Texas Instruments PLUS TI-89 - Manual (Page 94)

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) ù g(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)= ⌡
⌠
0
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 d 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).