Texas Instruments Titanium TI-89, User Manual

Page: 230 / 977

Symbolic Manipulation 227
• Transforms irrational numbers to standard forms as much as possible without
approximating them. For example,
transforms to and
ln(1000)
transforms
to
3 ln(10)
.
• Converts floating-point numbers to rational numbers. For example, 0.25 transforms
to 1/4
.
The functions
solve
,
cSolve
,
zeros
,
cZeros
,
factor
,
‰
,
fMin
, and
fMax
use only exact
symbolic algorithms. These functions do not compute approximate solutions in the
EXACT setting.
• Some equations, such as
2
L
x
= x
, have solutions that cannot all be finitely
represented in terms of the functions and operators on the handheld.
• With this kind of equation, EXACT will not compute approximate solutions. For
example,
2
L
x
= x
has an approximate solution
x
≈
0.641186
, but it is not displayed in
the EXACT setting.
Advantages Disadvantages
Results are exact. As you use more complicated rational
numbers and irrational constants, calculations
can:
• Use more memory, which may exhaust the
memory before a solution is completed.
• Take more computing time.
• Produce bulky results that are harder to
comprehend than a floating-point number.
12 2 3