Texas Instruments TI-89, TI-92 Plus Owner's Manual

Page 1
TI-89 / TI-92 Plus
TI
Calculus Tools
Getting Started
What is the Calculus T ools Application? Before You Begin Starting the Calculus Tools Application
F1:Tools F4:Seq F2:Deriv F5:Vector F3:Integ F6:Advanced
More Infor m a t ion
Calculus Tools Application Functions
8/10/01 © 2001 Texas Instruments
Page 2

Important Information

Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis.
In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed any applicable purchase price of this item or material. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
Graphing product applications (Apps) are licensed. See the terms of the
license agreementfor this product.
TI-GRAPH LINK is a trademark of Texas Instruments. All other trademarks are the property of their respective owners.
TI-89 / TI-92 Plus Calculus Tools Page 2
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What is the Calculus Tools Application?

The Calculus Tools application (App) is a Concept software application for the TI-89 / TI-92 Plus. Concept software applications are calculator software application prototypes that demonstrate a new concept area.
The Calculus Tools App extends the built-in power of your TI-89 / TI-92 Plus by providing more specialized functionality. Use the Calculus Tools App to investigate applications of differentiation; compare numerical integration techniques; and explore sequences, series, vector calculus, Fourier series, and more.
The Calculus Tools App is based on programs written or evaluated by CAS (Computer Algebra System) experts and educators Bernhard Kutzler, Bhuvanesh Bhatt, David R. Stoutemyer, Josef Böhm, Ray Barton, Ruth Dover, and Wolfgang Pröpper. We appreciate their contributions and evaluations.
Additional documentation for many of the Calculus Tools App features can be found at series.bk-teachware.com teaching and learning materials written for the TI-89 and TI-92 Plus are also available at the Web site, including Exploring Integration with the TI-89/92/92+ by Josef Böhm and Wolfgang Pröpper.
TI-89 / TI-92 Plus Calculus Tools Page 3
. Other
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Before You Begin

Concept applications are shared with our customers, educators, and students before product definition and testing is complete. These applications may contain software imperfections and/or incomplete coding areas. They are "alpha" software versions.
TI invites feedback from teachers and students concerning the functionality and educational value of the Calculus Tools App. Please send your comments and questions to
concept@list.ti.com

Mode settings

The Calculus Tools App requires specific mode settings to run correctly. If you try to access the application with incorrect mode settings, this error dialog box will appear:
.
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Before starting the Calculus Tools App, set modes to the
Mode
Setting
Graph
FUNCTION Display Digits
FLOAT or FLOAT # (1 - 12) Angle
RADIAN Split Screen
FULL Exact/Approx
AUTO or EXACT Base
DEC Language
ENGLISH
required values as follows:
1. From the Home screen, press dialog box.
2. Ensure that the following modes are set as indicated:
3. Press
¸

MEMORY and VAR-LINK screens unavailable

The MEMORY and VAR-LINK screens, accessed by the and
2 °
3
to display the MODE
. The Home screen displays.
2 ¯
keys, are unavailable for the Calculus Tools A pp.

TI-89 dialog boxes

The TI-89 Calculus Tools App dialog boxes default to alpha-lock. Press
TI-89 / TI-92 Plus Calculus Tools Page 5
j
to turn alpha-lock off before entering numbers.
Page 6

Using variables from the Main folder

Menu option
Variable defined as …
F2F3F4F5F6
Independent var
1 and 2;
4-7
4
Dependent var
4
Angle Parameter
7
Index var
1
Coordinate variables
All
Integration variables
5-8
Var n
2 and 3
x3All
Using variables from the Main folder places those stored values in the Calculus Tools App functions. The Calculus Tools App, however, clears the following types of variables for specified functions. As a result, the data stored in these variables is lost.

Viewing answers in split screen

The Calculus Tools App uses a split screen view to display the numerical and graphical representations of selected solutions.
For answers that are partially hidden when viewed in a split
screen, press For answers that are too long to be viewed in a full screen,
use the Display Answer You cannot switch back and forth between the split screen
portions.
to view the answer in full screen.
N
option.
TI-89 / TI-92 Plus Calculus Tools Page 6
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88VVLLQJQJ&&DDOOFXFXOOXXVV77RRRROOVV$$SSSS00HQXHQXVV
Access the Calculus Tools App menus using the F1 through F6 function keys. F1 menu options let you change the configuration of what you see on the screen, such as viewing the complete answer or data entered as a string, changing split screen settings, and restoring window defaults.
F2 through F6 menu options let you access calculus operations and are organized under the broad categories of derivatives, integrals, sequences, vectors, and advanced functions.
Most F2 through F6 options access a problem-entry dialog box that includes an example problem to help you get started. Work through the example problem, or replace it as desired.
Dialog boxes for most F2 through F6 menu options revert to default values after data is entered. Dialog boxes for the F3 menu options, however, display the values entered last.
This is the problem-entry dialog box for
TI-89 / TI-92 Plus Calculus Tools Page 7
1:Tangent Line
.
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F1:Tools

Tip
You can also go to the Home screen, type
answer
, and
press
¸
. Scroll to see the complete answer displayed
in Pretty Print.

F1 1:Display ANSWER

Lets you view an answer that is too long to fit on the screen. (Answers are displayed as a string.)
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F1 2:Display ENTERED

Tip
To run a Calculus Tools App function from the Home screen, type
entered
and press
¸
. The last command
(function and instructions) executed appears. Be sure to remove the quotes from the string before
executing the command.
Lets you view executed commands or functions as a string, including the Calculus Tools App functions entered from the problem-entry dialog box.
and operations
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F1 3:Change Split Screen

Lets you choose between left-right (default) and top-bottom split screens.
The TI-92 Plus lets you change the ratio of the split screen views.
1:1 displays the answer and graph views at the same size.
1:2 displays the answer view at half the size of the graph
view. 2:1 displays the answer view at twice the size of the graph
view.
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F1 4:Restore Window Defaults

Parameter
Default Value
xmin
-3.55102040816 xmax
3.55102040816 xscl
1 ymin
L
3
ymax
3 yscl
1 xres
2

F1 5:Special Thanks

F1 6:About

Restores the Calculus Tools App window parameters to default values. Dialog boxes accessed using the F3 menu options are also restored to default values.
Function Graph Window Parameters
Acknowledges some of the Calculus Tools App contributors.
Displays a variety of information about the application, including the version number.
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F2:Deriv

F2 1:Tangent Line

Displays the problem-entry dialog box for the tanLine(...) function along with an example problem (page 35).

F2 2:Normal Line

Displays the problem-entry dialog box for the prpendic(...) function along with an example problem (page 34).
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F2 3:Newton’s Method

Note
The number of iterations must be an integer
1.
Displays the problem-entry dialog box for Newton's Method along with an example problem. Enter a function f (x), Initial guess, and Number of iterations.
The solution appears in a split screen. One portion of the split screen displays a sequence of approximations to a real root of the functions.
The other portion of the split screen displays a graph of the function and draws tangent lines corresponding to consecutive iterations.
The application draws the first guess for you. Press either
¸
or
to view the consecutive guesses. This example
N
shows four iterations.
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F2 4:Implicit Derivative

Displays the problem-entry dialog box for the impDifN(...) function along with an example problem (page 32).

F2 5:Curvature

Displays the problem-entry dialog box for the curvatur(...) function along with an example problem (page 31).
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F2 6:Center of Curvature

Displays the problem-entry dialog box for the cntrCurv(...) function along with an example problem (page 30).

F2 7:Osculating Circle

Displays the problem-entry dialog box for the oscCircl(...) function along with an example problem (page 33).
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F3:Integ

F3 1:Left Sum

Displays the problem-entry dialog box for the Left Sum integration method along with an example problem. Enter a function f (x), Lower bound, Upper bound, and Number of intervals.
The answer appears in a split screen. One portion of the split screen displays the sum of the areas of the rectangles.
The other portion of the split screen displays the graph of the function and draws the rectangles.

F3 2:Right Sum

Displays the problem-entry dialog box for the Right Sum integration method along with an example problem. Enter a function f (x), Lower bound, Upper bound, and Number of intervals.
The answer appears in a split screen. One portion of the split screen displays the sum of the areas of the rectangles.
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The other portion of the split screen displays the graph of the function and draws the rectangles.

F3 3:Midpoint Rule

Displays the problem-entry dialog box for the Midpoint Rule along with an example problem. Enter a function f (x), Lower bound, Upper bound, and Number of intervals.
The answer appears in a split screen. One portion of the split screen displays the sum of the areas of the rectangles.
The other portion of the split screen displays the graph of the function and draws the rectangles.
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F3 4:Trapezoidal Rule

Note
The number of intervals must be an even integer 2.
Displays the problem-entry dialog box for the Trapezoidal Rule along with an example problem. Enter a function f (x), Lower bound, Upper bound, and Number of intervals.
The answer appears in a split screen. One portion of the split screen displays the sum of the areas of the trapezoids.
The other portion of the split screen displays the graph of the function and draws the trapezoids.

F3 5:Simpson’s Rule

Displays the problem-entry dialog box for Simpson's Rule along with an example problem. Enter a function f (x), Lower bound, Upper bound, and Number of intervals.
The answer appears in a split screen. One portion of the split screen displays the Simpson’s Rule approximation to the definite integral by using parabolic arcs.
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The other portion of the split screen displays the graph of the function and draws the parabolic arcs.

F3 6:Comparison

Returns the approximation to the definite integral using these previously mentioned methods: Left Sum
Midpoint Rule
, Trapezoidal Rule, and Simpson’s Rule (pages
, Right Sum,
16 through 18).
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F4:Seq (infinite series, sequences)

F4 1:Ratio Convergence Test

Displays the problem-entry dialog box for the ratioTst(...) function (page 34) along with an example problem.

F4 2:1st-Order Sequence

Displays the problem-entry dialog box for the seq1Solv(...) function (page 34) along with an example problem.
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F4 3:2nd-Order Sequence

Displays the problem-entry dialog box for the seq2Solv(...) function (page 35) along with an example problem.

F5:Vector

F5 1:Gradient

Displays the problem-entry dialog box for the grad(...) function (page 32) along with an example problem.
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F5 2:Divergence

Note
The number of components in
exprList
must equal the
number of variables in
varList
.
Displays the problem-entry dialog box for the div(...) function (page 31) along with an example problem.

F5 3:Curl

Displays the problem-entry dialog box for the curl(...) function (page 30) along with an example problem.
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F5 4:Potential

Displays the problem-entry dialog box for the potentl(...) function (page 33) along with an example problem.

F6:Advanced

F6 1:Error Function, erf

Displays the problem-entry dialog box for the erf(...)
function
(page 31) along with an example problem.
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F6 2:Comp. Error Function

Displays the problem-entry dialog box for the erfc(...) (page 31) along with an example problem.

F6 3:Gamma Function

Displays the problem-entry dialog box for the gamma(...) function (page 32) along with an example problem.
function
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F6 4:Fourier Series

Displays the problem-entry dialog box for the fourirCf(...) function (page 32) along with an example problem.

F6 5:Integral of Density

F6 5:Integral of Density > 1:over a Surface
Displays the problem-entry dialog box for the surfIntg(...) function (page 35) along with an example problem.
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F6 5:Integral of Density > 2:over a Polar Region
Displays the problem-entry dialog box and example problem to set up an iterated integral to integrate a density over a region in polar coordinates. Use
density
unweighted polar area.

F6 6:Centroid of Density

Displays the problem-entry dialog box for the aCntroid(...) function (page 29) along with an example problem.
1 for an
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F6 7:Inertia Tensor

Displays the problem-entry dialog box for the aInertia(...) function (page 30) along with an example problem.

F6 8:Arc Displacement

Displays the problem-entry dialog box for the plrArcLn(...) function along with an example problem (page 33).
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Working with Calculus Tools App Functions

Note
Calculus Tools App functions cannot be called from within the application. If you try to call a function using the application’s problem-entry dialog boxes, the error message,
Protected memory violation
, will appear. Exit
and re-enter the application to ensure normal operation.
Tip
To view help for a function, select a function from the catalog and press
.
Use Calculus Tools App functions outside the application when working with programs or other built-in, user-defined, and Flash application functions.

Accessing Calculus Tools App functions from the Catalog

1. From the Home screen, press (TI-92 Plus). The catalog appears.
2. Press c. The list of Flash application functions appears.
3. Scroll through the list and select the function you want to use.
4. Press
¸
line in the form
CalcTool
. The function appears on the Home screen entry
.function name
5. Add the required arguments to complete the command and press
TI-89 / TI-92 Plus Calculus Tools Page 28
¸
.
½
(TI-89) /
 
Page 29

Accessing Calculus Tools App functions from VAR-LINK

1. From the Home screen, press
VAR-LINK [ALL]
2. Press
2 
screen appears.
(TI-89) / g(TI-92 Plus). The list of Flash
2 °
. The
application functions appears.
3. Scroll through the list and select the function you want to use. You may need to expand the application's folder before you can view its functions.
4. Press
CalcTool
¸
. The function appears on the entry line as
.function name
5. Add the required arguments to complete the command and press
¸
.

List of Calculus Tools App Functions

aCntroid

(density, var1, lower1, upper1, var2, lower2(var1), upper2(var1))
Returns a two-element list denoting the of the centroid of a
to
lower1 var2
upper1
varies from expression
might depend on
, which must be independent of
var1
density
over a 2D region.
lower2
. Use
density
{var1, var2}
to expression
coordinates
varies from
var1
and
var1
upper2
1 for an area centroid.
.
var2
, which
Use F6 6:Centroid of Density
to display the problem-entry
dialog box and example for this function.
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alnertia
(density, var1, lower1, upper1, var2, lower2(var1), upper2(var1))
Returns a 2x2 matrix denoting the inertia tensor of a density over a two-dimensional region.
upper1
from expression depend on
, which must be independent of
to expression
lower2
var1
. Use
density
1 for an area inertia tensor.
varies from
var1
var1
upper2
lower1
and
var2. var2
, which might
Use F6 7:Inertia Tensor to display the problem-entry dialog box and example for this function.
to
varies

cntrCurv

(expression, var)
Returns a two-element list that is a parametric representation of the center of curvature of
Use F2 6:Center of Curvature
expression
to display the problem-entry
with respect to
var
.
dialog box and example for this function.

curl

(exprList, xVar, yVar, zVar)
Returns the three-dimensional rectangular Cartesian curl of the vector represented by coordinate variables
xVar, yVar, zVar
exprList
with respect to the
.
Use F5 3:Curl to display the problem-entry dialog box and example for this function.
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curvatur

Note
The number of components in
exprList
must equal the
number of variables in
varList
.
(expression, var)
Returns the curvature of Use F2 5:Curvature to display the problem-entry dialog box
and example for this function.
div
(exprList, varList)
Returns the rectangular Cartesian n-dimensional divergence of the vector represented by coordinate variables in
Use F5 2:Divergence to display the problem-entry dialog box and example for this function.
erf
(complexNumber)
Returns the approximate numeric error function of
complexNumber
Use F6 1:Error Function, erf to display the problem-entry dialog box and example for this function.
.
expression
exprList
VarList
.
with respect to
var
with respect to the
.
n

erfc

(complexNumber)
Returns the approximate complementary error function of
complexNumber
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.
Page 32
Use F6 2:Comp. Error Function to display the problem-entry dialog box and example for this function.

fourirCf

(expression, var, lowerLimit, upperLimit, n)
Returns the truncated Fourier series of
lowerLimit
to
upperLimit
, through the nth harmonic.
expression
for
var
Use F6 4:Fourier Series to display the problem-entry dialog box and example for this function.

gamma

(complexNumber)
Returns the approximate gamma function of Use F6 3:Gamma Function, Γ(z)
complexNumber
to display the problem-entry
dialog box and example for this function.

grad

(expression, VarList)
Returns the rectangular Cartesian n-dimensional gradient of
expression
with respect to the ncoordinate variables in
Use F5 1:Gradient to display the problem-entry dialog box and example for this function.

impDifN

(equation, IndependentVar, DependentVar, n)
Returns the nth derivative of the function implicitly defined by
equation
.
from
VarList
.
.
Use F2 4:Implicit Derivative to display the problem-entry dialog box and example for this function.
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oscCircl

Note
Does not verify that
exprList
is a gradient, so first see if
curl
(exprList, xVar, yVar, zVar)
simplifies to {0,0,0}, as it
should for a gradient.
(expression, var, circleParameter)
Returns a two-element list that is a parametric representation of the circle that osculates
expression
.
Use F2 7:Osculating Circle to display the problem-entry dialog box and example for this function.

plrArcLn

Returns the weighted arc displacement in polar coordinates, where var and Use
Use F6 8:Arc Displacement to display the problem-entry dialog box and example for this function.

potentl

Returns the scalar potential of the three-dimensional rectangular Cartesian gradient represented by the potential = 0 at
Use F5 4:Potential to display the problem-entry dialog box and example for this function.
(r(qVar), qVar, low, up, weight(qVar))
q
Var
varies from
weight(qVar)
weight
(exprList, xVar, yVar, zVar, x0, y0, z0)
being expressions that might depend on
1 for an unweighted arc displacement.
{x0, y0, z0}
lowerLimit
.
to
upperLimit
, with
exprList
r(qVar)
q
, with
Var
.
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prpendic

(expression, var, varValue)
Returns an expression for the line that is normal to at
var
=
varValue
.
expression
Use F2 2:Normal Line to display the problem-entry dialog box and example for this function.

ratioTst

(expression, indexVar)
Conducts the ratio test for the convergence of an infinite series, returning one of the strings
, or
inconclusive
unable to complete test
converges, diverges, test
.
Use F4 1:Ratio Convergence Test to display the problem- entry dialog box and example for this function.

seq1Solv

(p(n), r(n), n, nMin, ui)
Attempts to return an exact symbolic expression for u(n) that satisfies the linear 1st-order sequence equation
u(n)=p(n) Use F4 2:1st-Order Sequence
u(n-1)+r(n) with u(nMin)=ui.
to display the problem-entry
dialog box and example for this function.
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seq2Solv

(k, c, r(n), n, nMin, {u(nMin), u(nMin-1)})
Attempts to return an exact symbolic expression for u(n) that satisfies the linear 2nd-order constant-coefficient sequence equation u(n)=k
u(n-1)+cu(n-2)+r(n) and ui={u(nMin) , u(nMin-1)}.
Use F4 3:2nd-Order Sequence
to display the problem-entry
dialog box and example for this function.

surfIntg

(density, height, var1, lower1, upper1, var2, lower2(var1), upper2(var1))
Returns the integral of a might vary with
var1
and
density
var2. var1
which must be independent of expression
. Use
var1
density
to expression
lower2
1 for a surface area.
over surface whose
varies from
and
var1
upper2
var2. var2
, which might depend on
lower1
varies from
to
height
upper1
Use F6 5:Integral of Density > 1:over a Surface to display the problem-entry dialog box and example for this function.

tanLine

(expression, var, varValue)
Returns an expression for the line that is tangent to at
var
=
varValue
. (In contrast, the built-in LineTan command
expression
draws the tangent line but does not reveal its formula.) Use F2 1:Tangent Line
to display the problem-entry dialog
box and example for this function.
,
TI-89 / TI-92 Plus Calculus Tools Page 35
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Installing the Calculus Tools App

Detailed Flash application installation instructions are available from education.ti.com/guides.
You will need:
A TI-89 / TI-92 Plus with the latest Advanced Mathematics
Software Operating System. Download a free copy from
education.ti.com/softwareupdates
.
A computer using either Microsoft
Macintoshëoperating system software. A TI-GRAPH LINK™ computer-to-calculator cable, available
for purchase from the TI Online Store at
education.ti.com/buy
TI-GRAPH LINK connectivity software for the
TI-89 / TI-92 Plus. Download a free copy from
education.ti.com/softwareupdates
TI-89 / TI-92 Plus Calculus Tools Page 36
.
Windowsëor Apple
ë
.
ë
Page 37

Starting and Quitting the Application

Starting the Calculus Tools App

The instructions in this guidebook refer to this Flash application only. For help using the TI-89 / TI-92 Plus, refer to the comprehensive guidebook at education.ti.com/guides
.
1. Ensure modes
2. Press
3. Press
¸
are set to the required values.
1:FlashApps
and select
Calculus Tools
. The Hint screen displays.
.

Quitting the Calculus Tools App

Press
TI-89 / TI-92 Plus Calculus Tools Page 37
2 K
from the Calculus Tools App Hint screen.
Page 38

Deleting an Application

Deleting an application removes it from the calculator and increases space for other applications. Before deleting an application, consider storing it on a computer for reinstallation later.
1. Quit
2. Press
3. Press
the application.
2 °
2 
(TI-89) / (TI-92 Plus) to display the list of
to display the
VAR-LINK [ALL]
applications.
4. Select the application you want to delete.
5. Press
1:Delete
. The
VAR-LINK
delete confirmation dialog
box displays.
6. Press
¸
to delete the application.
screen.
TI-89 / TI-92 Plus Calculus Tools Page 38
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Concept Application Evaluation License Agreement

(Including Preview, Prototype, and Demo APPS)
By downloading the software and/or documentation you agree to abide by the following provisions.
1.
Copyright:
Licensee agrees that he/she wi l l not delete the copyright notic e, trademarks or protective notices from the Licensed Materials or copies made during installation.
2.
Support:
limited support for this concept application may be available from TI.
3.
Testing:
subjected concept appli cations to rigorous testing and that the concept application may cause problems with his/ her calculator, including its use in any kind of shared environment. Further, it is possi bl e for a concept application to c ause calculator crashes or lock ups which may be difficult to recover from. You are advis ed that use of the concept application is AT YOUR OWN RISK.
4.
Warranty:
meet your specific requi rem ents.
The Licensed Materials are mad e available "AS IS" to Licen see.
5.
Limitations: TI makes no warranty or condition, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regard i n g th e Licensed Materials.
In no event shall TI, any third party licensor, or TI's suppliers be liable for any indirect, incidental or consequential damages, loss of profits, loss of use or data, or interruption of business, w heth er the alleged damages are labeled in tor t, co n tract or indemnity.
Some states do not allow the exclusion or limitation of incidental or consequential damages, so the above lim itation may not apply.
6.
Restricted Rights:
duplication or disclos ure by the United States Government is subject to restric tions as set forth in subparagraph [c](1)(ii) of the Rights in Technical Data and Comput er S oftware clause at DFARS 252.227-7013 or in s ubparagraph [ c](1) and (2) of the Commercial Computer Software - Restrict ed Ri ghts at 48 CFR 52.227-19, as applicable.
The Licensed Materials are copyrighted by TI or the third party l i censor.
The Licensed Materials are provided by TI with the understanding that onl y
Licensee acknowledges that he/ she understands that TI has not in al l cases
TI does not warrant that the Licensed Materials will be free from errors or will
The Licensed Materials are provided with Restricted Rights. Us e,
TI-89 / TI-92 Plus Calculus Tools Page 39
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Page Reference
This PDF document contains electronic bookmarks designed for easy on-screen navigation. If you decide to print this document, please use the page numbers below to find specific topics.
Important Information............................................................................................. 2
What is the Calculus Tools Application?................................................................ 3
Before You Begin................................................................................................... 4
Mode settings ....................................................................................................4
MEMORY and VAR-LINK screens inactive.......................................................5
TI-89 dialog boxes.............................................................................................5
Using variables from the Main folder.................................................................6
Viewing answers in split screen......................................................................... 6
Using Calculus Tools App Menus.......................................................................... 7
F1:Tools............................................................................................................. 8
F2:Deriv ........................................................................................................... 12
F3:Integ............................................................................................................ 16
F4:Seq (infinite series, sequences) ................................................................. 20
F5:Vector ......................................................................................................... 21
F6:Advanced.................................................................................................... 23
Working with Calculus Tools App Functions........................................................ 28
Accessing Calculus Tools App functions from the Catalog............................. 28
Accessing Calculus Tools App functions from VAR-LINK...............................29
List of Calculus Tools App Functions .............................................................. 29
Installing the Calculus Tools App......................................................................... 36
Starting and Quitting the Application....................................................................37
Starting the Calculus Tools App ...................................................................... 37
Quitting the Calculus Tools App ...................................................................... 37
Deleting an Application.........................................................................................38
Concept Application Evaluation License Agreement ...........................................39
TI-89 / TI-92 Plus Calculus Tools Page 40
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