Texas Instruments TITANIUM TI-89 - Manual (Page 240)

Symbolic Manipulation 240
Using Exact, Approximate, and Auto Modes Using Exact, Approximate, and Auto Modes Using Exact, Approximate, and Auto Modes Using Exact, Approximate, and Auto Modes
The Exact/Approx mode settings, which are described briefly in Operating the Handheld,
directly affect the precision and accuracy with which the TI-89 Titanium calculates a
result. This section describes these mode settings as they relate to symbolic
manipulation.
EXACT Setting EXACT Setting EXACT Setting EXACT Setting
When Exact/Approx = EXACT, the handheld uses exact rational arithmetic with up to
614 digits in the numerator and 614 digits in the denominator. The EXACT setting:
• 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
Lx
= x , have solutions that cannot all be finitely
represented in terms of the functions and operators on the handheld.
12 2 3