[2.13] Try Comdenom() To Find Limits; [2.14] Define Functions That Cas Can Manipulate - Texas Instruments TI-89 Tip List

7. Try plotting the difference of the two functions over the range of interest.

[2.13] Try comDenom() to find limits

(Note: AMS 2.05 fixes the specific example in this tip, but the general idea may still be useful for other
limits. Thanks to John Gilbertson for pointing this out.)
Sometimes the 89/92+ CAS cannot find a limit to an expression, because of the way the expression is
structured. And, sometimes, comDenom() can restructure the expression so that the CAS
can find the limit. For example, the CAS cannot find the limit as x approaches 0 for this expression:
However,
returns
and the limit() function can find the limit of this expression, like this:
limit((1-√(x+1))/(x*√(x+1)),x,0)
(Credit to Olivier Miclo)

[2.14] Define functions that CAS can manipulate

The CAS will not be able to manipulate functions that you define in the program editor, nor from the
command line with Define. For example, if you create the cosecant function like this:
csc(x)
func
1/sin(x)
endfunc
the CAS will not be able to integrate or differentiate this function - it just returns the function. However,
if you create the function at the command line, like this
1/sin(x)→csc(x)
then the CAS can integrate and differentiate the function.
You need not create these functions from the command line. You can create one or more functions in a
program, like this:
makefunc()
Prgm
1/(sin(x))→csc(x)
1/(tan(x))→cot(x)
1/(cos(c))→sec(x)
EndPrgm
1
−1
1+x
x
comDenom((1/(√(1+x))-1)/x)
1− x+1
x x+1
= -1/2
2 - 8