Texas Instruments TI-89, TI-92

Chapter 3: Symbolic Manipulation 77

03SYMBOL.DOC TI-89/TI-92 Plus: Symbolic Manipulation (English) Susan Gullord Revised: 02/23/01 10:52 AM Printed: 02/23/01 2:12 PM Page 77 of 24

Refer to:

¦ “Creating and Evaluating User-Defined Functions” in Chapter 5.

¦ “Graphing a Function Defined on the Home Screen” and

“Graphing a Piecewise Defined Function” in Chapter 12.

¦ “Overview of Entering a Function” in Chapter 17.

You can use functions such as f(x), g(t), r(q), etc., that have not been

assigned a definition. These “undefined” functions yield symbolic

results. For example:

Use DelVar to ensure that f(x)

and g(x) are not defined.

Then find the derivative of

f(x)ùg(x) with respect to x.

You can use user-defined functions consisting of a single expression.

For example:

¦ Use § to create a user-defined secant function, where:

sec(x) = 1

cos(x)

Then find the limit of sec(x)

as x approaches p/4.

¦ Use Define to create a user-defined function h(x), where:

h(x)=⌡

⌠

sin(t) / t

Then find a 5th order Taylor

polynomial for h(x) with

respect to x.

User-Defined Functions and Symbolic Manipulation

You can use a user-defined function as an argument for the

TI-89 / TI-92 Plus’s built-in algebra and calculus functions.

For Information

about Creating a

User-Defined

Function

Undefined

Functions

Tip: To select

from the

Calc

toolbar menu, press

… 1

(or press

2 =

on the

keyboard).

Single-Statement

Functions

Tip: To select limit from the

Calc

toolbar menu, press

… 3

Tip: To select ‰ from the

Calc

toolbar menu, press

… 2

(or press

2 <

on the

keyboard). To select taylor,

press

… 9.

Define h(x)= ‰(sin(t)/t,t,0,x).