTER .

If you want to edit a previous expression to a new expression, have

the cursor on the entry line and press

►

. The cursor appears on

the right-hand side of the entry line expression. If you press

◄

the

cursor appears on the left-hand side of the entry line expression. Try

editing e

*0.027 to type e

3*0.027

•

To recall an expression prior to the current one (before the history area is cleared), press

2nd

ENTER (ENTRY).

You can also select any entry or answer from the history area and “auto-

paste” a duplicate of it on the entry line. This allows you to insert something previously typed or

calculated into a new expression. First, place the cursor in the entry line where you want to

insert the entry or answer. Second, move the cursor, repeatedly using

▲

, until what you are

inserting is highlighted. Third, press

ENTER

2. USI NG THE ANS MEMORY

Next we explore recalling previous expressions and answers to

use in new calculations. We also see how to use the TI-89 answer memory. Instead of again typ-

ing an expression that was just evaluated, use the answer memory by pressing

2nd

(

−

)

(ANS).

Find

415

895

−

using this shortcut.

Enter

Ans

with

2nd

(

−

)(ANS)

NOTE: Thelast-calculatedanswerisreferredtobytheTI-89ontheentrylineas

ans(1)

when you

enter each expression. The expression for the answer is substituted when the new expression

appears in the history area. You can also use auto-paste to enter the previous results.

3. ANSWER DI SPLAY We have

MODE

set to

AUTO

which means that an exact answer is given

whenever possible. If you have a decimal in an expression, a decimal value is returned for the

answer. If you want a decimal approximation for the expression that appears on the entry line,

press



ENTER .

We also illustrate how to retrieve a previous entry that is in the history area.

Type

press

ENTER ,

and then

press



ENTER .

Press

▲

until

1315

is highlighted. Press

ENTER .

Use

◄

and insert a decimal point after

the 7. Press

ENTER .

TI89-4

Chapter 1

The TI-89 can switch to scientific notation when the number is too

large for the display area in a table or graph. The TI-89’s symbol for

“times 10

−

”is

−

.So,

1.4675

−

means 1.4675*10

−

,whichis

scientific notation for 0.0000014675. Enter

“

”

by pressing

EE .

The result

1.5

means 15,000,000,000,000,000,000,000,000,000 =

1.5(10

). In the history area, an arrowhead (



) that points to the

right at the end of a number means that the number or expression

continues. Highlight the number or expression and press

►

scroll and see the rest of it. Press

▼

to return to the entry line.

4. STORI NG VALUES It often is beneficial to store numbers or expressions for later recall. To

store a number, type the number, press

STO



alpha

, type the letter(s) corresponding to the stor-

age location, and then press

ENTER .

Join several short commands with a colon between the

statements. Note that when you join statements with a colon by pressing

2nd 4

(

)

, only the value

of the last statement is shown as a result.

Store 5 in aand 3 in b,andthencalculate4a–2b.

To recall a stored value, press

alpha

, type the letter in which the

expression or value is stored, and then press

ENTER .

•

Storage location names on the TI-89 can be from one to eight characters long and use letters

and numbers, but they must begin with a letter. You cannot name what you are storing with

thesamenamethattheTI-89alreadyusesforabuilt-invariable(suchas

LOG

ans

•

Whatever you store in a particular memory location stays there until it is replaced by some-

thing else either by you or by executing a program containing that name. It is advisable to

use single-letter names so that the values will be cleared when you begin with

NewProb

NOTE: The TI-89 allows you to enter upper and lower case letters, but it does not distinguish

between them. For instance,

VOL, Vol, VOl, vol, voL

, and so forth all name the same variable. To

type a lower-case letter, press

alpha

before typing a letter key (note that a lower-case

appears

under the entry line). To type an uppercase-letter, press



alpha

(note that an upper-case

appears under the entry line) before typing the key corresponding to the letter.

If a variable is undefined (i.e., you have not stored a value in it), it

is treated as an algebraic symbol. If a variable is defined, its value

replaces the variable when you enter an expression containing that

variable. It is best, as we see in later chapters, to leave the names x

and yas undefined variables.

WARNING: You must be very careful when entering expressions containing variables. In the

next-to-last expression shown on the screen above, the TI-89 assumes “ax” refers to the name of a

single undefined variable. To tell the calculator that you want to multiply the variable aby the

variable x, you must use



between the letters. Also, because 5 has been stored to a, the TI-89

TI-89 Guide

TI89-5

substitutes that value when the expression is evaluated. All user-defined variables are stored in a

folder

called

MAIN

unless you create other folders to hold them. If you cannot remember the

name of a variable, press

2nd

−

(VAR-LINK)

and the names of the variables are listed. After

using

▼

to move the cursor to the name of the variable, you can delete, copy, rename, etc. using

the

F1 [Manage]

keyonthe

VAR-LINK

screen. We illustrate by deleting the variable

Deleting a single variable: Suppose we want to delete the variable

a. Gotothe

VAR-LINK

screen with

2nd

−

(VAR-LINK).

Delete a

by first highlighting it and then pressing

F1 [Manage] 1 [Delete]

ENTER

and

ESC .

(Note that your

MAIN

folder may contain more

or different variables from what is shown to the right.)

The “with” operator, which prints as

“|”

, gives a way to temporarily store values into a variable in

order to evaluate expressions so that you do not have to delete the variable when you finish. Ac-

cess this operator by pressing the key directly under

= .

Evaluate 5.3r–2.1h

for for r=6andthenforr=2.9andh=7by

typing in the instructions shown to the right. Access

“and”

with

CATALOG = (A)

▼

ENTER .

Press

2nd

−

(VAR-LINK)

and

see that

and

are not defined variables.

5. ERROR MESSAGES When your input is incorrect, the TI-89 displays an error message.

If you have more than one command on a line without using a colon

(:) to separate them, an error message results when you press

ENTER .

Press

ESC

and correct the error.

If you try to store something to a particular memory location that is

being used for a different type of object, an error results. (In the

screen shown to the right, the variable abc was defined as a data list,

so a number cannot be stored to it.) Consult either Trouble-Shoot-

ing the TI-89 in this Guide or your TI-89 Owner’s Guidebook.

•

The error message shown directly above usually occurs when you are executing a program

that is trying to store a value to a variable that you have previously defined as some other

type of object. Rename the other type of object and rerun the program. Remember, store

only numbers to single-letter names to avoid problems such as these.

A common mistake is using the negative symbol

(

−

)

instead of the

subtraction sign

−

or vice-versa. The TI-89 does not give an error

message, but a wrong answer results. The negative sign is shorter

and raised slightly more than the subtraction sign.

We work only in the MAIN folder. If you wish to create different folders, see pages 88-90 of the TI-89 Guidebook.

TI89-6

Chapter 1 Ingredients of Change:

Functions and Linear Models

1.1 Models, Functions, and Graphs

There are many uses for a function that is entered in the calculator. One of the ways we often

use functions is to graph them in an appropriate viewing windows. Because you must enter a

function on one line (that is, you cannot type fractions and exponents the same way you write

them on paper even though the TI-89 displays them in this form after they are entered), it is very

important to have a good understanding of the calculator’s order of operations and to correctly

use parentheses whenever they are needed.

1.1.1 ENTERI NG AN EQUATI ON I N THE GRAPHI NG LI ST The graphing list contains

space for 99 equations, and the output variables are called by the names

y1(x)=

y2(x)=

, ...,

and

y99(x)=

When you want to graph an equation, first enter in the graphing list. You must use

as the input variable if you intend to draw the graph of the equation or use the TI-89 table.

We illustrate graphing with the equation in Example 4 of Section 1.1: v(t) = 3.622(1.093

Press either



F1 (Y

)

APPS 2 [Y= Editor]

to access the

graphing list. If there are any previously entered equations that

you will no longer use, delete them from the graphing list. For

convenience, we use the first, or

, location in the graphing list.

To delete an equation from

the Y

list, position the

cursor on the line with the

equation. Press CLEAR .

We intend to graph this equation, so the input variable must be

called x, not t. Enter the right-hand side of the equation,

3.622(1.093x), with

3.622 ( 1 .093 ^

)ENTER .

Note that you must use the

key for x(under the

HOME

key), not the times sign key,



CAUTI ON: Press

▲

and notice the names

Plot 1, Plot 2,

…,

Plot 9

at the top of the

list.

These are the data plots that we will not use until Section 1.5. None of these plots should have a

check mark to the left of the name when you are graphing an equation and not graphing data

points. If any of these has a check mark, use

▲

until the cursor is on the plot name and press

F4 [

]

to make the check mark go away. Otherwise, you may receive an error message.

DEFINING A FUNCTION ON THEHOME SCREEN Functions can be entered in the

graphing list or defined on the home screen. We illustrate both of these methods, and you can

use the one you prefer. Press

2nd ESC (QUIT)

HOME

to return to the home screen.

Type in v(t) = 3.622(1.093

)with

F4 [Other] 1 [Define] alpha

0(V) (

) = 3 .622 ( 1 .093 ^

)ENTER .

On the home screen, any letter can be used for the variable.

Note that if you prefer, you can enter the equation with xinstead

of tas the input variable. (The TI-89 now knows this function

by two names:

and v.)

TI-89 Guide

TI89-7

1.1.2 DRAWI NG A GRAPH As is the case with most applied problems in Calculus Concepts,

the problem description indicates the valid input interval. Consider Example 4 of Section 1.1:

The value of a piece of property between 1980 and 2000 is given by v(t) = 3.622(1.093

)

thousand dollars where tis the number of years since the end of 1980.

The input interval is 1980 (t= 0) to 2000 (t= 20). Before drawing the graph of von this inter-

val, have the function venteredinthe

list using xas the input variable. (See Section 1.1.1 of

this Guide.) We now draw the graph of vfor xbetween 0 and 20.

Press



F2 (WINDOW)

to set the view for the graph. Enter 0

for

xmin

and 20 for

xmax.

(For 10 tick marks between 0 and 20,

enter 2 for

xscl.

If you want 20 tick marks, enter 1 for

xscl,

etc.;

xscl

does not affect the shape of the graph. Ignore the other

numbers −we set their values in the next set of instructions.)

The numbers

xmin

and

xmax

are, respectively, the settings for the left and right edges of the

viewing screen, and

ymin

and

ymax

are, respectively, the settings for the lower and upper edges

of the viewing screen.

xscl

and

yscl

set the spacing between the tick marks on the x-andy-axes.

(Leave

xres

set to the default value of 2 for all applications in this Guide.)

To have the TI-89 determine the view for

the output, press

F2 [Zoom] alpha =

(A) [ZoomFit]

or use

▼

to highlight

ZoomFit

and press

ENTER .

Note that any vertical line drawn on this graph intersects it in only one point, so the graph does

represent a function.

Press



F2 (WINDOW)

to see the view set by

ZoomFit.

The view has 0

≤

20 and 3.622

≤

21.446... .

(Note that

ZoomFit

did not change the x-values that you set

manually.)

Let’s now explore how to graph with the function defined on the home screen as v(t).

Press

HOME

and type

v(t)

ENTER

be sure you are using the correct func-

tion. Press



F1 (Y

)

and enter

v(x)

in the

location. Press

▲

and

[

]

to turn off

Draw the graph of

using exactly the same procedure as that for drawing the graph of

If you need to edit a function, press

ENTER

F3 [Edit]

to move the cursor to the entry line

from the graphing list. Press

F4 [

]

to deactivate

after you draw its graph.

WARNING: You must use xas the input variable when in the

list. If you use tor another

letter inside the parentheses following

, you will likely get an “undefined variable” message.

TI89-8

Chapter 1

1.1.3 MANUALLY CHANGI NG THE VI EW OF A GRAPH We just saw how to have the TI-

89 set the view for the output variable. Whenever you draw a graph, you can also manually set

or change the view for the output variable. If for some reason you do not have an acceptable

view of a graph or if you do not see a graph, change the view for the output variable with one of

the zoom options or manually set the

WINDOW

until you see a good graph. (We will later

discuss other zoom options.) We continue using the function vin Example 4 of Section 1.1, but

assume here that you have not yet drawn the graph of v.

Press



F2 (WINDOW)

, enter 0 for

xmin

,20for

xmax

,and

(assuming we do not know what to use for the vertical view),

enter some arbitrary values for

ymin

and

ymax.

(This graph was

drawn with

ymin

−

5and

ymax

=7). Press



F3 (GRAPH).

NOTE: If you see nothing on the screen, press



F1 (Y

)

and highlight

. If there is no

checkmarknextto

y1,

press

F4 [

]

and



F3 (GRAPH).

Evaluating Outputs on the Graphics Screen: Press

[Trace].

*Recall we are given in this application that the input

variable is between 0 and 20. If you now type the number that

you want to substitute into the function whose graph is drawn,

say

, you see the screen to the right. A

appears at the top

right of the screen because the equation of the function whose

graph you are drawing is in

Press

ENTER

and the input value is substituted in the function.

The input and output values are shown at the bottom of the

screen. (This method works even if you do not see any of the

graphonthescreen.)

Substitute the right endpoint of the input interval into the

function by pressing

20 ENTER

. We see that two points on

this function are approximately (0, 3.622) and (20, 21.446).

Press



F2 (WINDOW)

,enter

3.5

for

ymin

and

for

ymax

and press



F3 (GRAPH).

If the graph you obtain is not a

good view of the function, repeat the above process using x-

values in between the two endpoints to see if the output range

should be extended in either direction. (Note that the choice of

the values 3.5 and 22 was arbitrary. Any values close to the

outputs in the points you find are also acceptable.)

Instead of using TRACE, you could use the TI-89 TABLE or evaluate the function at 0 and 20 on the

home screen to find the range of values for the output value. We later discuss using these features.

1.1.4 TRACI NG TO ESTI MATE OUTPUTS You can display the coordinates of certain points on

the graph by tracing. Unlike the substitution feature of

TRACE

that was just discussed, the x-

values that you see when tracing the graph depend on the horizontal view that you choose. The

output values that are displayed at the bottom of the screen are calculated by substituting the x-

TI-89 Guide

TI89-9

values into the equation that is being graphed. We again assume that you have the function v(x)

= 3.622(1.093

) entered in the

location of the

list.

With the graph on the screen, press

F3 [Trace],

press and hold

►

to move the trace cursor to the right, and press and hold

◄

to move the trace cursor to the left. Again, note that the number

corresponding to the location of the equation (in the

list) that

you are tracing appears at the top right of the graphics screen.

Trace past one edge of the screen and notice that even though

you cannot see the trace cursor, the x-andy-values of points on

the line are still displayed at the bottom of the screen. Also note

that the graph scrolls to the left or right as you move the cursor

past the edge of the current viewing screen.

Use either

►

◄

to move the cursor near x= 15. We

estimate that yis approximately 13.7 when xis about 15.

It is important to realize that trace outputs should never be given

as answers to a problem unless the displayed x-value is

identically the same as the value of the input variable.

1.1.5 EVALUATING OUTPUTS ON THE HOMESCREEN The input values used in the eval-

uation process are actual function values, not estimated values such as those generally obtained

by tracing near a certain value. Actual values are also obtained when you evaluate outputs from

the graphing screen using the process that was discussed in Section 1.1.3 of this Guide.

We again consider the function v(t) = 3.622(1.093

) that is in Example 4 of Section 1.1.

Using xas the input variable, have

3.622(1.093)^

entered in

y1.

Return to the home screen by pressing

HOME .

Substitute 15

into the function with

1(15 )

and find the function value

by pressing

ENTER .

NOTE: We choose

as the function location most of the time, but you can use any of the

available locations. If you do, replace

in the instructions with the function you choose.

It is now a simple matter to evaluate the function at other inputs.

For instance, substitute x= 20 into the equation by editing the

entry line using

►

changing 15 to 20 by pressing



and typing

20 )

, and then pressing

ENTER .

Evaluate

using the same procedure.

If you defined the function vwith input t(see the bottom of page

C-6), it can easily be used to find the function outputs.

TI89-10

Chapter 1

1.1.6 EVALUATI NG OUTPUTS USI NG THE TABLE Function outputs can be determined by

evaluating on the graphics screen, as discussed in Section 1.1.3, or by evaluating on the home

screen as discussed in Section 1.1.5 of this Guide. You can also evaluate functions using the

TI-89

TABLE

. When you use the table, you can either enter specific input values and find the

outputs or generate a list of input and output values in which the inputs begin with

tblStart

and

differ by

∆tbl

Let’s use the

TABLE

to evaluate the function v(t) = 3.622(1.093

) at the input t= 15. Even

though you can use any of the function locations, we again choose to use

.Press



)

, clear the function locations, and enter

3.622(1 .093)^

in location

Choose

TblSet

with



F4 (TblSet).

To generate a list of values

beginning with 13 such that the table values differ by 1, enter

in the

tblStart

location,

in the

∆tbl

location, have

Graph



Table

set to

OFF

, and choose

AUTO

in the

Indpnt:

location. (Remember

that you “choose” a certain setting by having it high-lighted and

pressing

ENTER .

) Exit the setup with

ENTER .

Press



F5 (TABLE)

, and observe the list of input and

output values. Notice that you can scroll through the table with

▼

▲

◄

, and/or

►

The table values may be rounded in

the table display. You can see more of the output by highlight-

ing a particular value and viewing the bottom of the screen.

NOTE: If you wish, while in the table, you can change the cell width using the

F1 [Tools]

and option

9 [Format].

The cell widths can vary between 3 and 12, which result in as few as 2

columns and as many as 7 columns. All functions that are checked in the

list display in the

table, so we suggest leaving the width at its default setting.

If you want to evaluate a function at inputs that are not evenly spaced and/or you only need a

few outputs, you should use the

ASK

feature of the table instead of using

AUTO

. Note that

when using

ASK

, the settings for

tblStart

and

∆tbl

do not matter and are dimmed on screen.

Choose

TblSet

with

F2 [Setup]

from

within the table or



F4 (TblSet).

Choose

ASK

in the

Indpnt:

location. To

enter the x-values 15, 0, and 20, type

each value, press

ENTER

▼

type

the next value, and so forth.

NOTE: Unwanted entries or values in the table can be cleared by highlighting the value in the

column and pressing



or by using

F1 [Tools] 8 [Clear Table]

to delete all previous entries.

1.1.7 FINDING INPUT VALUES USING THE SOLVER Your calculator solves for the input

values of all the equations we use in this course. The expression can, but does not have to, use x

as the input variable. The TI-89 offers several methods of solving for input variables. We first

illustrate using the solve instruction. (Solving using graphical methods will be discussed after

using the solve instruction and the TI-89 numeric solver are explored.) You can refer to an equa-

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