Texas Instruments TI-89 Tip List page 422

AUTO modes function - what is it?
The AUTO mode will, through a predetermined method, display answers as either exact or
approximated results. This mode will display default to an exact answer unless the answer becomes
"messy" or would be better understood as an approximation.
Answer in back of the book is different from the TI-92 - why?
When a symbolic result is different than what you expected you can use several tools in the TI-92 to
help verify that the result is equivalent:
1. Try subtracting the result from the expected result to see if simplifies to zero.
2. Try graphing the result you expected and the result you got from the TI-92.
3. Try using some of the manipulation features like expand(), factor(), comDenom(), etc. to see if you
can force further simplification of either result or better yet, their difference.
4. Try substituting appropriate random values for some or all of the variables in each of the two
expressions.
avgRC() (average rate of change) algorithm
avgRC(f(x),x,h) => (f(x+h)-f(x))/h
cSolve() (complex solve) function algorithm
cSolve() is the same as solve() , except the domain is temporarily set to complex so that complex
solutions are sought and not rejected.
solve() (symbolic solve) algorithm.
solve() uses factoring together with the inverses of functions such as ln(), sin(), etc. Except in exact
mode, these techniques might be supplemented by heuristics to isolate solutions, followed by nSolve()
to refine approximations.
Control pad - how many directions will it move the cursor?
The control pad moves in eight directions.
cFactor() (complex factor) function algorithm
cFactor() is the same as factor(), except the domain is temporarily set to complex so that complex
factors are sought and not rejected.
Complex numbers sometimes round a component to zero - why?
The TI-92 rounds the real or imaginary part to 0.0 if its magnitude is less than 1E-13 times the
magnitude of the other component. This is done to recover real or pure-imaginary results when small
roundoff errors make both components non-zero.
Circular Definition Error.
A software change was made in the TI-92 to detect function and program calls that have expressions
of symbolic variable argument names that are the same as those used to define the function or
program. The error "Circular definition" will occur if that is detected.
Unexpected results can occur when a function or program is called with some form of the same
variable name that was used when defining the argument in the function or program definition.
For example, on the home screen:
define f(x)=ln(ln(x)+x)
f(x+1) simplifies to ln(ln(x+1)+x+2)
(Done)
(unexpected result!)
B - 11